Home » General Chat » Circular File » Puzzle thread May 3, 2011
| Re: Puzzle thread May 3, 2011 |
Thu, 05 May 2011 10:16   |
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 Ron |
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Ok, here we go. Only 2 users submitted answers for this Puzzle Thread, Gible and Azrael. Technically, they only got 4 correct answers each, but I gave them each #4 as each of them submitted multiple possible answers and reasoning to support each answer for #4.
Here are the answers.
1. The winner was Stan, and Dan was lying. With only Dan lying, Fred, Dan, and Steve couldn't have won. All other possibilities don't work in one way or the other.
2. Let the cost of one pen be D cents and the cost of one pencil be C cents. Therefore, 125C < 175D < 126C. This in turn means that 5C < 7D and 25D < 18C, so that 5C + 1 <= 7D and 25D <= 18C - 1. If we multiply these two inequities by 25 and 7 respectively, we obtain 125C + 25 <= 175D <= 126C - 7. This implies that 125C + 32 <= 126C and C >= 32. Now 7D >= 5C + 1 >= 161, or D >= 23. So C + 3D >= 32 + 3(23) = 101 cents, which means that 100 cents is not enough to buy one pencil and 3 pens.
3. 15 pawns can be placed on a chess board so that no more than 3 are in a line (horizontal, vertical, or diagonal). All pawns must have at least one neighbor next to it either horizontally or vertically.
[FONT=Courier]
.......
ppp....
..ppp..
....ppp
.p.pp..
.ppp...
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4. This question was in the Mensa section. Since both users gave multiple alternate answers and reasons for each of the 4 numbers I gave both of them this one free.
The answer I was looking for was:
4146: In all the others, AxC=B and B+C=D.
For example:
3628
ABCD
5. Note that the distances XY and YZ must each be less than the diameter of the circle. Also, segments XC and CZ must sum to precisely the diameter of the circle, because each one of these two segments is a radius.
Therefore, the sum of all four of these segments must be less than three times the diameter of the circle. But the circumference equals pi times the diameter, and pi is greater than 3, so the family member who walks along the straight paths arrives home first.
6.
...
[Updated on: Thu, 05 May 2011 10:18]
Ron Miller
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Puzzle thread May 3, 2011
By: Ron on Tue, 03 May 2011 17:11 |
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Re: Puzzle thread May 3, 2011
By: Ron on Wed, 04 May 2011 21:46 |
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Re: Puzzle thread May 3, 2011
By: Ron on Thu, 05 May 2011 10:16 |
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Re: Puzzle thread May 3, 2011
By: Azrael on Thu, 05 May 2011 10:44 |
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Re: Puzzle thread May 3, 2011
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Re: Puzzle thread May 3, 2011
By: Azrael on Thu, 05 May 2011 11:41 |
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Re: Puzzle thread May 3, 2011
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Re: Puzzle thread May 3, 2011
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Re: Puzzle thread May 3, 2011
By: Azrael on Thu, 05 May 2011 12:32 |
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Re: Puzzle thread May 3, 2011
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Re: Puzzle thread May 3, 2011
By: nmid on Thu, 05 May 2011 13:06 |
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Re: Puzzle thread May 3, 2011
By: dennis on Thu, 05 May 2011 15:05 |
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Re: Puzzle thread May 3, 2011
By: Ron on Thu, 05 May 2011 16:09 |
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Re: Puzzle thread May 3, 2011
By: dennis on Tue, 07 June 2011 15:35 |
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