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The Magic Cafe Forum Index » » Puzzle me this... » » The tower (0 Likes) Printer Friendly Version

Nir Dahan
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Munich, Germany
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This one is relatively easy yet fun. You can find it on the web, but for your convenience I copy it here with some clarifications.


the tower
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Two wise men were captured by a tyrant king. They were locked up in two separate cells in a tower in solitary confinement.

One of the cells pointed Eastwards and from there you could see half of the kingdom. The other pointed Westwards and you could see the other half. So, from their cells, the two wise men could see all the cities of the kingdom, but none of them was visible to both of them.

To prove their intelligence the tyrant told them the cities in his Kingdom were either 10 or 13. If any of them was able to guess correctly how many there were he would free them. A wrong answer would mean instant execution. Every evening a jailer would visit them, provide them with food and they could tell him the answer.

On the fifth evening both men were freed.


What logic reasoning did they follow to solve the problem? How many cities are there and how many did each man see?

clarifications
--------------
0) the interest of both men is to be freed as fast as possible

1) The correct number of cities in the whole kingdom is either 10 or 13 (one or the other) so the wise men have to determine WHICH is the correct choice between those two.


2) Each of the wise men doesn’t necessarily see at least one city. (0,10) and (0,13) should be contemplated.


3) None of the cities is on the border between the two views and visible to both men. In other words, each city is wholly in view of EITHER one man or the other but NOT both.


4) No other conversations are maintained with the jailer until telling him the correct answer. No conversations take place between the wise men since they are in solitary confinement. Giving the correct answer to the jailer by ANY of the wise men means freedom to BOTH of the wise men.


5) The men have no way to communicate with each other.

6) The expression ‘half of the kingdom’ is literal, and refers to the area/expanse of land. It doesn´t refer to ‘half of the cities’.
the Sponge
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Atlanta
2479 Posts

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I'm going to guess they count the shadows of the other cities as the sun rises/sets and adds that to what they see?

.....

I just looked online, but I don't understand. Mainly because of this statement of the riddle: "A wrong answer would mean instant execution."
Nir Dahan
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Munich, Germany
1390 Posts

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No shadows involved...
The Mighty Fool
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I feel like a big-top tent having
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Okay, after day 1 we know that there isn't a 0-13 combo, because that would result in freedom

If either man sees more than 10 cities, he would immediately know it was 13, and since it took 5 days, neither man saw more than 10
Everybody wants to beleive.....we just help them along.
sourcerer
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Netherlands
175 Posts

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So we also know that none is seeing 1 city, because if he did he'd know (after day one) the other would have to see 9, as 12 had already been ruled out after day one. Since it took 5 days, 1 is elimated.

By extension we know one can't see 2. as 11 had been ruled out as well the day before.

If one sees 3 however he can't know what the other sees, 3 or 7. 3 is still in the running.

So after day 2, we also know that neither saw 1 or 2.......I think?

Kaj
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