# The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

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mathgrant
A very tilted cell member

 Posted: Wed Feb 13, 2002 8:43 pm    Post subject: 1 I had a dream that I was playing the Pokemon Card Game with a statistician. He left the room while we were playing, and I was losing. I was tempted to look at his cards, but decided to do something with my own cards instead. I had Weezing, Squirtle, and Pikachu on my Bench. I shuffled them thoroughly (tough to do when you only have three cards!) and chose one at random. Then I got out a sheet of paper with the numbers 1 through 6 and wrote next to the 1 the name of the Pokemon I chose. I did this five more times, writing each new Pokemon next to the next number. Now, as we all know here at the GL, that would be a great technique for generating a random number between 1 and 729, but that wasn't what I was interested in. I then rolled an evenly weighted 6 sided die and whatever Pokemon was next to that number, that would be the Pokemon I would use after my current one was Knocked Out. But before I could see the number, I woke up! Oh no! I thought. Which one was I about to choose? Well, I couldn't be totally sure, I never saw the number, best I could do was remember what Pokemon appeared in each slot on the paper and use simple statistics to estimate what could've happened. But oh no! I couldn't remember anything! Except that each Pokemon was in at least one of the six slots. And Weezing appeared at least twice. But that was it. I then proceeded to calculate, with only that information, the probability that I would've chosen Pikachu. I went back to sleep and had the dream again. The statistician seemed to be a better psychic than Miss Cleo; not only did he know what I did when he was away, he even knew what had happened when I woke up. I told him the probability I had calculated, and he was impressed at my statistics skills. He then resigned the Pokemon game and started having a talk with me about statistics instead. That was the best dream I'd ever had in my life. Now, two questions: 1. What was the probability of me choosing Pikachu? 2. Hidden somewhere in this problem there is a reference to a famous graph theory chestnut. What is it? [This message has been edited by mathgrant (edited 02-13-2002 03:56 PM).]
ZutAlors!
Daedalian Member

 Posted: Wed Feb 13, 2002 9:26 pm    Post subject: 2 1. How about 15/54?
Chuck
Daedalian Member

 Posted: Wed Feb 13, 2002 10:08 pm    Post subject: 3 1. Maybe 7/24?
mathgrant
A very tilted cell member

 Posted: Thu Feb 14, 2002 1:03 am    Post subject: 4 Number 1 was answered correctly by: Chuck
Chuck
Daedalian Member

 Posted: Thu Feb 14, 2002 1:21 am    Post subject: 5 Graph Theory has chestnuts? That's hard to believe.
mathgrant
A very tilted cell member

 Posted: Thu Feb 14, 2002 5:08 am    Post subject: 6 But it does. Can you find one?
ZutAlors!
Daedalian Member

 Posted: Thu Feb 14, 2002 12:41 pm    Post subject: 7 Ok, what am I missing? Step 1: "...each Pokemon was in at least one of the six slots. And Weezing appeared at least twice" = without loss of generality, assume slots 1-4 are WWSP. Step 2: Slots 5 and 6 are equally likely to be any of the Pokemon. Therefore, there are nine possible combinations, all equally likely: WWSPWW, WWSPWS, WWSPWP, WWSPSW, WWSPSS, WWSPSP, WWSPPW, WWSPPS, and WWSPPP. Step 3: Given any of the above combinations, the probablity of choosing Pikachu is simply (#P/6), which is, in order, 1/6, 1/6, 2/6, 1/6, 1/6, 2/6, 2/6, 2/6, and 3/6. Step 4: Total probability is then (1/9)*(1/6 + 1/6 + 2/6 + 1/6 + 1/6 + 2/6 + 2/6 + 2/6 + 3/6) = 15/54 = 5/18
ralphmerridew
Daedalian Member

 Posted: Thu Feb 14, 2002 1:04 pm    Post subject: 8 I figured out what the chestnut is, and I will say that it involves the three pokemon cards. Figuring out the chestnut will require some knowledge of pokemon.
extropalopakettle
No offense, but....

 Posted: Thu Feb 14, 2002 1:22 pm    Post subject: 9 ZutAlors!, I haven't done the math, but I'm suspicious of step 2. Let's say I perform a large number of trilas where I randomly fill the 6 slots with W's, S's and P's. I only consider those trials that have at least 2 W's and at least 1 each of S and P - all other trials are discarded. Now remove 2 W's and 1 S and 1 P. There are nine possible combinations for the remaining two cards - WW, WS, WP, SW, SS, SP, PW, PS, PP. But I'm not sure all are equally likely. The reasoning being along the same lines as, if I flip two coins, and at least one is heads, the probability of two heads is 1/3 (not 1/2).
tigg
Daedalian Member

 Posted: Thu Feb 14, 2002 1:40 pm    Post subject: 10 I got the exact same answer you did, Zut. Did we make a bad assumption?
tigg
Daedalian Member

 Posted: Thu Feb 14, 2002 1:51 pm    Post subject: 11 I'm starting to think your step 1 was our bad assumption. Looks like there IS a loss of generality. extro's example of the two coins makes a good point.
ZutAlors!
Daedalian Member

 Posted: Thu Feb 14, 2002 4:14 pm    Post subject: 12 Ah, OK. This is akin to the famous "A couple have two children; at least one daughter; what are the chances they also have a son?" I should have realized it wasn't as easy as I thought.
mathgrant
A very tilted cell member

 Posted: Thu Feb 14, 2002 10:08 pm    Post subject: 13 So, what's the graph theory chestnut I'm looking for?
mole
Subterranean Member

 Posted: Fri Feb 15, 2002 1:04 am    Post subject: 14 The one with the three houses and the gas and water and stuff? That's the only one that comes to mind - can't see it here yet though
mith
Pitbull of Truth

 Posted: Fri Feb 15, 2002 2:50 am    Post subject: 15 weezing=gas, squirtle=water, pikachu=electricity
mole
Subterranean Member

 Posted: Fri Feb 15, 2002 2:53 am    Post subject: 16 Gas isn't a type of pokémon, is it? Maybe all these houses want to be connected to the poison supply...
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