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# Picking his sentence

## Question

At the end of a trial an eccentric judge sentenced the accused individual to some number of years in prison. However, the judge pointed out that this individual should 'select' the number of years to be served by himself! The judge placed 12 boxes on the circumference of a circle. Each box was numbered, the clockwise sequence of numbers on the boxes was, 7, 10, 1, 3, 6, 11, 8, 4, 5, 9, 0 and 2. The sentenced man was told that there was a number of coins in each box; again, the clockwise sequence o numbers of coins was 0, 1, 2, 3, 4, 5, 6,7, 8, 9, 10, 12. The sentenced man should select a box and the number of coins in the box would determine the length of the sentence. However, before the man pointed to any box, he asked the judge whether he could get any additional information, namely, how many boxes had numbers which exactly matched the number of coins they contained? The judge replied that such information could not be disclosed, as it would allow him to determine teh empty box. The man thought a little and pointed to the empty box anyway! How did he know? Which box did he point to?

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If the judge had said that there were 3 boxes whose labels matched their contents, then those boxes must have been the ones labelled 4, 5, and 10. In this scenario, box #3 would contain 0 coins. The only other possible answers the judge could give (that I can see) are 0 or 1, neither of which would have been helpful to the accused. So, the answer the judge neglected to give must have been 3, and Box #3 should be chosen.

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The man selected box #0. Number of coins in each box matched number of the box, except for box #11, which contained 12 coins.

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In the various settings, there are 6 settings where there are no matches, 3 settings with 1 match, 2 settings with 3 matches and 1 setting with 2 matches.

Given the Judge's claim, there must be 2 matches and the order of boxes is 7, 10.... 2 and the coins respectively are 0,1,2...12
So the prisoner selected box 7 with 0 coins.
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Hello, this is my first stab at answering a riddle, since I am a new member .

But Here is my Logic:

IF >>> "The judge placed 12 boxes on the circumference of a circle. Each box was numbered, the clockwise sequence of numbers on the boxes was, 7, 10, 1, 3, 6, 11, 8, 4, 5, 9, 0 and 2."

AND >>> "man was told that there was a number of coins in each box; again, the clockwise sequence of numbers of coins was 0, 1, 2, 3, 4, 5, 6,7, 8, 9, 10, 12."

So it is safe to say the boxes and # of coins match up sequencially in clockwise order therefore :

7, 10, 1, 3, 6, 11, 8, 4, 5, 9, 0, 2
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12

The extra information the judge told him was just that...extra. Which is why it took the criminal only a few seconds to determine it was box number 7 with 0 coins.

Edited by Ms. Logic
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If you imagine two rotary dials of the 12 numbers, one inside the other - there are 12 combinations of numbers. 6 will have no matches, 3 will have 1, 2 will have 3 but only one combination has 2. Given that the judge said this information would give the game away it must be the combination with only 1 match - Box number 7... Or did I miss something?

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Hello, this is my first stab at answering a riddle, since I am a new member .

But Here is my Logic:

IF >>> "The judge placed 12 boxes on the circumference of a circle. Each box was numbered, the clockwise sequence of numbers on the boxes was, 7, 10, 1, 3, 6, 11, 8, 4, 5, 9, 0 and 2."

AND >>> "man was told that there was a number of coins in each box; again, the clockwise sequence of numbers of coins was 0, 1, 2, 3, 4, 5, 6,7, 8, 9, 10, 12."

So it is safe to say the boxes and # of coins match up sequencially in clockwise order therefore :

7, 10, 1, 3, 6, 11, 8, 4, 5, 9, 0, 2

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12

The extra information the judge told him was just that...extra. Which is why it took the criminal only a few seconds to determine it was box number 7 with 0 coins.

Yes quite sneaky use of language - I get the same answer a different way (but yours is much simpler!)

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