MATH PUZZLES BY MAX MILLARD Adjust Background: Darker / Lighter

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I love to make up math puzzles. I never consciously write them, but whenever something occurs in my daily life that makes me to stop and ponder the math, I take the first opportunity to work out the problem and devise a puzzle. The result is a collection of math puzzles ranging from quite basic to fairly complex, whose solutions depend more on creative thinking than pure mathematics. Here are 10 of my favorites. The easiest ones appear first.


This is the first math puzzle I ever invented. It popped into my head on the morning of my 29th birthday, during a visit to my parents' home in Maine, as I lay in bed and heard my father in the adjacent kitchen. His birthday would be the next day.

Problem: If I turned 29 on December 4, and my father turned 58 on December 5, on which day was I exactly half his age? Do not use leap years in the calculation.

Hint: This problem requires simple algebra.


You need to find out which day of the week is June 10, 2007. You have only a 2006 calendar. How do you use it to find out which day of the week is June 10, 2007?


There are two brands of napkins in the supermarket. Brand 1 costs $2.50 for 360 napkins. Brand 2 costs $3.50 for 500 napkins. By using the calculator just once, how can you determine the better deal?


Jupiter takes 12 years to orbit the sun and Saturn takes 30 years. If they are moving in the same plane and in the same direction, how often does Jupiter pass Saturn?


A man and his son Carl go to the Yerba Buena Ice Skating Center. It takes dad 50 seconds to skate all the way around the rink. It takes Carl 1 minute and 25 seconds.

If dad and Carl start at the same point and the same time, dad will immediately take the lead. But at what point will dad pass Carl again? Choose one of the following:

1. Before dad has gone around twice.

2. Just before dad has gone around three times.

3. Just before dad has gone around two and a half times.



It takes 2 minutes and 30 seconds to heat a cup of coffee or a cup of tea in the microwave by itself, but 4 minutes and 30 seconds to heat them both together, because they each absorb a certain amount of heat.

Question: If I put the coffee in first, and heat it for 1 minute, then add the cup of tea, when do I take each of them out so that they are the right temperature? The answer must be exact.


At 9 o'clock, the hands of a clock form a right angle. When is the next time they'll form a right angle? Calculate to the closest second.


You have a piece of paper that measures 8 by 10 inches. You want to be able to trim the paper so that when you cut it in half, then cut the halves in half again, and keep cutting as long as you can, every piece will have the same proportion as the original piece.

For a piece of paper that is 8 inches wide and 10 inches long, the proportion of width to length is .8. If you cut it in half, the proportion of the new pieces will be 5/8 = .625.

Problem: If you keep the paper 10 inches long and trim off some of the 8-inch width, how wide will it be when the proportions of width to length will always be constant, no matter how many times you halve the paper?


If you're blowing bubbles in the bathtub, you'll notice that when a bubble hits the water, it immediately changes from a sphere to a half sphere. What is the proportion of the diameter of the whole bubble to that of the half bubble? Use this formula: volume = pi r cubed. You may use a calculator if necessary.


Place seven round coins in a circle, with one in the middle and the other six on the outside.

Problem: If each coin has a diameter of 1 inch, what is the area of the space between the coins? Use the value of 3.14 for pi.

Approach: If you draw a line from the center of each coin to the coins on either side of it, you will form a hexagon. The distance from the center of the hexagon to each of the most distant points on the outside is 1". Calculate the area of the hexagon, then subtract the area of the circles inside the hexagon. This will tell you the area of the space between the coins.