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?
February 2022 - Math Problem
A list of 4 numbers has a mean, median and mode all equal to 5. Find four numbers that meet this criteria.
Solution:
One possibility is 5, 5, 5, and 5. Another is 1, 5, 5, and 9. Can you think of any more?
January 2022 - Math Problem
1 cm linking cubes are put together to form a rectangular prism that has dimensions 4 cm by 6 cm by 9 cm. You position the prism so you can see three faces. How many 1 cm linking cubes can you see?
Solution:
You will be able to see 96 1 cm linking cubes. What if the prism was 5 cm by 10 cm by 15 cm?
December 2021 - Math Problem
You have a set of 9 cards that are numbered from 1 to 9. Can you place the cards in 3 piles so that the sum of the numbers on the cards in each pile is the same?
Solution:
Yes. You can have 3 piles of 15: 1, 5, 9 and 2, 6, 7 and 3, 4, 8.
Are there other ways to get 3 piles of 15?
November 2021 - Math Problem
A bag contains 10 blue blocks, 10 green blocks and 10 red blocks. What is the minimum number of blocks you have to remove from the bag to ensure that you get 4 blocks of the same colour?
Solution:
You would have to remove 10 blocks to ensure that you get 4 blocks of the same colour.
What if each bag started with 20 blocks of each colour?