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.


  1. Puzzle #4: I disagree with all the answers. You are *likely* to have found a four-leaf clover when the probability of finding one is greater than 50%, which occurs after you have checked 5,000 flowers (or 10 ft²).

    Put another way, if the odds of finding a four-leaf clover are 10,000:1 then *on average*, it should take examining 5,000 clovers to find one that's four-leaf. So, again, we should expect to have to examine 10 ft².

    It's late here. I hope my explanation is clear and makes sense. ;-)

  2. Hi Thad,

    Yep, I get your answer. I think it depends how one defines that he/she is likely to do something. Are 50% certainty enough? If you crawl 10 square ft you do have a 50% chance. But if you definitely need this four-leaf clover then you want a 100% certainty. I guess the word "likely" is ambiguous or perhaps my statistics is rusty.

  3. I agree with Thad, but I also get your point about semantics. I think that you are "likely" (meaning >50% possibility) of finding a four-leaf-clover after 10 sq ft, but not even really "certain" (meaning 100% possibility) after 20 sq ft. You are only certain after searching the entire farm, as there may just be 1 small patch of 4-leaf clovers in the corner. What do you call it at 20 sq ft? I don't know a good mathematical term for it...


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