[EdrickV]

Originally posted by Sesquipedalian


Unless the gameshow host would have simply opened the door and granted the prize if you had chosen correctly, in which case you would know you had chosen incorrectly by his giving you a second chance.  But assuming that he would not have done so, then as above, and "Which is better?" is a meaningless question.

If the gameshow host would open your door if you found the prize, and open a door that doesn't have the prize if you didn't find it, then everyone would win. The original phrasing suggests that the host would always open a door that the prize is not behind.

[Sandwich]

M'kay, here goes:

Three men stopped at a hotel one night and went to three seperate rooms. The charge for the rooms was $10 each, so the men paid $30 all told. The next day the desk clerk found out that the rooms could be renter for $25, instead of the $30 paid. Accordingly, he gave the bellboy the rebate to take to the three men.

As it happened, the bellboy was not entirely honest, so he gave each man $1 and kept $2 for himself.

Now, each man, after receiving the $1 rebate, paid only $9 for is room. That made $27 for all three. The bellboy kept the other $2, which makes $29. What happened to the other dollar?

[Kazashi]

There is no missing dollar. Start off with $10 times 3, making $30. The clerk sends up a $5 rebate, supposed to make the end total $25. The three men each get $1, making a total of $3, add to that the extra $2 stolen, and you get $5 - the total of the rebate.

[Tiara]

Originally posted by Sandwich
M'kay, here goes:

Three men stopped at a hotel one night and went to three seperate rooms. The charge for the rooms was $10 each, so the men paid $30 all told. The next day the desk clerk found out that the rooms could be renter for $25, instead of the $30 paid. Accordingly, he gave the bellboy the rebate to take to the three men.

As it happened, the bellboy was not entirely honest, so he gave each man $1 and kept $2 for himself.

Now, each man, after receiving the $1 rebate, paid only $9 for is room. That made $27 for all three. The bellboy kept the other $2, which makes $29. What happened to the other dollar?

10+10+10=30

5 refund = 25

9+9+9=27

27-25=2

So, no missing dollar.

[ZylonBane]

Originally posted by Knight Templar
so i was right?

Yup.

Although you get points taken away for having a semicolon in your sig where you should have a colon.

[Sandwich]

MEh - that one was too easy. So's this one:

A man went to town one day with $5 in his pocket, but returned in the evening with $15.

He bought a hat at the men's furnishings store and some meat at the meat market. Then he had his eyes tested for glasses. Now, this man got paid every Thursday by check, and the banks in town are open on Tuesday, Friday an Saturday only. The eye doctor does not keep his office open on Saturday, and the meat market is not open on Thursday or Friday. What day did the man go to town?

[Tiara]

Originally posted by Sandwich
MEh - that one was too easy. So's this one:

A man went to town one day with $5 in his pocket, but returned in the evening with $15.

He bought a hat at the men's furnishings store and some meat at the meat market. Then he had his eyes tested for glasses. Now, this man got paid every Thursday by check, and the banks in town are open on Tuesday, Friday an Saturday only. The eye doctor does not keep his office open on Saturday, and the meat market is not open on Thursday or Friday. What day did the man go to town?

Eh, he still had money on his account on tuesday from last thursday. He withdrew some that day and did these things on the same day.

[Knight Templar]

Although you get points taken away for having a semicolon in your sig where you should have a colon.

ouch

I expected that from Sesqky, but not you.

meh, i was going to make it shorter sometime soon anyways

[EdrickV]

Originally posted by Tiara


Eh, he still had money on his account on tuesday from last thursday. He withdrew some that day and did these things on the same day.

Actually, he probably cashed last Thursday's check, (It never said he didn't have a check with him.) but he did go on Tuesday.

[Sesquipedalian]

Mrs. Harrison has 6 lovely hats, 3 blue, 2 yellow and one pink. Alice, Betty, Cindy and Debbie are lined up as shown below. Mrs. Harrison puts the hats on them so they will not see what color hat they have on.

Alice->Betty->Cindy->Debbie

Alice can see what color of hats Betty, Cindy and Debbie are wearing, but not her own (since it is on her head).
Betty can see what color of hats Cindy and Debbie are wearing, but neither her own nor Alice's.
Cindy can see what color hat Debbie is wearing, but neither her own nor Betty's nor Alice's.
Debbie can not see any of the hat colors.

Mrs. Harrison ask them what color of the hat they are wearing. Alice said she can not tell. Betty said she can not tell either. Cindy also can not tell. However, Debbie was able to tell what color she was wearing after knowing that everyone else could not tell.

How did Debbie figure out what color she was wearing?

[Sandwich]

Originally posted by Sesquipedalian
Mrs. Harrison has 6 lovely hats, 3 blue, 2 yellow and one pink. Alice, Betty, Cindy and Debbie are lined up as shown below. Mrs. Harrison puts the hats on them so they will not see what color hat they have on.

Alice->Betty->Cindy->Debbie

Alice can see what color of hats Betty, Cindy and Debbie are wearing, but not her own (since it is on her head).
Betty can see what color of hats Cindy and Debbie are wearing, but neither her own nor Alice's.
Cindy can see what color hat Debbie is wearing, but neither her own nor Betty's nor Alice's.
Debbie can not see any of the hat colors.

Mrs. Harrison ask them what color of the hat they are wearing. Alice said she can not tell. Betty said she can not tell either. Cindy also can not tell. However, Debbie was able to tell what color she was wearing after knowing that everyone else could not tell.

How did Debbie figure out what color she was wearing?

Mein Gott!

[Goober5000]

Yeesh.

Hmm hmm... methoughts to check all the combinations...This is of course the brute force, nonintuitive way, but what the heck.

And here they are.  Now the trick is to figure out how to narrow them down.

Code: [Select]

A B C D
-------
B B B Y
B B Y B
B Y B B
Y B B B

B B B P
B B P B
B P B B
P B B B

B B Y P
B Y P B
Y P B B

B Y B P
Y B P B

Y B B P

B B P Y
B P Y B
P Y B B

B P B Y
P B Y B

P B B Y

B B Y Y
B Y Y B
Y Y B B

B Y B Y
Y B Y B

Y B B Y

Y Y P B
Y P Y B
P Y Y B

Y Y B P
Y P B Y
P Y B Y

Y B Y P
Y B P Y
P B Y Y

B Y Y P
B Y P Y
B P Y Y

[Goober5000]

Got it - Debbie was wearing pink.

My solution method: Group all the duplicates together until you run out of duplicates.  Messy, but it works.  (I was feeling too tired to put much effort into thinking rationally about it.)  Now I want to know what the intuitive solution is.

[Ulala]

*scratches head* My riddles are Fenrises against Colossuses!

[Sesquipedalian]

Originally posted by Goober5000
Got it - Debbie was wearing pink.

My solution method: Group all the duplicates together until you run out of duplicates.  Messy, but it works.  (I was feeling too tired to put much effort into thinking rationally about it.)  Now I want to know what the intuitive solution is.

*Goober5000 looks under the cap liner to see if he won the prize*

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| Sorry.  Please play again. |
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[Vortex]

I think it's Blue, here's my reasoning:

First start with Alice, since she doesn't know what she's wearing, there has to be at least two distinct choices out of the hats she can choose. Since three people have taken hats, there are three left to choose from. Possiblities are:

Alice

YYP
BYP
BBY

Now moving on to Betty, since she doesn't know what she's wearing, not only does there have to be at least two distinct choices, but no matter what color hat she chooses, the remaining three unchosen hats have to match the above condition for Alice. These leave:

Betty

BBYP
YYBP
BBYY

To clarify, for the BBYP possibility, if she has a blue hat, then the remaining hats are BYP, similarly if she chooses a yellow or pink hat, the remaining hats are BBP and BBY respectively.

Now moving on to Cindy, again since she doesn't know what she's wearing, not only does there have to be at least two distinct choices, but no matter what color hat she chooses, the remaining four unchosen hats have to match the above condition for Betty (which in turn will match the condition for Alice). All that is left is:

BBYYP

If blue is taken, BYYP is left, if yellow is taken, BBYP is left, if pink is taken, BBYY is left.

Finally, the only remaining hat is blue, which belongs to Debbie.

[Vortex]

How in the world did Debbie figure all that out in her head just like that??...

[Goober5000]

Originally posted by Sesquipedalian

*Goober5000 looks under the cap liner to see if he won the prize*

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| Sorry.  Please play again. |
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Huh?  I was positive that was right.  Unless I missed a combination or so. :doh:

[Sesquipedalian]

Originally posted by Vortex
I think it's Blue, here's my reasoning:

We have a winner!  Your logic reasoned in the opposite (and harder) direction from what I did to solve that puzzle, but it worked.

My easy explanation for anyone interested:

1) If none of Betty, Cindy, or Debbie were wearing a blue hat, Alice would know she must be wearing a blue, but she does not know, so one of the other three must be.  

2) Therefore, Betty knows that at least one among herself and the girls in front of her are wearing blue.  If neither of the girls in front of her were wearing blue, she would know she was wearing blue, but she does not know, so at least one of Cindy and Debbie must be wearing blue.

3) Therefore, Cindy knows that if Debbie is not wearing blue that she must be, but she does not know what she is wearing, so Debbie must be wearing blue.

*Vortex receives a cookie*

[Goober5000]

Aha!  Okay.  A very simple explaination.


Now the only question is where did my combination approach go wrong. But I don't really feel like figuring that out, and I suspect noone else does either.

Any other good brain teasers?