Silence Is The Key
One day, Greg was bored and decided to play a little experiment with his 2 friends--Harry and Ivan--. Greg told them that he would be using the five numbers: 1, 2, 3, 4 and 5.
Greg then, separately, told Harry the sum of the 2 of the five numbers and told Ivan the sum of 2 of the remaining 3 unused numbers.
Greg then told both Harry and Ivan that the sums that they were told are equal in value.
Without any communication between either party, can both Harry and Ivan figure the remaining unused number?
Assume everyone is perfectly logical.
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1 solution
The solution is almost trivial. Let S be the sum of two numbers told to Harry. Then the sum of the two numbers to Ivan would also be S . It is given that the two sets of two numbers are distinct and were taken from 1 , 2 , 3 , 4 , 5 .
Therefore the unused number would have to be 1 + 2 + 3 + 4 + 5 − S − S = 1 5 − 2 S . Since, both Harry and Ivan know the value of S , both can figure out the unused number.