Posted tagged ‘weight’

Selection of weights to weigh a thing

August 8, 2008

(Extracted from Leino’s puzzle page)

You are given a balance (that is, a weighing machine with two trays) and a positive integer N. You are then to request a number of weights. You pick which denominations of weights you want and how many of each you want. After you receive the weights you requested, you are given a thing whose weight is an integer between 1 and N, inclusive. Using the balance and the weights you requested, you must now determine the exact weight of the thing.

As a function of N, how few weights can you get by requesting?

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The fake coin

December 15, 2007

(Can be found in Leino’s puzzle page)
You have 12 coins, 11 of which are the same weight and one counterfeit coin which has a different weight from the others. You have a balance that in each weighing tells you whether the two sides are of equal weight, or which side weighs more. How many weighings do you need to determine: which is the counterfeit coin, and whether it weighs more or less than the other coins. How?