A carpenter is sorting a stack of 10 large blocks. He bought a mixture of heavy and light blocks but mixed them up at the checkout, and now he can't tell which are which.
What is the minimum number of times he'd have to individually lift blocks in order to separate all the light ones from the heavy ones?
UK Version
A carpenter has received a shipment of ten large blocks. He knows there's a mixture of two kinds of blocks, light and heavy. Unfortunately, he doesn't know how many there are of each, and he can't tell which are light and which are heavy without lifting them up one by one and comparing them.
For this current project, the carpenter is only looking for one light block. What is the maximum number of blocks he might need to lift until he finds a light one?
This puzzle doesn't require any tricky calculations, but that's not to say there isn't a trick to it.
Consider which of the conditions in the puzzle are concrete and which are vague.
US Version
From the puzzle description, you know for sure there are ten blocks, some of which are heavy, some light.
If that's the case, what's the maximum number of light blocks there could be, and what's the minimum number?
Thinking about the maximum and minimum should lead you to the solution.
UK Version
From the puzzle description, all you know for sure is that there are ten blocks, and a mixture of two different kinds: light and heavy.
If that's the case, what's the maximum number of blocks that there could be, and what's the minimum number?
Thinking about the maximum and minimum should lead you to the solution.
There is at least one light block here.
US Version
If we assume there's only one, then in the worst-case scenario, you would have to lift nine blocks before you could work out which was the light one.
But what if there were nine light blocks?
UK Version
In the worst case scenario, the carpenter might have to lift nine heavy blocks and then he'd know the final block has a light one.
Or would he? What if in fact the first nine blocks he'd lifted were light?
US Version
If you were to lift nine blocks and find them all the same weight, you wouldn't know if they were the lighter or the heavier blocks. So how many blocks would you have to lift to find out if those first nine were light or heavy?
UK Version
If the carpenter were to lift nine blocks and find them all the same weight, he would know the tenth one was different, but he wouldn't know for sure whether it was lighter or heavier than the nine others.
So how many blocks would he have to lift in total to find out if those first nine were light or heavy?
Solution
Incorrect
Too bad.
US Version
Think carefully, and make sure you haven't overlooked anything.
UK Version
Think carefully and make sure you haven't overlooked anything.
Correct
That's right!
US Version
Whether there are nine light blocks or just one, he still needs to lift all 10 blocks.
UK Version
If he's unlucky, he'll need to lift all ten blocks. If the first nine blocks he picks up are the same weight, he won't know if the last block is light or heavy without lifting it up as well.