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A Shamefaced Clock is a puzzle in Professor Layton and the Azran Legacy.

Puzzle

A teacher asks a student if he knows how to tell the time. The student nods, so the teacher presents him with the following puzzle:

"This wall clock fell down and broke into three pieces. You can't see the numbers from here, but I can tell you that the total of the numbers on each of the three pieces is the same. So, can you tell me what time this clock is showing?"

According to this clock, what time is it?

Hints

Click a Tab to reveal the Hint.

Add up all the numbers on a clock face, from one to 12, and you get a total of 78.

Dividing 78 by three gives you 26.

Since the teacher said that the numbers on each of the three clock pieces came to the same total when added up, you know that the numbers on each piece add up to 26.

Try thinking of combinations of numbers that add up to 26. Here's one for you:
1 + 2 + 11 + 12.

9 + 10 + 3 + 4 is another.
Once you've got those two, the only numbers you've got left are 5, 6, 7 and 8. Guess what? They add up to 26 as well.

You should now have a fairly good idea of how these three clock pieces fit together!

Looking at the pieces you've got, it soon becomes apparent that the piece of clock which contains the two hands also contains the numbers 3, 4, 9 and 10. That means the big hand is either pointing at 3 or at 9.

If it's pointing at 3, it's quarter past something. If it's pointing at 9, it's quarter to something.

Take a close look at the position of the little hand. It should make it clear that the time the clock indicates is quarter to something, not quarter past. You now know that the big hand is pointing at 9, and that the little hand is pointing between 3 and 4.

You should therefore know exactly what time it is.

Solution

Incorrect

Pay close attention to where exactly the little hand is pointing.

Correct

Right on time!

The clock is showing 3:45 (or 15:45).

Once you know what the numbers on each of the three clock pieces are, you can work out where exactly the big hand is pointing at by paying attention to the little hand.

Then, when you know exactly where the big hand is pointing, you can work out what time it is!

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