by Stephen Hogg
Published Friday May 24 2024
On his 35th birthday, maths teacher Al’s three younger half-sisters bought him “The Book of Numbers for Nerds” as a tease. It showed how to find right-angle triangles with whole-number sides using any two unequal odd square numbers. You take half their sum; half their difference; and the square root of their product to get the three sides. Any multiple of such a triplet would also work. He told his sisters this and that their ages were the sides of such a triangle. “Algorithm Al!” they yelled.
Knowing the age of any one sister would not allow you to work out the other ages with certainty, but in one case you could be sure of her place chronologically (youngest, middle or oldest).
Give the three sisters’ ages (youngest to oldest).
Sunday Times Teasers Discussion Group 
Actual answer required is not specified but easy to work out the age and relative position of one half-sister.
Teaser seems to have been updated with answer required (maybe I missed it earlier?)
In any case, still fairly straightforward to reach the answer.
I used Brian’s table of pythagorean triples a,b,c from c=34 downwards and looked where both, c+a and c- are odd.
Very easy to calculate the 12 possible triangles with young enough ages, the first logical step narrowing it to 2 and the second logical step giving the one unique set of 3 ages.
I found the clue wording difficult to understand? Also, I had understood the use of the word “stepdaughters” to hint they were significantly younger than Al.
I understood “younger half-sisters” to indicate that the eldest could be almost 35, or the youngest very young indeed. They didn’t need to be with the normal range of siblings’ ages.