February 2023 - Problem of the Month
This Month’s Problem
Consider the following pattern.
January 2023 - Problem of the Month
In the puzzle below, the value of a square in any of the top three levels is the sum of the two squares directly beneath it. What will be the value in the top square?
December 2022 - Problem of the Month
How many squares do you see in this picture? (There are more than 20)
Answer
There are 30 squares. What if instead of a 4x4 grid, we started with a 5x5 grid. How many squares would there be?
November 2022 - Problem of the Month
74 means 7x7x7x7 which is equal to 2401 so when 74 is expressed as an integer, the last digit is a 1.
What is the last digit of 711 when it is expressed as an integer?
Solution
The last digit is a 3. What is the last digit of 7200 when it is expressed as an integer?
October 2022 - Math Problem
This Month’s Problem
Consider this list of numbers
1, 1, 1, 4, 4, 4, 7, 7, 7, 10, 10, 10
Pick any 3 numbers from the list and add them together.
Repeat the process with a new set of numbers from the original list.
What do you notice about the sums?
Solution
The sum is always a multiple of 3.
September 2022 - Math Problem
The Mayan Mathematics Page on The Story Of Mathematics website includes this chart that shows how to convert numbers from the Arabic system that we normally use to the Mayan Base 20 Number System.
June 2022 - Math Problem
Use this Scratch program to play "High-Low". Click on the green flag to start.
Try to come up with a strategy to minimize the number of guesses that it takes to come up with the number.
May 2022 - Math Problem
The number 15 can be written as the sum of consecutive whole numbers in three ways.
15 = 7 + 8
15 = 4 + 5 + 6
15 = 1 + 2 + 3 + 4 + 5
In how many ways can you write 105 as the sum of whole numbers?
Solution:
Here are five ways:
105 = 52 + 53
105 = 34 + 35 + 36
105 = 19 + 20 + 21 + 22 + 23
105 = 12 + 13 + 14 + 15 + 16 + 17 + 18
105 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14
In how many ways can you write 24 as the sum of whole numbers?
April 2022 - Math Problem
Create a set of 9 cards that are numbered 1 to 9. Select 4 cards at random and use the numbers on all 4 the cards and the 4 operations (add, subtract, multiply and divide) so that the result is 24. For example if the numbers are 9, 6, 8, 1 then one possibility is 1 x (9 - 6) x 8.
What if the numbers were 6, 2, 7, 3?
You can also play the interactive game online.
Solution:
One possibility is 7 x 6 / 2 + 3
March 2022 - Math Problem
Without using a calculator, can you figure out which product will be greater: 27 x 39 or 28 x 38?
Solution:
Think about 28 x 39...
- For 27 x 39 you would need to add another group of 39.
- For 28 x 38 you would only need to add another group another group of 28.
- This means that 28 x 38 is larger.
Which is larger 134 x 215 or 135 x 214? How much larger?