Office Weighings Puzzle - Solution

The Puzzle:

Office Weighings

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?

Our Solution:


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.
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