Problem
First name
Mitchell Sparrowhawk
School
St Mary and all Saints Primary, Beaconsfield
Country
Age
9
Abbie has a set of 10 plastic cubes, with edges of lengths 1,2,3,4,5,6,7,8,9 and 10 cm. She tries to build two towers of the same height using all of the cubes.
Prove that this is impossible.
After just doing 2 attempts at this problem in Impossibilities I believe I know why this is impossible. I know this because if you add 1,2,3,4,5,6,7,8,9,10 together you will find that it equals 55. 55 is an odd number so if you halve it, it will not be a whole number. Therefore if Abbie wants 2 towers split evenly, she will need to split one of the cubes into half.