You have a two-arm balance and four weights to weigh any object in one pound increments up to 40 pounds. How m

Question

How much does each of the four weights weigh?

Please, explain your reasoning!

Answer 1

1lb, 3lbs, 9lbs, and 27lbs.

EDIT: After information posted

If the balances could be only on one side of the scale, then the answer would not be possible with only four weights. But since there is no such limit, let us assume that weights can be put on either side of the scale. A 1lb weight is, of course, necessary.

Now, if it could be only put on 1 side of the scale, then the answer for the next heavier weight would be 2lb. But since we can use differences here, we need to find out what MINUS 1 equals 2, so we can use that. The answer here is 3lb.

Now, 3lb + 1lb = 4lb, but what about 5lb? So, now again, we need to find what minus 4lb will give us 5lb. The answer here is 9lb.

Repeat for the next step: Now, 9lb + 3lb + 1lb = 13lb, but what about 14lb? So, now again, we need to find what minus 13lb will give us 14lb. The answer here is 27lb.

Now, 27lb + 9lb + 3lb + 1lb = 40 lb. An exact answer! An all four weights have been used.

Answer 2

1,3,9,27

Together or against, they combine all possible weights.

1=1
2=3 on one side, 1 on other side
3=3
4=1+3
5= 9 on one side, 3+1 on other side
6= 9 on one side, 3 on other side
and so on

Answer 3

1, 3, 9, 27. Thanks for the thought invoking question.