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
What if the numbers were 9, 3, 7, 7?
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?
October 2021 - Math Problem
Can you find 4 consecutive numbers that add to 30? How about 50 or 90?
Solution:
30=6+7+8+9
50=11+12+13+14
90=21+22+23+24
Can 100 be written as the sum of 4 consecutive numbers? Is there a quick way to determine if a number can be written as the sum of 4 consecutive numbers?
September 2021 - Math Problem
A set of stairs has 24 steps numbered 1 to 24 going up. A rabbit can only hop 3 or 5 steps forward or backward. Starting at the bottom (step 0), is there a step that can not be reached?
Solution:
No, all steps can be reached. Is it possible to get to the 24th step and touch every step exactly once?
June 2021 - Math Problem
What is the smallest number that is divisible by the numbers 1, 2, 3, …, 10?
Solution:
2520. What about the smallest number divisible by the numbers 1, 2, 3, …, 20?