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Aug-17-06
 | | OhioChessFan: *** Hints to Stumper of August 17 ***
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1. The answer is absolute, ie, you will not say "I think that the answer is __". You will be 100% certain. 2. The answer is the last member of the set. |
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| Aug-17-06 | | ughaibu: No idea.
http://www.research.att.com/~njas/s... |
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Aug-18-06
| | OhioChessFan: ROTF <ughaibu> that's a unique way to try to solve the problem. ** Another big hint to August 17 problem **
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Don't bother using math to solve it. |
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| Aug-18-06 | | ughaibu: Seventeen. |
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Aug-18-06
| | OhioChessFan: A round of applause to <ughaibu> |
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Aug-20-06
| | OhioChessFan: *** Answer to Stumper of August 17 **
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As <ughaibu> posted, the answer is seveneteen. The series is a descending list of integers with 9 letters. |
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Aug-20-06
| | OhioChessFan: Migrating birds typically fly in a V shaped pattern. Why is one side of the V usually longer? |
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| Aug-20-06 | | Rocafella: The ones with the bigger birds :o| |
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Aug-20-06
| | OhioChessFan: That's an alternate answer, <Rocafella> but acceptable. I was looking for "One side has more birds." :) |
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Aug-20-06
| | OhioChessFan: This is a very hard word puzzle. I gave up after spending 5 minutes on it and don't know if I'd have found it in an hour. What's the next word in this series?
Earn
Male
Ride
Seal
Bowl
Nags
Tear
Laos
Tern
Sail
Sick
Rose
Char
Is the next word:
Time, Clam, Lobe, or Pole?
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Aug-20-06
| | OhioChessFan: ** Hints to August 20 Stumper **
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1. I changed one of the words in the list for clarification purposes, so don't spend much time trying to find some pattern of letters between words. 2. Per the above, the first 3 words in the list could be: West, Late, Rate. 3. Per the above, the last word (the answer) could also be: Toes, Seed, or Mica. |
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Aug-26-06
| | OhioChessFan: ** Answer to August 20 Stumper **
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Each of the words can form a five-letter anagram when successive letters of the alphabet are added at the beginning: earn + a = arena
male + b = blame
ride + c = cider
seal + d = deals
bowl + e = elbow
nags + f = fangs
tear + g = great
laos + h = halos
tern + i = inert
sail + j = jails
sick + k = kicks
rose + l = loser
char + m = march
The only word out of the four choices that will form an anagram when an "n" is added is lobe (noble). |
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Aug-27-06
 | | Sneaky: I hand you a trick coin which I explain is not a fair coin. It has a bias. I won't tell you if it's biased toward heads or tails, nor will I tell you how much the bias is. Your job is to come up with a perfectly fair 50% random decision using this unfair coin. (There are multiple solutions but one of them strikes me as being the most simple and elegant.) |
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Aug-27-06
| | Sneaky: <OhioChessFan> That's wicked hard. |
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| Aug-28-06 | | centrumspits: I just use the coin, Sneaky. Since I do not know which side is biassed I have a 50%-50% chance to allocate either choice A or choice B to the biassed side. Hence tossing the coin will give me a perfectly fair 50% random decision. But I am curious as to the other solutions! |
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Aug-28-06
| | OhioChessFan: <Centrumspits> I had some similar thoughts, but none captured the point of the problem. ie, set the coin on heads, and turn it over or not based on a person's birthdate, number of letters in their name, etc. But those bypass the point of the coin in the first place. I'm leaning toward the old kid's method of letting the other person offer 2 options and I get to choose one. For example, after observation, it seems the heads comes up 55% of the time. Therefore, I am offered the option of:
1. Choosing option A, wherein I win if heads comes up 55 times before tails comes up 45 times.
2. Choosing option B, wherein I win if tails comes up 45 times before heads comes up 55 times. I think that works, although I think it possible that the idea of observation may not be within the spirit of the puzzle. |
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| Aug-28-06 | | zarra: Centrumspits is right. I just pick heads or tails and toss the coin. The bias of the coin is balanced out by my random choice of heads or tails. (Since I don't know which way the coin is biased, my choice will be perfectly random.) |
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Aug-28-06
| | Sneaky: The idea of using the fact that you don't know which way it's biased is very good. I hadn't even have thought of that. I certainly can't say your answer is incorrect, but it's not in the spirit of the intended solution. Let me rephrase the question so that you can't use this technique. Suppose instead I tell you that I have three coins in my pocket, two are biased towards heads, and one is biased towards tails. I give you one of these coins at random. OK, *now* how do you use it to make a fair 50/50 decision? |
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Aug-28-06
| | Sneaky: I guess the weakness in your solution--if there is any--is that you can only do it once. After the first flip, say it comes up heads, you now have a little bit of information about the bias (e.g. if you were forced to guess, you'd guess it was biased for heads). Of course I didn't say you had to make a series of decisions, but that's the main idea. OhioChessFan had a pretty good idea, and I think it would work, but you can really cut a lot of the fat out of his solution if you think about it. Speaking of coin flipping, suppose you're talking on the phone with a friend and you agree to wager him $1000 on the flip of a coin. He says, "OK I'll flip the coin and you tell me which side it landed on, then I'll tell you if you're right." You say "Hey I didn't just fall of a turnip truck, how do I know you won't lie?" How can you flip a coin over a telephone without the need for trust? I'm not going to make this a puzzle, I'll just tell one possible answer. Spoiler below ... . . . . . How to flip a coin over the telephone
You use a little cryptology 101 to help you. Your friend flips the coin and then picks two really big prime numbers that he generates himself. The primes that he generates have a property dependent upon the coin flip. For example, if it comes up heads then he makes sure that one of the primes contains a 7 in the 13th digit, but if it comes up tails neither prime will have this property. He then multiplies those primes together to get a positively gigantic number and he gives this gigantic number to you. THEN you make your guess. He tells you if you are right or wrong, and to prove that he isn't lying he then reports to you the two prime numbers. This is an effective solution because multiplying the primes together is an "intractable" operation--i.e. given the solution it is very computationally expensive to factor it back into the primes, but given the primes its trivial to multiply them to get the gigantic number. You could cheat him if you just had some "instant factoring machine" but to date nobody has ever designed such a device, and so this is considered a fairly cheat-proof method. |
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| Aug-28-06 | | ganstaman: There should be several answers. I can't seem to find some number of flippings where the results aree 50/50 regardless of the odds of each flip. However, the coin still provides some 50% odds. For example, flip the coin until you get a tails. Then flip the coin until you get a heads and count the number of flips this takes. Do it again. If the first count if higher than the second count, go with choice A. If the second count is higher than the first, go with choice B. If the counts are the same, repeat. Or, flip the coin twice. If it comes out HT, go with A. If it comes out TH, go with B. If it comes out HH or TT, repeat. I like this option best so far, but I'm not sure if it's what you're looking for. |
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Aug-28-06
| | Sneaky: <Or, flip the coin twice. If it comes out HT, go with A. If it comes out TH, go with B. If it comes out HH or TT, repeat. I like this option best so far, but I'm not sure if it's what you're looking for.> Bingo, that was the answer that I had in mind, but really all of these answers are at least workable. No matter what the bias is, the odds of the "heads-tail" combo is exactly equal to the odds of the "tail-heads" combo, so I can't think of any way that would solve this task with fewer flips. Of course, even then, if it's radically biased to one side it might take you a while to get past all the ties. It's also true you could flip the coin 100 times and count the heads, then flip it another 100 times and count the heads, and see whether you got more heads in trial #1 or trial #2. But that's a lot of work! If it comes out to be a tie you have to start again, oy! A pejorative answer that nobody suggested would be to put the coin in one of your hands, go to your friend and say "Hey buddy, guess which hand has the coin..." ;-) This reminds me a little bit of the old story where the professor asked his physics class to come up with methods to measure the height of a building with a barometer. He got answers like "drop the barometer and time its decent to the ground", and "take some chalk and mark off 'barometer units' up the side of the building", and even "go to the superintendent and tell him that you'll give him a shiny new barometer in if he'd tell you the height of the building." |
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Aug-28-06
| | OhioChessFan: <This reminds me a little bit of the old story where the professor asked his physics class to come up with methods to measure the height of a building with a barometer. He got answers like "drop the barometer and time its decent to the ground", and "take some chalk and mark off 'barometer units' up the side of the building", and even "go to the superintendent and tell him that you'll give him a shiny new barometer in if he'd tell you the height of the building."> <Sneaky> I recall Omni Magazine running one of their puzzle contests. They had one complicated puzzle which posited the solver as a Marine Sergeant. The goal was to use a certain length of rope and a pulley system to get a flag to the top of a certain height flagpole. My favorite answer (which they didn't accept) was the solver who said their answer was to tell the Marines under his command, "Men, get that flag to the top of that flagpole." |
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Sep-02-06
| | Sneaky: Here's a REAL stumper courtesy of David Copperfield. It's a famous stage illusion known in the business simply as "Motorcycle to Girls." http://www.youtube.com/watch?v=xz28...
Nevermind where the girls came from. The real stumper here is ... where did the motorcycle go? I happen to know the secret but I can't give the answer to this one--if I did, I'd ruin it for everybody. I can tell you this, however. If you actually knew how it was done, you could look at this very video and be 100% sure that you cracked the mystery, as all the "clues" to confirm your suspicions are right there before your eyes. No, it's not camera trickery--and yes, that motorcycle is 100% real. (If you do figure it out, and some brainy person here probably will, please have some respect and don't just expose the secret here. If you do you'll ruin the enjoyment of it for others.) |
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Sep-14-06
| | OhioChessFan: <Sneaky> I am sort of close. I need a better computer to be sure of what I think happened. |
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Sep-30-06
| | OhioChessFan: There is only one solution to the equation below, in which each letter stands for a single, unique digit. AB × C.DE = AB + C.DE
What digit does each letter in this equation represent? |
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