Question 31898
Five men took turns weighing themselves on a scale. However, they weighed each other two at a time, ten times total , so that every possible combination of two men was weighed. The scale had the following readouts for the pairs: 236 pounds, 244 pounds, 228 pounds, 250 pounds, 258 pounds, 230 pounds, 246 pounds, 238 pounds, 242 pounds, and 252 pounds.
How heavy was the heaviest man?
LET THE WEIGHTS 5 MEN IN ORDER OF DECREASING WEIGHT BE A,B,C,D,E
WHEN THEY WEIGH IN PAIRS WE GET 5C2=5*4/2=10 DIFFERENT PAIRS OR 20 MEN
HENCE THE TOTAL WEIGHT IS FOUR TIMES THE WEIGHT OF THE 5 MEN'S TOTAL WEIGHT
4(A+B+C+D+E)=236+244+228+250+258+230+246+238+242+252=2424
A+B+C+D+E=606..............I
NOW HEAVIEST IS A+B=258.........II
NEXT HEAVY IS A+C=252...........III
LIGHTEST =D+E=228.................IV
EQN.I-EQN.IV...GIVES..
A+B+C+D+E-D-E=606-228=374
A+B+C=374.....................V
EQN.II+EQN.III GIVES
A+B+A+C=258+252=510
2A+B+C=510.................VI
EQN.VI-EQ.EQN.V...GIVES...
2A+B+C-A-B-C=510-374=136
A=136
SO HEAVIEST MAN'S WEIGHT =136