You are given a fair balance, consisting of a pair of scales. Each time the bala

Question

You are given a fair balance, consisting of a pair of scales. Each time the balance is used, either the right scale will tip (if the weight on the right is strictly greater than the weight on the left), or the left scale will tip, or the two scales will be in balance (if the two weights are exactly equal). You are also given an infinite supply of two types of weights: small weights, each weighing m ounces, and large weights, each weighing n ounces. Finally, you also have a golden crown that weighs exactly x ounces, where x is a positive integer. Your goal is to determine the weight of the crown. (a) Suppose that m = 100 and n = 441. Can you determine the weight of the crown? If yes, explain why. If not, explain why not. (b) Now suppose that m = 6 and n = 9. Can you determine the weight of the crown? If yes, explain why. If not, explain why not. (c) Can the crown's weight be determined if m = 6 and n = 88?

Explanation / Answer

(a.) No, because there is no common factor between 100 and 441 , so the minimum weight that u can measure is 41 ounces.

(b.) No, because the minimum common facto b/w 6 and 9 is 3 so you can meausre the weight which is a multiple of three, not 2 or 1 ounces.

(c.) No, here also minimum weigh that you can measure is 2 ounces (88-15*6=2), not the weight of 1 ounces

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