January 2021 - Math Problem
One hundred pennies are arranged in a row on a table. Every second coin is replaced with a nickel. Then every third coin is replaced with a dime. Finally, every fourth coin is replaced with a quarter.
What is the total value of coins left on the table?
Solution:
You will have $9.93.
What if you started with 1000 pennies?
December 2020 - Math Problem
The number 29 is interesting because when the sum of the digits (2+9) is added to the product of the digits (2x9) the answer is 29, the number that we started out with (11+18=29).
Can you think of any other numbers with this property?
Solution:
Another such number is 59 (5 + 9 + 5 x 9 = 14 + 45 = 59). Can you think of any others?
November 2020 - Math Problem
There are seven seats on a boat all in one line from front to back.
Only one person can be on a seat at any point in time.
The seat at the centre of the boat is empty and the other six seats are occupied.
The three people at the front of the boat want to move to the back of the boat and the three people at the back want to move to the front of the boat.
A person may move to the next seat if it is empty or may step over one person to get into an empty seat.
What is the minimum number of moves required to reach their goal?
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!
|
22 |
12 |
18 |
87 |
|
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.