9514 1404 393
Answer:
4
Explanation:
We assume you are using a balance, and that weights can be put in either pan. In that case, weight values can be either added or subtracted, so there are 3 possibilities for the contribution each weight makes. In other words, we need to find how many digits are required to count to 40 in base 3.
The largest 3-digit number in base 3 is ...
3^2 +3^1 + 3^0 = 13 (base 10)
The largest 4-digit number adds 3^3 = 27 to this: 27 +13 = 40.
Hence, we can weigh values 0 to 40 using 4 weights, of sizes 1, 3, 9, 27.
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Some example weights are ...
5 = 9 - 3 - 1
38 = 27 + 9 + 3 - 1
where the "negative" weights are placed in the same pan as the unknown.