Solution to Puzzle #57: Sam Lloyd’s Puzzling Scales

I got relatively fewer responses to this puzzle, perhaps people found it to be too simple. First person with the correct answer this time was Ethan Stock from California and then Shruti Mittal from Mumbai. Well done.

My iPad is not with me at the moment, the answer would have been easier to explain. In general, it is tempting to use algebra, but lets try without it.

If you look at the first two figures, one realizes that there is a top on the left side in both the balances. In the second figure, therefore, where we have the top on the left and a block along with 8 marbles on the right, one can add 3 blocks on both sides, and the scale should still be balanced. On the left now you will have the top along with 3 blocks, which is the same as the first figure. Therefore, the right sides of both the balances should match as well, implying that 4 blocks + 8 marbles should be the same as 12 marbles, therefore leading to the conclusion that a block weighs the same as a marble. Once we have established this, the rest is easy – in the second figure we see that a top is equal to a block + 8 marbles. If we replace the block with a marble (since they weigh the same), we can figure out that a top is equal to 9 marbles!

Hope you enjoyed the puzzle!

 

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