Millicent & Maximus Mathscot’s Maths Challenge
Dear Parents,
– the answers!
I would like to extend my gratitude and congratulations to all the parents who took part in our recent
mathematical challenges; I was overwhelmed by the number of entries – all of which were correct!
For those of you still puzzled by the problems set, here are the solutions:
Q1 When it was her birthday, my mathematical aunt told me:
“Three years ago my age was a square number. Next year it will be a prime number, and in twelve years it will
be a cube number.”
How old is my aunt?
Square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100. So, she is 4, 7, 12, 19, 28, 39, 52, 67, 84 or 103.
If her age is a prime number next year that narrows the possibilities down to 4, 12, 28 or 52.
Cube numbers are 1, 8, 27, 64 and 125.
She must be 52, as 52 + 12 = 64.
Q2. The sum of the ages of the five people in the Salter family is 120 years.
The ages of Tom and Sue total 58 years. The ages of Sue and Dick total 28 years. The ages of Dick and Jane
total 48 years. The ages of Jane and Harry total 52 years.
Who is the mother and how old is she?
T + S + D + J + H = 120 (we are told this at the beginning)
T + S = 58 and D + J = 48 (we are told this too)
so 58 + 48 + H = 120
106 + H = 120, so H = 14
From this we can calculate everyone’s age:
J = 38, D = 10, S = 18 and T = 40.
So Jane is the mother and is 38 years old.
Thank you for taking part and for encouraging your children to enjoy their mathematics!
Kind regards,
Mrs L Wales