# Squares, Scores and Ages

Bagheri
Posers and Puzzles 27 Jul '07 11:06
1. 27 Jul '07 11:07
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 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 have each scored. C is then able to deduce that A and B could not have played each other in the tournament. He also calculated correctly that the product of their score and the age (in years) of B is exactly equal to the age ( in year) of A plus the total of squares on a chess board.

Your puzzle is to work out the scores and the age of A and B.

I will post the solution next week J
2. wolfgang59
27 Jul '07 12:07
B is 64 years older than A. Their scores were B; 1/2 and A zero. Good job it was their birthdays!
3. 02 Aug '07 11:08
Originally posted by wolfgang59
B is 64 years older than A. Their scores were B; 1/2 and A zero. Good job it was their birthdays!
sorry but you are well off the mark try posting the way you arrive to that conclusion
4. SwissGambit
Caninus Interruptus
02 Aug '07 15:58
Originally posted by wolfgang59
B is 64 years older than A. Their scores were B; 1/2 and A zero. Good job it was their birthdays!
The boy is 64 years older than the adult?! ðŸ˜•
5. whirlpool
absolute beginner
02 Aug '07 16:14
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
26 4
6. wolfgang59
02 Aug '07 17:091 edit
To deduce that A & B have not played eachother one must have all wins or all losses and the other a draw or a draw short of maximum OR they both have maximum. (but that cannot be because we are told B's score is higher than A's)

So
0 & 0.5 product of score = 0
5 & 4.5 product of score = 22.5

Now P + B = A + 64
since A & B are whole numbers P must be a whole number, therefore P=0
If P=0 then B=A+64
the boy is 64 years older than the adult.

ðŸ˜•
7. whirlpool
absolute beginner
02 Aug '07 17:191 edit
Originally posted by wolfgang59
To deduce that A & B have not played eachother one must have all wins or all losses and the other a draw or a draw short of maximum OR they both have maximum. (but that cannot be because we are told B's score is higher than A's)

So
0 & 0.5 product of score = 0
5 & 4.5 product of score = 22.5

Now P + B = A + 64
since A & B are whole numbers P ...[text shortened]... e number, therefore P=0
If P=0 then B=A+64
the boy is 64 years older than the adult.

ðŸ˜•
from above

"He also calculated correctly that the product of their score and the age (in years) of B is exactly equal to the age ( in year) of A plus the total of squares on a chess board. "

4.5*5*4=26+64

... product of their score and the age of B (who is 4)
8. SwissGambit
Caninus Interruptus
02 Aug '07 17:50
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.
9. whirlpool
absolute beginner
02 Aug '07 18:19
Originally posted by SwissGambit
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 scor ...[text shortened]... e Adult is 31 years old and scored 4.5, and the boy is 10 years old and scored 5.0
.[/b]
maybe ...

I think the statement "product of their score and the age (in years) of B" needs to be clarified. It does not say the product of their "combined" score and the age in years - just the product of their score.

If he meant that you needed to combined their scores first, he should have made this clear.

If he meant a*b*c, that is obviously a different answer than (a+b)*c ...

This has become less of a math puzzle and more of an English test.
10. SwissGambit
Caninus Interruptus
02 Aug '07 19:25
Originally posted by whirlpool
maybe ...

I think the statement "product of their score and the age (in years) of B" needs to be clarified. It does not say the product of their "combined" score and the age in years - just the product of their score.

If he meant that you needed to combined their scores first, he should have made this clear.

If he meant a*b*c, that is obviously a ...[text shortened]... swer than (a+b)*c ...

This has become less of a math puzzle and more of an English test.
Yeah, the wording is vague. Let's see what OP says on the matter.