Sunday Times Teaser 2943 – Keep Your Balance
by Danny Roth
Published February 17 2019 (link)
George and Martha have a set of a dozen balls, identical in appearance but each has been assigned a letter of the alphabet, A, B….K, L and each is made of a material of varying density so that their weights in pounds are 1, 2…. 11, 12 but in no particular order. They have a balance and the following weighings were conducted:
1) A + C + I v G + J + L
2) A + H + L v G + I + K
3) B + I + J v C + F + G
4) B + D + I v E + G + H
5) D + F + L v E + G + K
On all five occasions, there was perfect balance and the total of the threesome in each was a different prime number, that in 1) being the smallest and progressing to that in 5) which was the largest.
In alphabetical order, what were the weights of each of the twelve balls?
and here is a version that is based on solving the five equations: