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Puzzle thread May 3, 2011 
Tue, 03 May 2011 17:11 

Ron   Commander Forum Administrator Stars! AutoHost Administrator  Messages: 1232
Registered: October 2002 Location: Collegedale, TN  

It's been 6 years since I've done a puzzle thread.
Here goes. 24 hour time limit, PM me your answers. If you answer 5 questions correctly, you get 1 chance to be the Puzzle Master. If you get all 6 questions correct, you get 2 chances.
The thread will be locked until then.
1. Four chess players, Fred, Stan, Dan, and Steve competed in a tournament. At the end of the tournament, they said the following:
Fred: "I did not win 1st or 4th place."
Steve:"I got 4th place."
Stan: "I did not get 4th place."
Dan: "I won 1st place."
One, and only one of the chess players is not telling the truth. Who won the tournament? How can you tell?
2. The cost of 175 pens is greater than that of 125 pencils, but less than that of 126 pencils. The cost of one pen is a whole number of cents, as is the cost of one pencil. If you wanted to buy 1 pencil and 3 pens, would 100 cents be enough? (Show your work.)
3. What is the highest number of pawns that can be placed on a chess board so that no four pawns are in a line? Lines to avoid are verticals, horizontals, and all types of diagonal. No pawn may be isolated, all pawns must be a neighbor with at least one other pawn either vertically or horizontally. (use the CODE tag and Courier font to diagram your answer)
4. Which number is the odd one out and why?
3628, 2426, 4146, 1448
5. The diagram below features 4 houses, labeled C, X, Y, and Z. One of the houses, C, is located at the center of a circle, and the other 3 houses, X, Y, and Z are somewhere on the circumference. There are paths connecting the various houses as shown. A member of family Y decides to take a walk starting from his house going clockwise around the circular path. Meanwhile, another member of family Y walks along the straight path, visiting houses X, C, and Z in order, but not stopping, before returning home by the direct ZY path.
Assuming that the two members of family Y walk at the exact same rate, who arrives home first?
...
Ron Miller
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Re: Puzzle thread May 3, 2011 
Thu, 05 May 2011 10:16 

Ron   Commander Forum Administrator Stars! AutoHost Administrator  Messages: 1232
Registered: October 2002 Location: Collegedale, TN  

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...
[/FONT]
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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Re: Puzzle thread May 3, 2011 
Thu, 05 May 2011 13:06 


darn.. dunno how I missed this.
When is the next one coming out? I would like to try my hand* too.
*  Brain
[Updated on: Thu, 05 May 2011 13:06]
I know my minefields.. but I'm a chaff sweeper.
I used to curse when I got stuck in traffic... till I realised I AM traffic.Report message to a moderator


   
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