Learn / Library / Brainteasers

Doubling weights on one pan

BrainteasersEasy

You have $5$ weights of $1$ , $2$ , $4$ , $8$ and $16$ grams. You may put any subset of them on one pan of a scale. How many different positive total weights can you form?

Checking an answer needs JavaScript. The hint and the solution open without it.

Hint

Count the subsets and check whether different subsets can give the same total.

Solution

Each weight is either on the pan or not, so there are $2^{5} = 32$ subsets.
The empty subset gives total $0$ , which is not positive, so remove it.
Every total from $1$ to $31$ appears exactly once, because each integer has a unique binary representation.
So the number of distinct positive totals is $31$ .

Answer: $31$

Next question Back to the library