From: laurab@dip.cs.wisc.edu (Laura Berg)
Newsgroups: rec.puzzles
Subject: Re: 3 puzzles
Date: 23 Jul 92 20:35:41 GMT
Article-I.D.: cs.laurab.711923741
Distribution: rec.puzzles
Organization: U of Wisconsin CS Dept

markc@eomer.hw.stratus.com (Mark Christensen) writes:

>Here are three puzzles:

>[1]
>	What is the first number, when spelled out (e.g. O-N-E) is
>in alphabetical order?
forty, not eight.  (sing it with me now: a b c d e f g h i j k l....  See the
i after the g and h?)

>[2]
>	A man walks into a hardware store and goes to the clerk
>and says he wants an item.  "I'll take one", he says. The clerk
>says that that will be $1.  "How much for 12", the man asks?
>That will be $2 the clerk respond.  "OK, I'll take 125", the
>man says, to which the clerk responds, "That will be $3 please".
>What is the item that the man is buying.
sticker numbers (like for a mailbox)

>[3]
>  A king decided to have some fun one night and summoned three
>prisoners to be brought up from the dungeon.  They were brought
>before him and the king made an offer:

>"I have a box with five hats in it", he started.  "There are
>three red hats and two white hats. You will be blindfolded
>and asked to take one hat from the box.  At that time, each
>one of you will be unblindfolded and shown the hats of the other
>two prisoners (but not your own).  Then you will be asked to
>identify the color of your hat.  If you are wrong, your head
>will get chopped off.  If you don't know, back to the
>dungeons with you.  If you guess correctly, I will set you free."

>(Assume these prisoners are somewhat intelligent and give
>correct answers.)

>The first prisoner took his blindfold off, looked at the other
>two prisoner's hats and said, "I can't tell what color my hat is".

>The second prisoner also responded as the first prisoner.

>The third prisoner, who was blind, said, "I know exactly
>what color my hat is".

>What color is the third prisoner's hat and why can't it be the
>opposite color?

At first there are seven possiblities:

Prisoner #    1      2      3
------------------------------
color of hat: R      R      R        (1)
	      R      R      W        (2)
              R      W      R        (3)
              R      W      W        (4)
    	      W      R      R        (5)
              W      W      R        (6)
              W      R      W        (7)
(no more than 2 hats may be white)
										By the statement made by the first prisoner, we can rule out combination (4),
since by seeing two whites, prisoner #1 would know his hat was red.

By the statement of the second prisoner, we can rule out combination (7) for
the same reason (4) was ruled out.

By the statement made by the second prisoner, we can rule out combination (2).
This is a little harder to see, and assumes that prisoner #2 heard what
prisoner #1 said.  In combination (2), prisoner #2 would know that his hat was
red, because the only way for prisoner #1 not to know the color of his hat
was to have either #2 or #3 have a red hat (or both).  So, by seeing the color
of #3's hat being white, he would know his had would have to be red.

That leaves combinations (1), (3), (5), and (6), all of which have #3 wearing
a red hat.