Question

There are 3 people A, B and C. Three of them have
positive integers written on their hats. One can only
see the numbers written on other hats and can not
see the number written on his own hat. The number
on one of the hats is the sum of the numbers on the
other 2 hats. Now the following event occurs
A was asked about the number on his hat. He replies
"Don't know".
B was asked about the number on his hat. He also
replies "Don't know".
C was asked about the number on his hat. He also
replies "Don't know".
A was asked again the number on his hat. He replies
"65".
Find the product of the three numbers on the hats.​

Answer 1

Step-by-step explanation:

Given :

A = B + C

B = A + C

C = A + B

& A = 65 & (B + C) = 65

A × B × C

65 × (A + C) × (A + B)

65 × [A(C + B)]

65 × [65(65)]

65 × 65 × 65

= 274,625