Originally posted by Bagheri
Two of the main characters in the puzzle are young adult and a boy. Let us call them A and B respectively. They have finished playing in a five round weekend open tournament (with normal scoring rules: 1 point for a win, 1/2 for a draw and 0 for a loss), and B has a higher score than A, but both players are happy because it is their birthday.
A third pers ...[text shortened]... puzzle is to work out the scores and the age of A and B.
I will post the solution next week J
The only way C can deduce that A and B have not played is if B scored 0.5 and A scored 0 [because B and A don't have a full point between them, and if they had played, they would have], or B scored 5 and A scored 4.5 [B has won all games and A has not lost].
C's calculation has the formula:
(SA+SB)AB = AA + 64
where SA and SB are the scores of A and B, and AA and AB are the ages of A and B.
It's easy to see that the first scoring scenario (SA = 0 and SB= 0.5) won't work. AA has to be at least 18 for him to be an adult. The right side of the equation is at least 82. AB would have to be at least 164 years old to satisfy the equation, but then he wouldn't be a boy anymore (or living, for that matter).
The second scenario (SA = 4.5 and SB = 5.0) must be correct. AB must be even to get rid of the fraction on the left side (because it's their birthday). He must be at least 10 years old to get the left side of the equation over 82. However, if he's 12, the adult must be 50 years old, which is not exactly 'young'.
By elimination, the Adult is 31 years old and scored 4.5, and the boy is 10 years old and scored 5.0