Always, Sometimes or Never?

Well done to everybody who investigated these statements and found examples or counter-examples. We haven't received many solutions to this problem yet, so please email us if you have a solution you'd like to share with us.

Usmaan and Mayeda from Marner Primary School in the UK each sent in a solution for one statement. Mayeda said:

When you add two odd numbers together the sum is an odd number?

I think it's never true because if you find the sum of any odd number together like 23 plus 59 it equals 82 and 82 is an even number not an odd number. Also if you do 97 plus 65 it equals 162 and 162 is even so this means that adding two odd numbers equals an odd number is not true.

Usmaan said:

When you multiply a number by itself the answer is even?

It's sometimes true because if you do 4x4 the product is 16 and if you do 9x9 it's 81 and 81 is an odd number so it's sometimes true.

Good ideas - it's easy to show that a statement is 'sometimes' true when you can find both an example and a counter-example for it! I wonder why adding two odd numbers together never gives an odd number?