Math Problems

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?

Math Problems

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.  

Can you increase the list by six numbers so that selecting three of them will always result in a sum that is a multiple of 3?

Math Problems

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?

Math Problems

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?

Math Problems

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?

Math Problems