20 buckets

Question:

You have 20 buckets of blocks, a knife, and a weighing scale. Each bucket has 100 blocks. 19 of the buckets have blocks that weigh 16oz each, and one bucket has blocks that weigh 17oz each. How do you figure out which bucket has the 17oz blocks by weighing only once?

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Solution: Number the buckets 1 through 20. Take one block from the bucket 1, two from bucket 2, three from bucket 3, and so on, until you have 20 blocks from bucket 20.

Then stack and weigh the 210 blocks (1 + 2 + 3 + … + 18 + 19 + 20 = 210). If all the blocks weigh 16oz each, then the scale would read 3360oz.

However, the scale will actually read over this by a number of ounces that corresponds to the numbered bucket with the heavier blocks since each heavy block adds 1 ounce.

For example, if the heavier blocks are in bucket 10, the scale would read 3370 oz since there are 10 blocks that weight 17oz each. Subtracting the weight on the scale with 3360 oz will give the bucket number: 3370 – 3360 = 10.

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