So I have this problem in Calculus... It's driving me crazy! I can't figure it out

Four weights of 1, 3, 9, and 27 pounds sit on a table along with two identical boxes. One of the boxes contains an object which weighs X pounds where X is an integer between 0 and 40. Explain how, for any such X, it is possible to place some or all of the weights in the boxes so the contents of the boxes then have the same weight.

This isn't calculus.

For x = 40, place all of the other weights in the other box.
For x = 39, place 27, 9, and 3 in the other box
For x = 38, add the 1 to the 38 to get 39, and place the rest of the weights in the other box.
For x = 37, 37 and 27, 9, 1
for x = 36, 36 and 27 + 9
for x = 35, 35 + 1 and 27 + 9
for x = 34, 34 + 3 and 27 + 9 + 1
for x = 33, 33 + 3 and 27 + 9
for x = 32, 32 + 3 +1 and 27 + 9
for x = 31, 31 and 27 + 3 + 1
for x = 30, 30 and 27 + 3

It's very easy to go all the way down to 0 and 0.

Try it, it's easy

This is number theory, not calculus, otherwise I would offer you a proof instead of examples.

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