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Sorting Blocks is a puzzle in Professor Layton and the Miracle Mask.

Puzzle

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?

Hints




Click a Tab to reveal the Hint.

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.

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.

There is at least one light block here. 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?

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?


Solution

Incorrect

Too bad.

Think carefully, and make sure you haven't overlooked anything.

Correct

That's right!

Whether there are nine light blocks or just one, he still needs to lift all 10 blocks.

A big thanks to http://www.youtube.com/user/LaytonKyouju

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