You own a standard two-pan balance scale and exactly four solid weights: 1 kg, 3 kg, 9 kg, and 27 kg. By placing weights either on the object's pan or the opposite pan, how many distinct whole-number kilogram weights from 1 kg up to 40 kg can you measure?
40
Every integer from 1 to 40 can be uniquely expressed in balanced ternary (base-3 with coefficients -1, 0, and +1) using powers of 3: 3^0, 3^1, 3^2, and 3^3. Therefore, every whole-number weight from 1 kg up to 1 + 3 + 9 + 27 = 40 kg can be weighed.
About this riddle
Math riddles hide a calculation inside a short story. Pull out the numbers, work out what is being asked, and watch for a trick such as a unit change.
Difficulty: Hard. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
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