Last week in the evening class I teach we were discussing systems of linear equations. This is a highly enjoyable topic that, despite its initial simplicity, contains a wealth of truly fascinating mathematics (though we don’t cover the fascinating stuff in my class). I was delighted, therefore, when a friend sent me the following riddle this week, and I thought I’d post it up for the health and enjoyment of all. The first person to post the solution shall be rewarded with . . . a well-deserved sense of satisfaction. (The person who sent me the riddle — and he knows who he is — is excluded from the fun.)
Here we go:
It’s their birthday, you see,
The same for all three,
It’s strange but it’s perfectly true.
There’s Bertie and Ben
Who differ by ten;
Eight years older than one there is Sue.
Double one brother,
Plus treble the other,
Plus Sue’s age makes seventy-two.
From what’s on this page
You can find the girl’s age.
It’s really quite easy to do.
[J.A.H. Hunter, Fun with Figures. Dover Pub. 1965. p. 67]
Only integer solutions shall be accepted.