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Topic: Another hat riddle (Read 847 times) |
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BNC
Uberpuzzler
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Another hat riddle
« on: Mar 3rd, 2003, 2:00am » |
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Three uberpuzzlers participated in the riddle Olympics, and naturally got to the finals. As the three puzzlers are equally smart, and follow the exact same thinking process, they all got the same (highest possible) score at the final stage.
To decide which would win, they were blindfolded, and a hat was placed on each of their heads. They were placed in such a way so that each could see the hats of the other two contestants, but not his own. They were asked the same question:
“On each of the hats you’re wearing there in a natural number. The numbers form an algebraic series. The first to guess the number on his hat would win the Olympics.”
The blindfolds were then removed. One of the contestants saw the numbers 4 and 6 on the other hats. After a while he stood and said: “The number on my hat is ____”
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| « Last Edit: Mar 3rd, 2003, 2:01am by BNC » |
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wolfgang
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Re: Another hat riddle
« Reply #1 on: Mar 3rd, 2003, 11:59am » |
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I'm not completely sure, but I guess 8.
The reasoning being
He could have a 2, 5, or 8.
If he had a 2, 6 would have seen 2,4 and known he couldn't have a 3 because then 4 would have seen 2,3 and known he couldn't have a 1 because 6 would have seen 1,2 and known he had to have a 3.
If he had a 5, 6 would have seen 4,5 and known he couldn't have a 3 because then 5 would have seen 3, 4 and known he couldn't have a 2 because 4 would have seen a 2,3 and known he couldn't have a 1.
But if he had an 8, 4 would have seen 6,8 and quickly ruled out 7 for similar reasons, but would have taken a longer time to rule out 10; and 6 would have seen 4,8, and ruling out 12 would probably take a long time to rule out (it's all making me too dizzy to actually work through it all the way).
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Chronos
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Re: Another hat riddle
« Reply #2 on: Mar 5th, 2003, 9:09pm » |
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It's a shame that I didn't make it to the finals, because I have a faster answer. I would stand up and say "My number is 2. My number is 5. My number is 8." as fast as I could. I can probably talk faster than the other two can metareason, and one of those is, in fact, the correct guess.
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BNC
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Re: Another hat riddle
« Reply #3 on: Mar 5th, 2003, 11:27pm » |
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Yeah, I thought at first to state the question's final sentence as "The first to guess the number on his hat would win the Olympics. Guessing wrong would result in eternal shame"
But then I figured it might confuse, and be considered a "hint".
Oh well. Can't win them all.
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TimMann
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Re: Another hat riddle
« Reply #4 on: Mar 6th, 2003, 10:26pm » |
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I was stumped on this one when I got to the term "algebraic series". From the answers, it looks like you mean what I was taught to call an "arithmetic sequence." Is the term "algebraic series" common?
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| « Last Edit: Mar 6th, 2003, 10:27pm by TimMann » |
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Icarus
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Boldly going where even angels fear to tread.
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Re: Another hat riddle
« Reply #5 on: Mar 7th, 2003, 3:27pm » |
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I too was confused by "algebraic series". This was not a term I had heard of before. A search with Google turned up several references to algebraic series. But it turns out they are much more complicated beasties than the simple arithmetic sequences desired here.
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"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
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Jeremiah Smith
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Re: Another hat riddle
« Reply #6 on: Mar 7th, 2003, 3:50pm » |
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I interpreted "algebraic" as meaning "either arithmetic or geometric".
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