October 2020 - Math Problem
How many toothpicks would it take to make a 4x4 square?
Solution:
It takes 40 toothpicks.
How about a 20x20 square?
September 2020 - Math Problem
There is a sequence of numbers called the Fibonacci sequence in which the first two numbers are 1 and then the rest of the numbers are the sum of the previous two numbers. Here are the first 12 terms of the sequence.
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144
How many of the first 25 terms of the sequence are even numbers?
Solution:
8 of the first 25 will be even. How many would be even in the first 100 terms?
June 2020 - Math Problem
A magic square has the property that each column, each row and each diagonal add up to the same number. The magic square below is a special one called Ramanujan’s square. Notice that each column, row and diagonal sum to 139. What other combinations of squares add up to 139? Enjoy!
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22 |
12 |
18 |
87 |
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88 |
17 |
May 2020 - Math Problem
Many sports that have playoffs use a best-of-seven format. This means that the two teams play until one team wins four games. If two teams are evenly matched, how many games would you expect it to take to end a best-of-seven series? Simulate this problem by tossing a coin and recording heads or tails. The first to four wins. Repeat this experiment and each time keep track of the number of games it took to end the series. Finding the mean of these values will approximate the expected number of games. In general, better approximations can be
April 2020 - Math Problem
Suppose that you have a can of red paint, a can of blue paint, and a large supply of identical wooden cubes. If you paint each face either solid red or solid blue, how many different cubes can be made?
Solution:
All red 1
Five red and one blue 1
Four red and two blue 2
Three red and three blue 2
Two red and four blue 2
One red and five blue 1
All blue 1
March 2020 - Math Problem
What is the largest number of pieces of (round) pie that you can get with five straight cuts? The pieces do not all have to be the same size.
Solution:
You can get 16 pieces. What if you did 7 straight cuts?
February 2020 - Math Problem
What is the largest number of pieces of (round) pie that you can get with five straight cuts? The pieces do not all have to be the same size.
You have an unlimited supply of water and two unmarked cylindrical containers. The first container holds 5 litres and the other holds 3 litres. How would you get exactly 4 litres of water?
Solution:
Fill the five and pour what you can into the three
Empty the three and pour what remains in the five into the three.
January 2020 - Math Problem
You have a jar full of nickels, dimes and quarters. If you select 3 coins, how many different sums of money are possible?
Solution:
10 sums are possible (15, 20, 25, 30, 35, 40, 45, 55, 60 and 75). What if the jar also had loonies?
November 2019 - Math Problem
If there are three dots on each side of a hexagon as shown, then there are 12 dots in total.
If there are five dots on each side of a hexagon as shown, then there are 24 dots in total.
Following this pattern how many dots would there be in total if there were 10 dots on each side?
September 2019 - Math Problem
There are 50 tiles in a row. Every third tile is red. Every fourth tile has a star printed on it.
Every remaining tile is green and unmarked.
How many green and unmarked tiles are there?
There are 26 green and unmarked tiles. What if we started with 500 tiles instead of 50? How many would be green and unmarked?
Solution:
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