Question

3 people are given a chance to win 20 dollars.

They are lined up in a row so that one is in front of the other. The last person can see the front two, and the middle can see the only the front one, and the front person can see noone.

C -> B -> A

They are shown a box that has 5 cards in it, a king of spades, a queen of hearts, a 2 of spades, a 4 of diamonds, and an 8 of clubs.

A card is taken from the box and pinned to the back of the shirt of each person.

If they can determine logically, what color the card is on their own back, they will win the prize.

Who wins the prize and .........

Answer 1

Who wins the prize and what color was their card?

Answer 2

I remember something similar to this......

Answer 3

me too, which is why i changed it so people couldnt cheat too much lol

Answer 4

So... what does each individual know?

Answer 5

each individual can see the card on the back of the person or persons in front of them

Answer 6

Let's say I am the dude in the back... then: I know what color the card on the middle dude is, and I know what color the card on the front dude is.

Answer 7

correct

Answer 8

I (dude C) know that there are only 5 cards, 3 of them black, and 2 of them red.

Answer 9

So, if the 2 front dudes both have black cards, I scream "I've got a red card! you guys both have black cards!" and we all claim $20 each.

Answer 10

oops, I mean the other way around: I see dudes A and B have red cards, so I scream" I've got a black card!, you two both have red cards!"

Answer 11

or... can they each communicate by yelling at each other?

Answer 12

there is only one prize to win, so they work it out in secret .. no talking to the others

Answer 13

oh...

Answer 14

So yeah, if I were dude C and I saw that both dudes A and B have red cards behind them, I think 'I must have a red one' and claim my $20

Answer 15

I mean 'I must have a black one'

Answer 16

that would be logical if the front 2 had reds, yes.

Answer 17

spose C doesnt say anything, what does that lead B to think?

Answer 18

I thought none of them could hear each other walk away or speak

Answer 19

i guess i should include a time limit for clarity eh ....

and at the last second one of them answers .... that sort of thing

Answer 20

but if I were dude B, and I can still sense dude C behind me, I might think 'if we both had red cards, then that lucky guy would have left already. Therefore either dude A or dude B (me) has a black card.' and then I see if dude A has a black or red card

Answer 21

so if C saw 2 reds, hed now right away that he had a black, but C says nothing .....

Answer 22

so the final answer would be that they all know?

Answer 23

only one figures it out in the end ...

Answer 24

:-( so perhaps only the middle guy would figure out

Answer 25

the possibilities are set up as this:

C B A
------
b b b
b r r ; not it since C would speak up first
r b r
r r b
b b r
b r b
r b b


C B A
- ----
b b b

r b r
r r b
b b r
b r b
r b b

notice from whats left that B cant decide either; which means that there is only one possible solution for A

Answer 26

That's a nice way to approach it.

Answer 27

A has a black card

Answer 28

so if nobody speaks up, A has a black one?

Answer 29

yep

Answer 30

B A
----
b b
b r
b r
b b
r b
r b

these are the options for B sees A

Answer 31

I wish JamesJ came over here and gave us some really convincing inductive proof or something... :(

Answer 32

If A is red, B is black or red

If A is black, B is black or red

lets delete the uncertainties: br bb

B A
----
r b
r b

A has to be black

Answer 33

At the last second, if guy C speaks up and says "I see a black card"... then what?

Answer 34

then its a different universe and they are playing a different game by different rules ....

Answer 35

:-D so the full proof is:

Nobody speaks up. Therefore A has to be black.

Answer 36

since if people spoke up then they would know they had reds on their back?

Answer 37

correct; and i had a misthought in there; should go like this,

If A is red, B is black

If A is black, B is black or red

Answer 38

If they spoke up then they would know what color they had, since they dont speak up; that plays into the reasoning