Best Time For Lunch

No matter where you work, at some point during the day you have to gobble something to refuel your energy. Most of us at least occasionally leave our desks for a lunch in a cafeteria or a restaurant. Frequently accompanied by coworkers or friends.
What's the best time to go out for lunch?
When one is hungry?
When a majority of the people in the lunching group are hungry?
But what if 5 minute of waiting till your colleague will finish his non-urgent email may cost you 20 extra minutes of waiting at the salad bar, or leave you without the daily special or a table to sit at.

People that are very particular about what they eat and when usually develop mathematical theories that define when they need to start heading towards food. Below are a few of the theories I heard. 
  1. Most of the people decide to go out for lunch at round hours or half-past an hour: 12:00, 12:30, 13:00, 13:00. This results in "waves" of crowding a few minutes past these times. To avoid the crowds try to come a bit ahead of either wave: 12:20 or 12:50.
  2. To guarantee the specials, the seat and the fresh salad bar come ahead of the crowds: leave your desk at 11:53 so that you could be among the first customers at noon.
  3. Do not follow your instincts.  Most of the people seek salad on Mondays recovering after the weekend feast, soup on a rainy or cold day, light fare in warm weather, turkey in October-November. Avoid these trends to guarantee a quick lunch.
When do you head for lunch? Share your thoughts or theories.

All About Anne

As customary on TheMathMom's website we are honoring each of our 50-puzzle points winner with an exclusive interview. This week it is Anne.

Q: Dear Anne. Does your work have anything to do with math?

I am recently retired and after working in a hospital I spent most of my career as a visiting nurse for my county.  Of course I had to use math for medication administration and proper dosage.  When going into a home there was much problem solving and creativity involved which I enjoyed.  The home environment, especially on a new visit, does not have all the health amenities of a hospital and you must figure out how to proceed with what is there, which can be very little and/or not as hygienic as you need or would prefer.  You must also problem solve to assist the patient in following instructions and adapting them to a sometimes challenging household environment or because of personal reservations.

Q:If you could go back, what profession would you choose and why.

I love the basis of the healthcare field (forget about the insurance, politics, etc!).  It is based on science, something new is always being discovered, it is challenging and it helps people.  If I could choose again I would definitely choose a scientific field, maybe healthcare again or something in astronomy or physics or medical research, and I think it would be fun to be a detective or someone who can crack sophisticated codes!

Q: Is there a childhood mentor who infused your interest in math?

I would have to say my parents.  My father was an engineer and my mother was a science major in college so their interest in things math/science related was always there.  I guess you take for granted your father's tinkering, contraptions and the lack of repairmen coming to the house!  They definitely supported and encouraged a full math/science curriculum for me when it was not the usual way for a girl.  I loved the subject matter but not the fact that I could be the only, or one of a few, girls in the class ...... but I continued and was a math major in college.

Q: Do you think math helps you in your daily life?

I definitely think math helps in your daily life, from simple things like cooking, sewing, smart shopping to home repairs and financial decisions to a certain way of thinking that solves problems.

And may I add that my children are grown and my days as a Math Mom are over.  Neither child avoided math and, in fact, took many advanced mathematics courses.  My son in an engineer with an MBA and my daughter is a neuropsychologist,  both professions where math is used.  I have two grandchildren now and, while I know their parents will raise them with an appreciation for math, I have moved on to Math (Grand)Mom!

Anne is the 8th person to reach such a celebrity status on our pages. Before her there were: Kim, Tom, Jerome, Ilya, TracyZ, Anne-Marie, and Wang. 

A Holiday Greeting for You from You

My mom is our family poet and a writer who has been composing little humorous personalized sonnets for almost every birthday, wedding, anniversary or other significant events in our family and her work clusters.  Last weekend she worked on a non-rhymed New Year greeting, and the fact that the year 2014 is a year of the Horse in Chinese calendar gave her a lot of ideas to write about. Here it is, loosely translated from the Russian;

We already work hard as a workhorse; pull the plow as peasant horse; strive to come to the finish line first , like a racehorse; fear losing our jobs as an old horse; easily bought by sweets like a circus horse;  devoted to our owner (employer , children, friends ) as domestic horse.
Therefore we are ready to welcome the 2014 NEW YEAR!
And let every home and every heart find a place for a small horseshoe, which will bring us a little luck and much happiness!
Be healthy, as a young horse, racing all year long.
and so long....

She sent the greeting by email to me and seven of her closest friends from Israel and Russia on December 30th. A day later she received an email with her own greeting from one of my dad's friends who resides in Florida. Interestingly the text was edited to exclude parts about life in Israel that were not so applicable to the Florida retirees. What are the chances for an email to go around the globe (at least once) and among millions of potential recipients, and come back to the original writer!

Actually, this is not so rare.  Something similar may have likely happened to you.
While our world is inconceivably large, our circle of friends is rather small and typically based around age, interests, education, socio-economic status. And some of our friends' friends are likely to know each other. Moreover, there are those of us who serve as "network hubs", social butterflies with extremely large circle of friends and acquaintances that goes outside of their age, interests, education and socio-economic status, which allows to connect people from different networks together.

In Hollywood this paradigm is known as 6-degrees of separation from Kevin Bacon, stating that any actor could be linked to the well-known Kevin Bacon with up to 6 steps.  Mathematicians are counting their "proximity" to  Paul Erdős in Erdős numbers.  This prolific Hungarian mathematician apparently spent large portion of his life travelling around and writing papers with those who would give him room and board. He published more than any other mathematician in history. LinkedIn has used this chain-of-connections concept to help anyone reach almost everyone for a professional contact.

Going back to our New Year week, let's contemplate our enormous world being tightly connected and inter-dependent, and how anything good we do could spread around bringing so much happiness and ricocheting back to us just when we need it. Happy New 2014, the Year of the Horse.

Happy Holidays! Next year challenge - think outside of a box.

Happy holidays to all my dear readers!
Thank you so much for your loyalty, comments and ideas. Please keep them coming.
Wishing you a healthy and successful year.
Today I would like to tell you a story and give you and myself a New year challenge: Lets try thinking outside of a box.

the story:
You have likely heard of a field of cryptography that is dealing with secure data storage, transfer and access. It is applicable to anything from protecting your personal medical information, sending online payments to breaking into the Pentagon computers. In the past century very complex algorithms have been developed to encode and decode such secure data. Many algorithms are using extra-large prime numbers. $150,000 dollar prizes were announced to people that could find such large primes consisting of hundreds of thousands of digits. Even since the Second World War cryptography has been a very hot field and many brilliant scientists are working in it.

A group of them just published a ground-breaking study announcing that you can decode the encrypted message that your computer is sending or receiving by ... looking outside of the computer box. You don't need to break into the computer, instead concentrate outside of the box, just listen to it.  Computer at the end is just a machine that process any keystroke into series of bits that are translated into electrical signals: on and off. And as we all know these on-off switches usually makes tiny noise. In the computer case this noise could be captured by any smartphone microphones. So, if you are a secret agent you can spy on your enemy by accidentally leaving a smartphone near his laptop, taping and transferring the noise to your computer and de-crypting the data at home.
This is one of those things when many other scientists and lay people probably think: It is so simple. Why haven't we thought about it before? We have been concentrating so hard and deep inside the box that we forgot about the outside options.

Next year - let's try to thinking outside of the box.  At work or at home, let's try to step aside and find creative unconventional solutions to any challenge we may face.
Happy New 2014!

Holiday Cookies: the chemistry and math of making them. Plus, a recipe.

How the ball of dough flattens, spreads and bubbles in the oven?
Why tasting raw dough is like playing a Russian roulette?
Why your cookies won't brown at the standard 350F?
How could you figure out that they are ready without using a kitchen timer?

All the answers and much much more interesting details are in this TedEd video:

But wait, there is more:
When you use melted butter instead of the room temperature butter chunks, the dough will spread out faster in the oven creating larger diameter cookies. At the same time meted butter will create more but smaller sized air pockets (holes) making the cookies chewier. Source: molecular biologist Liz Roth-Johnson, UCLA.

And the biggest secret is to make the dough 3 days ahead and refrigerate it for about 36 hours prior to shaping and baking in order to allow all the ingredients slowly penetrate each other and achieve better dough consistency. More details on that are in this NYTimes article.

Finally, as we learned all the science, let's try making the cookies.
My friend and excellent baker Sherene Michlin recommended two of her favorite recipes. One that is adapted from NY baker Jacques Torres and requires two types of flour, two types of sugar and very precise measurements. NYTimes subscribers could find it here.
Another: basic, straight-forward, no-fail - is from the NESTLE website.  I am posting it below.

2 1/4 cups all-purpose flour
1 teaspoon baking soda
1 teaspoon salt
1 cup (2 sticks) butter, softened
3/4 cup granulated sugar
3/4 cup packed brown sugar
1 teaspoon vanilla extract
2 large eggs
2 cups (12-oz. pkg) NESTLÉ® TOLL HOUSE® Semi-Sweet Chocolate Morsels
1 cup chopped nuts


preheat oven to 375° F.

combine flour, baking soda and salt in small bowl. Beat butter, granulated sugar, brown sugar and vanilla extract in large mixer bowl until creamy. Add eggs, one at a time, beating well after each addition. Gradually beat in flour mixture. Stir in morsels and nuts. Drop by rounded tablespoon onto ungreased baking sheets. 

bake for 9 to 11 minutes or until golden brown. Cool on baking sheets for 2 minutes; remove to wire racks to cool completely. 

Girl Rising

October 11st the UN's International Day of the Girl celebrating the power of education that transfers lives of girls all around the world.  While our cultural stereotypes are preventing our daughters from being strong in math and going for degrees that will ensure their economic independence, cultural traditions or poverty in many other countries preventing girls from receiving any education at all. A new groundbreaking documentary Girls Rising, directed by Academy Award nominee Richard Robbins, tells the stories of 9 extraordinary girls from 9 countries. It is written by 9 celebrated writers and narrated by 9 renowned actresses. You can check for the screenings near you or  organize your own screening:

 Aside from the movie Girl Rising is a campaign and its website help you to create a curriculum that teaches students to think critically about issues related to girls education, ways for each to realize their own potential and and our global responsibilities. Click to bring Girl Rising to your school.

Renovations Math, Smiles and Tears

They told us - be careful; renovations always take twice longer than expected, cost twice more than you planned, stress your work and family life to an unprecedented level and double your chances for divorce.  We thought: Nonsense!  It is just the stairs and a suite on the roof; a few months of work, with contractor and architect from our extended family. I thought I could keep an eye on the whole project while assembling the posts from this blog into a book.  Life showed that they were absolutely right.

It all went like in the kids' classic: "If you give a mouse a cookie." Stair redesign led to flooring changes and required a new kitchen layout; while we were at it we extended the kitchen into the garage that demanded new garage doors; since the floors were open we were advised to renew the pipes; then came the bathrooms and the doors. It all got so expensive that we gave up on the roof suite dreams and re-planned for it in the basement. At the end we thought that perhaps the original stairs were OK but with 5 workers and a cement mixer inside the house it was too late:).

Double the time and double the budget but still married, we are now only in the middle of the process. My book dreams were put aside, as well as summer travel.  Museum and park visits got replaced with tile, parquet and furniture shopping. The whole adventure did give us a lot of valuable construction knowledge that unfortunately will not come to use as we swore to never ever renovate again.

As I was immersing in, more and more renovation math shoved on me daily by general contractor and designer. I was trying to keep our kids involved and stimulated by occasionally translating to them these real life math puzzles:

  • If it took 3 days to destroy all the walls, how long may it take to build new ones?  1) 3 days. 2) one week 3) three months.  #3 is the correct answer.
  • Which room is bigger? Calculate the area and compare.
  • Can you help me figure out how much tile will we need for your room?  What about the whole basement (split into rectangles and calculate)?
  • What is the length of the railings that we will need to order for the roof?
  • How many stairs are we going to have? Our old stairs were surprisingly cumbersome: uneven, too high, slightly tilted. To lower the stair height we had to increase the overall staircase area extending it into the kitchen. The new stairs were supposed to be 7" each so my daughter and I calculated the number of these new stairs:  (ceiling height + ceiling-to-second-floor thickness) /7
  • How many 6" tiles could you fit into a 60" x 60" area? 100? We were wrong! There is a 3mm-wide grout in-between every tile connection.
  • How many parts a bathtub shower and faucet may possibly have?  More than you could see and imagine!
  • How many white colors do you think exist in this world? One? Wrong again! But they all would look the same to you if it were not for your designer biasing your perception.
I am sure you all have your own share of renovations math puzzles or experiences that I invite you to share with us to make me feel a little bit better.

Summer Learning Activities from PBS Kids

Summer is officially here and for most of us it is an opportunity to do things we couldn't do throughout the school year - take it easy, spend more time outdoors, do something adventurous, learn new skills, and spend more time with the friends and family. It is a time to see who really your kids are, what they like and where they need a bit more confidence, tell them about things you like and teach them to manage their leisure time with some structure. Below is a list of resource links from the PBS Kids of fun summer science and math activities.

PBS KIDS Lab Home Activities:

Keeping Kids’ Math Skills Sharp All Summer Long

Fun Summer Science Projects:

Transitioning family from summer to school:

13 Ways to sneak learning into summer fun

Simple Tips for Summer Math Learning

Creative Car Game for Summer Road Journeys

Summer crafts

The Power of Ten, by Eames.

The Eames Chair: one of the design gems of the 20th century, a unique combination of beauty and comfort. Designed in 1956 and continuously produced by Herman miller ever since; available at the Design Within (Without?) Reach for $3,500+.

Turns out that the designer couple behind this legendary chair, Charles Eames and Bernice Alexanda ("Ray") Eames, were interested not only in furniture but also textiles, photography and film. Fascinated by the relative size of things around us and our perception of the universe they created an interesting short movie called Powers of Ten. It starts with a couple on a lakeside picnic near Chicago and every 10 second shows the same scene from 10 times further out until the galaxy is visible only as a speck of light. It then quickly goes back down to the picnicking couple and zooms deep into the men's skin. Short and powerful! Click on the image below to open the film in a new window. Watch with the kids.

All About Tracy

This week we are cheering to Tracy Z. who slowly and consistently climbed toward 50 puzzle points, and honoring Tracy with an exclusive interview.

Congratulations, Tracy! As you were answering these questions, you were preparing to go camping on the Cape Cod. In this picture you sent you are also hiking with a baby in tow and what seems like a giant backpack. What an amazing energy!

This picture is of me and one of my kids on a trip that we take every winter.  We and friends hike into a very rustic cabin (no electricity, no plumbing) in VT for a long weekend, and carry all our gear in via backpacks and sleds.  We’ve been doing it since pre-kid days.  I spend a lot of time for work and at home in front of computers.  Many of my fondest memories though come from the times when I unplug the computer and get outside for a weekend, a week, or longer.  I love hiking, biking, kayaking, and cross-country skiing and snowshoeing.  

Tracy, have you ever had a big or little life dilemma that you solved with math?
Little:  I’ve used math to estimate a number I can’t actually fully compute.  For example, in a contest to guess the number of peanuts in a very large bag, I came closer than anyone else and won the whole bag.  It was too much to eat. 

Bigger:  At my house, we once wanted to estimate where a property line was located without having to hire a surveyor.  We wanted to know which trees were on our property and which were on an adjacent property.  We found survey markers for two corners (A & B) on one side of the property and used very long pieces of string and triangle geometry to estimate the border on an adjacent side of the property.  Here are the details: We took the straight line distance between A and B (let’s call the distance x) and assumed the adjacent border from corner A to the unknown point C would be a right angle to side AB (the assessors’ property maps suggested the angle was 90% or very close to it).   We created a string of length x and a second string of length (sqrt(2))*x.  We tied the x- length string at corner A, and tied the (sqrt(2))*x-length string at corner B.  At corners A and B, we then rotated the two strings until they intersected when each string was fully extended.  This intersection point was point C.  Once we knew C, we knew side AC was on the property border.  AC was long enough to go past the trees in question, but if it had not been, we could have run another longer string along AC as far as needed. 

Have you ever did any miscalculation using logic and numbers in real life?
One type of miscalculation I make far too frequently is underestimating how long it will take me to get somewhere, such as for an appointment.  I think about what time the appointment starts, and then make the assumption that that time it will take me to get there will be the minimum time that such a trip would take under ideal conditions with no delays of any kind.  I allow for little margin of error and as a result I am often a wee bit late. Fortunately, I had just a few times where I have been very late.  Too bad personal teleportation is not yet an option. 

Do or did you ever use math professionally?
I use math personally and professionally almost every day. I was a math major in college. In my professional life, I have had positions gathering and analyzing data regarding: the energy and cost savings of energy-efficient household appliances; the population, economic, and land use trends for regions and communities; and the contributing factors behind motor vehicle crashes and fatalities.  I currently work in a research laboratory that conducts studies of driver behavior (such as driver distraction) in driving simulators and on-road environments.  We collect a variety of data on our participants during their sessions, including their demographic and driving histories, and their eye movements, head movements, their travel speed, acceleration, and lane deviation while driving, and use this data to develop training programs to improve drivers’ skills. 

Some people say that best ideas come to them in the shower, for some it is while they are asleep, for some - while they are jogging. For you, what conditions, mood or environment are the most optimal to tackle a hard puzzle?
I get many of my best ideas for how to proceed on a hard problem when I outside walking or biking.   I also get great ideas, especially for Math Mom puzzlers and other brain teasers, by talking them over with my spouse or kids.  They love math and logic puzzles as much as I do.  

To whom or what you are attributing your interest in math – a teacher, parent, TV program?
There are two people to whom I attribute my interest in math and logic.  The first is John Powers, a wonderful teacher who mentored me in middle school. He encouraged me to create a book of logic puzzles and to develop a curriculum to teach logic skills to kindergarteners and first graders. The second is Dr. Arthur Eisenkraft, my high school physics teacher. He frequently had us put down our textbooks and engage in real-life exercises to better understand the concepts he was teaching us.  We’d have labs where we threw and hit baseballs (studying speed and distance); dropped objects out of 3-story windows (gravity), and honked car horns while driving at different speeds (Doppler effect). He made science and equations live.  Dr. Eisenkraft now runs a center at UMass-Boston that focuses on improving the teaching and learning of science and math for all students, from kindergarten through graduate school.

Thanks, Tracy!
Curious to know more about our other puzzle-solvers? See our previous interviews: All About Ilya, All About Jerome, All About Anne-Marie, All About Tom, and All About Kim.

Bat Mitzvah Favors, Messy And Full of Math.

This is a guest post by my very good friend Ellina who is celebrating her daughter's Bat Mitzvah in a few weeks.

In a strange and unexpected moment of creative inspiration (channeling my inner Martha Stewart, which I didn't know I could!), I decided to make chocolate-covered Oreos as favors for my daughter's Bat Mitzvah party, where we will have 70 kids in attendance. Some strong math should really have been involved in my decision, but I usually shy away from having to calculate anything, so I thought I'd "be creative" and "enjoy the process." What is there to do - buy a few packs of Oreos, dip them in chocolate, use food coloring spray and stencil to "Mazel Tov" on each, pack them in bags of 3, and here we go - 70 delicious and festive favors.

I was told that there is a person who charges $2 per cookie when she does this, and I thought it was an exorbitant price. I needed 70 x 3 = 210 of those and wasn't ready to pay $420 for that. 

Preparing the project, I created a list of supplies:

  • I have three molding trays that make 6 Oreos each, so I can make 18 at a time
  • I have three different decorative stencils -- one says "Bat Mitzvah", one says "Mazel Tov!", and one is a Star of David -- every favor will get three cookies, one of each design
  • There are 36 Double-Stuf Oreos in one package
  • A package of chocolate melt wafers is 14 oz.
  • A can of pearl white food coloring spray (that is used to spray the stencil design onto each cookie) is 15 oz.
  • Each set of 3 cookies will go into a little cellophane baggie, tied with a piece of decorative ribbon (about 8" of ribbon per baggie)
  • Ribbon comes in rolls of 9 feet
  • Baggies come in packs of 100 (so I will need only one pack -- this one is easy!!)
  • Each baggie will have a piece of cardstock stuffed into it, as "decorative backing" for the cookies.
  • Cardstock comes in sheets of 12" x 12"
  • Each baggie will need a 4" x 4" piece of colored cardstock
  • I want to alternate lavender and light blue cardstock (trying to stick to the party's color scheme of lavender, white, and light blue)
Just in time, the AC Moore store was having a sale on chocolate melt wafers (normally 2.49/bag, sale price of 1.99/bag), so I stocked up, got 12 bags. The first time. Little did I know that I will have to go back two more times, for wafers and other ingredients... 16 bags of wafers total.
Got 6 spray bottles of white food coloring -- with the way my spraying was going, I knew I'd need a few!  Got 4 more during a later trip. 
Double-Stuf Oreos were also on sale (normally 3.69/box, sale price of 2.99/box), I got 7 boxes and then went back for another 4 (36 cookies in each, I needed to make a total of 210, but underestimated the amount of broken cookies, eat-while-I-work cookies, cat-stole-and-dropped-down-off-table-to-share-with-dog cookies, and family-sneaking-finished-product-late-at-night cookies). 
Found cute ribbon for only $1 per roll (9 feet each), but all I could find was 3 rolls (will not be enough, as I need 8" per baggie, and need to make 70 baggies, which would mean almost 6 full rolls). Tried to find 3 additional rolls later that would be the same, scared away fellow shoppers as I frantically clawed my way through the $1 ribbon bin -- alas, to no avail. Will end up with two types of ribbons closing up the baggies. Keep reminding myself that kids don't care.

Then, I planned the actual steps and slowly perfected them through trial-and-error:

  • Melt chocolate wafers (three 30-second intervals in the microwave)
  •  Pour a bit of the chocolate melt into one cookie mold slot

  • Put Oreo into cookie mold, and push down to get the chocolate to come up around the sides
  •  Pour a bit more chocolate over the top, and spread to cover up the cookie
  •  Tap the bottom of the mold a few times to get air bubbles out, and to ensure the chocolate has spread evenly around/over the cookie
  •  Repeat for remaining 5 cookies in the mold
  •  Put into freezer for 15 minutes

  • Repeat with remaining two mold trays, ending up with 18 cookies 
  • Pop out cookies, take a stencil (one of the three choices), place over cookie, spray with food coloring

  • Put 18 cookies into large ziplock bag, make bag airtight by sucking all air out with a straw
  • Store bag in kitchen cabinet
  • Repeat while tolerating rolling-eye expression from daughter and husband
  • Curse Martha Stewart. 

Now, you are probably starting to wonder what got me thinking that this could be fun. Well, so did I, but this was already too late into the adventure. The kitchen was an ugly mess. Every few hours I was going into sugar-induced shock from breathing cheap candy wafer fumes, and food coloring spray fumes. I then run to the fridge, took pickles out of a jar and ate them to decrease the sugar overload. Ate them quickly, to balance out the sugar.  At that point it is important to recognize that the assembly of the favors was still to come....

Favor Assembly Steps:

  • Take pre-cut piece of cardstock, put into cellophane baggie
  • Put three cookies (one with each design) into baggie, with cardstock as background
  • Take pre-cut pieces of ribbon
  • Tie ribbon into knot
  • Repeat
The final result:

Overall time investment: 35 hours so far.  

Total money spent: about $110 .
Chocolate consumed: 1 pound+

59 done, 11 to go... I've somehow miscalculated my sets of 18, so I now have too many Magen Davids, 7 Bat Mitzvahs (need 11), and no Mazel Tovs at all... Bought one more box of Double-Stuf Oreos...
Honestly, when this is done, I don't think I'll be able to be anywhere near another Oreo for what is likely to be years... :-)

Plan on bringing the not-yet-assembled pieces to a Memorial Weekend retreat to get the extended family help me put it together. Need to feed them ice cream before to prevent any pieces being eaten.

Exhaustion and excitement are up.
Time to the party: 2 weeks
Next on my list: video montage and table centerpieces.

From TheMathMom:  Ellina -  I am sure these elaborate multi-week home preparations make the anticipation even more special and the whole event much more personal and memorable.

St Patrick’s Day Math Pop Quiz

Prepare for St Patrick's Day with this fun math pop quiz.  A simpler version of this quiz was originally created for and published by in 2011. Here is the old link.

Puzzle #1 Two Airplanes Puzzle

A Boston man decides to surprise his friend in Ireland for St Patrick’s Day and boards a plane for Dublin. Meanwhile, his Dublin friend has the same idea and boards a plane for Boston. The Dublin-bound plane is flying at 565 miles per hour and the Boston-bound plane at 485, because it is bucking a jet stream. Which plane will be closer to Dublin when they meet above the Atlantic?

  1. Boston-to-Dublin plane; 
  2. Dublin-to-Boston plane; 
  3. same distance

Correct answer is 3. At the point when they meet, of course they will each be the same distance from Dublin.

Puzzle #2: The Snake Myth

Legend holds that St. Patrick banished snakes from Ireland. It's true that no snakes exist in Ireland today.  What do you think most likely have happened:

  1.  Snakes were scared of St Patrick and slowly slid away; assuming they were traveling 5 miles per hour, in 60 hours they could cover the 300-mile length of Ireland.
  2. It was the Pied Piper that run all thee snakes away.
  3. Snakes never lived in Ireland, since it is an island surrounded by icy waters and snakes never had an opportunity to migrate there

Answer #3 is correct

Puzzle #3: Root Beer Puzzle

You bought a homemade root beer kit in celebration of St Patrick’s Day. But you decide to skip reading the directions and just mix up everything in the kit.  As soon as you plug the bottle and shake it, the brownish mix starts growing with an astronomical speed. It looks like it is doubling in volume every minute. If you start with one glass (250ml) of mix, how long will it take to expand and fill the whole 2-liter bottle?

Answers: 8 min, 4 min, 3 min

Correct answer is 3 min.  If the mix is doubling in volume every minute, then after the first  minute 250ml will grow into 500ml, after the second minute 500ml will grow into 1000ml and after the third minute 1000ml will make 2000ml, which is the whole bottle.

Puzzle #4: Tough Luck

The three-leaf clover (shamrock) has been a symbol of Ireland for hundreds of years.  Very rarely a clover with more than three leaves can be spotted. It is believed that encountering it brings good luck.  It is actually a tough luck to find as there are approximately 10,000 three-leaf clovers for every four-leaf clover. But you promised one for your friend. If you are searching in a one-acre field that has 500 clovers per square foot, how many square feet of field you are likely to crawl and scan before you find the lucky clover?

  1. 1,000
  2. 500
  3. 20

Correct answer is 3) 20. You are likely to look through approximately 10,000 clovers to find the four-leaved one. If there are 500 clovers per square foot, then you will crawl 10,000/500=20 square feet.

Puzzle #5: Parade Puzzle

St. Patrick's Day Parade starts at 1pm and goes at approximately 3mph through the South Boston. You are watching the parade start on TV but still want to experience it for real midway through, 1 mile from its start. It is a 15min walk from your apartment, but you are really hungry. Do you have extra 5 min to grab a lunch on your way?

  1. Forget about lunch, run as fast as you can. 
  2. Sure you do.

Correct answer: 2. With a speed of around 3mph, it will take the parade 20min to move 1 mile.  15min to walk and 5min to get a lunch.

Puzzle #6: The Celtics' logo
The name Boston Celtics reflects the city's Irish heritage. Celtics logo was designed by Red Auerbach's brother, Zang, in the early 1950s. He assembled the familiar leprechaun with the words Boston Celtics arched around it in a circle. You surely saw this logo hundreds of times. Do you recollect how many three-leaf clovers are featured on the leprechaun?

  1. 3    
  2. 7   
  3. 12  
  4. 15

Correct answer: 12 (3 on the hat, 2 on the tie and 7 on the vest)

Puzzle #7: Grandma’s Recipe

Every St Patrick’s Day you are making soda bread for a family dinner.  Your favorite grandma’s recipe lists ingredients for a loaf-shaped 12” x 5” x 3” pan. You just threw the rusty pan out and only have a square 9” x 9” x 2” pan.  Will the dough overflow?

  1. Yep  
  2.  No

Correct answer: 1) Go look for another pan or use 2/3 of the ingredients. It will overflow. Your original pan had a 12x5x3=180 cubic inch volume. The new square pan has 9x9x2=162 cubic inch.

Puzzle #8:  I can see you, can you see me?

Your band has been invited to participate in the St Patrick’s Day Parade. You are rushing to Parade start point in the car and finish applying make-up at the red lights, looking in the rear view mirror.  While applying lipstick you see in the rear view mirror the eyes of the driver from a car behind you.  He seems to be staring at you. Can he see your beautification routine?

  1. yes he can 
  2. no way, he is in the car behind

Correct answer is 1) The driver in the car behind you sees at least part of your face reflected in your rear view mirror (unless your car back is tinted).  Light is reflected with the same angle it falls on the mirror. If I can see you, you can see me.

Puzzle #9: Celtics Pride

The TD Garden has 17 NBA championship banners hanging from the rafters, one for each of the NBA championships Celtics team has won (most than any other NBA team). Celtics team was formed in 1946 and championships were held from 1947. At this rate, would they win their 34th championship by 2075?

Answers: a) yes b) no

Correct answer is a): The Celtics won 17 games in the past (2010-1947+1) = 64 years. With the same winning rate, it will take another 64 years for 17 more wins: 2011+64=2075

Puzzle #10: The Magical Year
Your father was telling you about the memorable Celtics NBA final when the TV cameras zoomed in on the year at the end of the game, then slowly zoomed out and rolled (rotated) revealing, to his amazement, that the year number is the same upside down. Which year and game this was?
  1. 1969 
  2. 1991  
  3. 1961

Correct answer is 3) 1961 will be 1961 upside-down if 1’s are written as lines.

I Can See You Breathing

This is fresh from the oven - terrific new technology from the MIT Computer Science team.

You know how it is easier to recognize someone from a caricature than from a photograph?  This is because caricaturists exaggerate our imperfections and exasperation help our brain to do the match.  What if we can apply such exaggeration to other fields?  For example, what if we can exaggerate small motions? A hand tremble, eye movement, chest raising while breathing, blood pulsation  on the neck or cheek? Computer Scientists from the MIT propose to process a video stream with such motions and use some surprisingly simple math to detect and amplify these motions so that they will be clearly visible to our eye.  This is the beginning of a great technology.  Technology that can allow you to easily check whether your baby is breathing by just glancing at the video camera, check his pulse without EKG, observe your body's blood flow without going to an alternative medicine clinic, define guilt during a trial through involuntary eye movements, and even verify whether Batman is still alive.  Check the clip:

Playful Family Statistics

This came via Facebook.  It is written by Orit G. in Hebrew.
Since it is so funny and true, plus it is family statistics, I decided to translate it for your enjoyment:

Questions that kids are asking mom:

  • Mom, where is my towel?
  • Mom, what are you making to eat?
  • Mom, when are you coming back?
  • Mom, what time is it?
  • Mom, what day is today?
  • Mom, where is my pencil?
Questions that kids are asking dad:
  • Dad, where is mom?

How to Help Your Kids Handle Test Stress

It may be a dance or piano recital, SAT test or mid-term exam for your kids; a job interview or important conference call for you. Perfectly prepared, you became more anxious as time gets close and fail to deliver at your best.  Does it mean that you or your kid are just not built for stressful situations and should avoid them altogether?

Last week I stumbled upon a very important article in NYTimes by Po Bronson and Ashley Merryman  "Why Can Some Kids Handle Stress While Others Fall Apart"  In case you don't have a subscription or time to read all 6 pages, here is a short summary.

Some of us are striving in a competitive stressful environment (school tests, sport or arts competitions) while others worry and perform worse than they could in a regular "peaceful" surrounding. Turns out that people of this second type can be trained to embrace the stress and out-perform on a long run. So the answer in not less testing but more testing of the right kind.

Few recent studies pinpointed an "anxiety-related gene" that can have either Worrier or Warrior state.  Since we all inherit one gene from our mother and one from our father, a quarter of the population has two Worrier genes, a quarter has two Warrior genes and a half of the population has one of each genes.

Worrier gene gives us cognitive advantage: better reasoning, concentration, higher IQ. And this advantage appears to increase with the number of years of education. However, this advantage disappears at the time of stress and leads to under-performance.

Warrior gene, on opposite, lights up at the time of competition. People with to Warrior genes are "like Superman emerging from the phone booth in times of crisis; their abilities to concentrate and solve problems go up." (BC professor Adele Diamond)

Should Worrier types avoid stress altogether? No. "In fact, shielding them could be the worst response, depriving them of the chance to acclimate to recurring stressors. Training, preparation and repetition defuse the Worrier’s curse." (UCSD professor, Douglas C. Johnson) Some early studies show that " Worrier-genes can still handle incredible stress — as long as they are well trained. Even some Navy SEALs have the Worrier genes, so you can literally be a Worrier-gene Warrior. "
"There are many psychological and physiological reasons that long-term stress is harmful, but the science of elite performance has drawn a different conclusion about short-term stress. Studies that compare professionals with amateur competitors — whether concert pianists, male rugby or female volleyball players — show that professionals feel just as much anxiety as amateurs. The difference is in how they interpret their anxiety. The amateurs view it as detrimental, while the professionals tend to view stress as energizing. It gets them to focus."
Studies show that a similar mental shift  helps students in test-taking situations. Grades of the students improved only after their were told to see stress as beneficial.
"David and Christi Bergin, professors of educational and developmental psychology at the University of Missouri, have begun a pilot study of junior high school students participating in math competitions. They have observed that, within a few weeks, students were tackling more complex problems than they would even at the end of a yearlong class. Some were even doing college-level math. That was true even for students who didn’t like math before joining the team and were forced into it by their parents. Knowing they were going up against other teams in front of an audience, the children took ownership over the material. They became excited about discovering ever more advanced concepts, having realized each new fact was another weapon in their intellectual arsenal.
Maybe the best thing about academic competitions is that they benefit both Warriors and Worriers equally. The Warriors get the thrilling intensity their minds are suited for, where they can shine. The Worriers get the gradual stress inoculation they need, so that one day they can do more than just tolerate stress — they can embrace it. And through the cycle of preparation, performance and recovery, what they learn becomes ingrained."
So, what can help any Worrier to do better at a test time? It is:
  • training, preparation and repetition
  • change of attitude toward stress - looking at it as excitement, energizing physiological process
  • participation in more tests, especially group-type confidence-boosting academic competitions
Top image by db photography, distributed under CCL.

How Long Should Your Phone Number Be?

Arranging a carpool recently I was surprised to discover that the father of my daughter's friend has a very suspicious and easy to remember number ending with "9999." Inquiring whether he is anyone very important to be assigned such a number, I received a straight answer from his 9-year old daughter: "He got this number as a payback after being very mad at his cell service."

Most of us cannot keep more than 4 digits in a memory for too long. Why then our phone numbers should be so long we have to bribe or threaten  phone providers to get an easy-to-remember number?

As you may have guessed the answer is in math, simple and applicative.  Exactly the type of math that many argue should be taught at school. Blessed with a free afternoon this week, I decided to try the following on my 9 and 12 year old kids.

Imagine that we have just 10 people spread around the world. Just 10 people, no one else. And a fully functioning cell phone system. Do these people really need 10-digit phone numbers to dial each other?
Since there are only 10 of them, we can give them 1-digit numbers:  0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

But as soon as eleventh person is born and grows mature enough to get her/his phone number, we need to use number 10. And we add to all the other numbers 0 in front: 00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 10.
Then another person (twelfth) grows and gets number 11.
We can continue adding up more phone customers till a hundredth person gets number 99.

So, we see that:
1 digit is enough for 10 people.
2 digits - 100 people.
continuing this we get:
3 digits - 1,000 people.
4 digits - 10,000 people.

How many people live in our home state of MA?  6.5 million.  Let's see how many digits do we need so that everyone can get a unique phone number.
5 digits are enough for 100,000 people.
6 digits - 1,000,000 people. Still less than we need.
7 digits - 10,000,000 people.

So, using 7 digits in a phone number will allow us to create 10 million various phone numbers that will be more than enough for all the people of MA.  And guess what, check your home phone number.  Not counting the 3 area code digits, it is exactly seven digits long!  Someone thought it through.

Now, imagine that you want to establish a new cell phone service in Russia. How long should your numbers be?  I let my kids to Google Russian population (160 million) and come up with a 9 digit answer.

Then we tried China with 1 billion 344 million people and realized that we need 10 digits.

Now think car license plates or zip codes. Imagine yourself planning a Mars colony. How many digits in their phone numbers, flying saucer license plates and zip codes would you need?

Top image by Ed Yourdon, distributed under the CCL.