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Heavier or Lighter? is a puzzle in Professor Layton and the Curious Village.

Puzzle

Below are 12 weights that are visually identical to one another. Among these is a single weight that has a different weight from the others. The problem is that you don't know whether this weight is heavier or lighter than the others.

Use the scales exactly three times to determine which weight is different from the others.

Hints




Click a Tab to reveal the Hint.

There is no one definitive way to solve this puzzle, but it's best to start by putting four weights on each side of the scale.

If the scale tips one direction, you know that the four weights off the scale don't contain the weight you are looking for.

If the scale stays level, you know that one of the four weights you didn't load on the scale is the irregular weight.

If the scale tips after you weigh eight weights in the fashion described in the first hint, take one set of weights off the scale and keep the other four where they are. Next, put the four unweighed weights on the empty side of the scale.

If you make it this far, all you need to do is narrow the possible choices down one more time in the next step.

If your scale doesn't tip after your second weighing as described in the earlier hint, you know the odd weight is somewhere within the four weights you took off the scale. If the scale tips in the same direction as before, you know that the irregular weight is somewhere within the four weights that you kept on the scale. If it tips in the opposite direction than before, the weight you seek is one of the four you loaded on the scale before the second weighing.


Solution

Incorrect

Too bad.

The irregular weight changes each time you try the problem. Think about what you need to do and try again.

Correct

That's correct!

This challenging problem is well known to many puzzle aficionados. If you're lucky, it's possible to find the answer without too much work.

Think of how you could do this if you could use the scale as many times as you wanted.

A big thanks to http://professorlaytonwalkthrough.blogspot.com

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