Ok..two people..a young adult and a boy..who we shall call "A" and "B"
respectively have just playing in a five round weekend open
tournament (with normal scoring rules: 1 point for a win, 1/2 point 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 person "C" , who knows the ages of "A" and "B", asks them
about their scores in the tournament. "A" and "B" only tell "C" how
many points they each have scored. "C" is then able to deduce
that "A" and "B" could not have played each other in the tournament.
He also calculates correctly that the product of their scores and the
age (in years) of "B" is exactly equal to the age (in years) of "A" plus
the total number of squares on a chess board.
What is the scores and the ages of "A" and of "B".
Dave
Here's a solution: A and B both score 5 in the tournament
(bastards). It is because of this that C can deduce that A and B did
not play each other. Other score combinations would also lead to this
deduction (e.g.,.5 for B, 0 for A). There is some ambiguity in your
phrase "product of their scores and the age of B" This could either
mean the product of their summed scores and the age of B (5+5) xB,
or it could mean the product of their scores and B (5x5xB). I'm
assuming you meant to be interpreted in the first manner. So we
have the equation 10B = A+64. Now since it is their birthday, their
ages have to come out even. That means A's age must be such that
when addes to 64 the sum is a multiple of 10. The only number that
fits and leaves A's age in the "young adult" range and B's age in
the "boys" age is 16. So A's age is 16 and B's age is 8.
Bennett
