# Office Weighings Puzzle - Solution

### The Puzzle:

You have a balance and the following items of which you know the weights: a small coin weighing 5g, a pen weighing 10g, an eraser weighing 20g, a holepunch weighing 40g, and a stapler weighing 80g.

How many different possible weights can you measure with these items?

How many different possible weights can you measure with these items?

### Our Solution:

31.

We could list all combinations, but noticing the doubling of each weight (5,10,20,40,80) we can see what happens as we introduce each weight (I include "0g" as a weighing on purpose):

5g: can weigh 0g or 5g (2 possibilities)

5g and 10g: can weigh 0g or 5g or 10g or 15g (4 possibilities)

5g, 10g and 20g: can weigh 0g or 5g or 10g or 15g or 20g or 25g or 30g or 35g (8 possibilities)

It doubles each time!

So with 4 weights there are 16 possibilities

And with 8 weights there are 32 possibilities

If you don't like "0g" as a weighing, just subtract one, for an answer of 31.

We could list all combinations, but noticing the doubling of each weight (5,10,20,40,80) we can see what happens as we introduce each weight (I include "0g" as a weighing on purpose):

5g: can weigh 0g or 5g (2 possibilities)

5g and 10g: can weigh 0g or 5g or 10g or 15g (4 possibilities)

5g, 10g and 20g: can weigh 0g or 5g or 10g or 15g or 20g or 25g or 30g or 35g (8 possibilities)

It doubles each time!

So with 4 weights there are 16 possibilities

And with 8 weights there are 32 possibilities

If you don't like "0g" as a weighing, just subtract one, for an answer of 31.

*See this puzzle without solution*

*Discuss this puzzle at the Math is Fun Forum*