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Squares, Scores and Ages - 2007/07/30 16:58
Solution
the adult is 21 years old and scored 4,5 points; the boy is 10 years old and scored a perfect 5/5
this requires some explanation:
we were told that the boy had a higher score than the adult in five rounds tournament. So the boy’s score must be somewhere between ½ and 5 while the adult’s score must lie in the range of 0 to 4.5.
However the third person, C, was able to deduce, from being told only the actual scores that the adult and the boy could not have played each other in the tournament. This is a crucial fact, which narrows the options for the score of the adult and boy to either 4,5 , 5; or 0, ½. The latter case can be quickly ruled out as it would make the product of the scores equal to zero. This would be inconsistent with the statement concerning “product” mentioned in the puzzle
Therefore the adult, A, scored 4.5 points, and the boy,B,scored 5 points(because B did not concede any point, he would have had won if he had played A , but, since A dropped only half a point, A and B could not have played each other
The total number of squares on a chess-board is 204 (64 squares of size 1x1;49 of size 2x2;36 of size 3x3;25 of size 4x4;16 of size 5x5;9 of size 6x6;4 of size 7x7; 1of size 8x8 this final one being the whole board)
it is also significant that in the puzzle, it is the birthday of A and B. So we can safely assume that the age of A and B are both exact whole numbers of years. If B was less than 10 years old, then the product of the two scores and his ages could not be more than 4.5x5x9=202.5, which is less than the number of squares on a chess-board. So B must be at least 10 years old. 4.5x5x10=225=204+21 which gives the answers which were stated earlier. It only remains to show that there are no alternative answers where B is more than 10 years old . 4.5x5x11=247.5 which is not a whole number. 4.5x5x12=270=204+66, but it was mentioned in the puzzle that the adult is “young”. I hope I am not offending anyone by not describing 66 as a young age!
Clearly, if we started to consider ages more than 12 for B, then it would not help A to feel younger! therefore the answer given are the unique solution
the ability to think logically can, as with most skills, be cultivated through practice,and is a great asset in solving puzzle such as my lengthy one we have just considered. Personally I have tried to improve my capacity for logical thought,and,in so doing, I feel that my chess strength has increased too
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