Question 29
In a safe there are $128$ bags of gold, all looking the same, but all of different weights. The treasurer wants to determine the two heaviest bags and to do so he has a two-pan scale. The only operation allowed is to place a bag on each plate and thus establish which of the two is heavier. Decide whether the treasurer can achieve his objective by carrying out $133$ permitted operations. If the answer is affirmative, indicate the sequence of weighing; If negative, explain why.