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March 24, 2014
PUZZLE -- GUESSING AGE PARTY GAME
The 'mind-reader' asks you to multiply your age by 10 (applies to persons not less
than 10 years old). Then you are asked to pick a number between 1 and 9, multiply
it by 9 and then subtract this product from your age multiplied by 10. You tell the
'mind-reader' this difference, and he promptly guesses your age correctly. He even
tells you the number (between 1 and 9) randomly chosen. How?
(Scroll down for the solution)
Solution: Whenever a two-digit number is multiplied by 10 and a single-digit number
multiplied by 9 is subtracted, the first digit of the difference has to be the single-digit
number. Thus
Difference = 10 Age - 9 Number
= 10 Age - 10 Number + Number
10 Age - 10 Number = Difference - Number
Age = (Difference - Number)/10 + Number
Example:
Age = 25, Number = 3
10(25) - 9(3) = 223
Thus the number chosen is 3 and the age is 22 + 3 = 25
Confirmation from formula:
Age = (Difference - Number)/10 + Number
= [(223 - 3) /10] + 3 = 22 + 3 = 25
PUZZLE -- GUESSING AGE PARTY GAME
The 'mind-reader' asks you to multiply your age by 10 (applies to persons not less
than 10 years old). Then you are asked to pick a number between 1 and 9, multiply
it by 9 and then subtract this product from your age multiplied by 10. You tell the
'mind-reader' this difference, and he promptly guesses your age correctly. He even
tells you the number (between 1 and 9) randomly chosen. How?
(Scroll down for the solution)
Solution: Whenever a two-digit number is multiplied by 10 and a single-digit number
multiplied by 9 is subtracted, the first digit of the difference has to be the single-digit
number. Thus
Difference = 10 Age - 9 Number
= 10 Age - 10 Number + Number
10 Age - 10 Number = Difference - Number
Age = (Difference - Number)/10 + Number
Example:
Age = 25, Number = 3
10(25) - 9(3) = 223
Thus the number chosen is 3 and the age is 22 + 3 = 25
Confirmation from formula:
Age = (Difference - Number)/10 + Number
= [(223 - 3) /10] + 3 = 22 + 3 = 25