I recently came across another interesting puzzle that goes like this:
During a game show, the host who has 4 red stamps and 4 blue stamps has placed three contestants (A, B, C) in a closed room. The host places 2 stamps on each of the contestant’s forehead in such a way that each contestant can only see the other stamps, but not his own. The remaining unused 2 stamps are thrown away and the colors are unknown to the contestants. It is known that all three contestants are superb and honest logician. The host then asks each contestant to see if he figures out the colors of the stamps on his forehead. The host continues asking the same question to each contestant until one of them knows the correct colors of stamps on his forehead:
A: “I don’t know”
B: “I don’t know”
C: “I don’t know”
A: “I don’t know”
B: “I know!”
What are the colors of B’s stamps?
P.S.: You guys know the drill, we need to deduce the answer based solely on the known facts and the above conversations. No smart moves like using hands to grab the stamps or something of that sort.
Posted by Felix Halim on October 27, 2010 at 3:11 am
1 red and 1 blue >:)
First, we list down all possible configurations.
A configuration is represented as 3 integers corresponds to the stamps on A,B,C’s heads.
The integer is:
0 if both stamps are red
1 if both stamps are blue
2 if the stamps is mixed (1 red and 1 blue)
So, a configuration “012″ means
A has two red stamps
B has two blue stamps
C has 1 red stamp and 1 blue stamp
Here is all possible configuration in the beginning:
001
010
011
012
021
022
100
101
102
110
120
122
201
202
210
212
220
221
222
Now, A says “I don’t know”. This means the configuration has to be ambiguous according to A.
Meaning that when A looks at the other person stamps, A can have more than 1 possible configuration.
So, we remove the configurations that are unique to A, which are: 100 and 011.
The updated possible configurations:
001
010
012
021
022
101
102
110
120
122
201
202
210
212
220
221
222
Now, B says “I don’t know”. Again, we need to remove configurations that are unique in B perspective (otherwise, B can answer it).
The unique configurations to B are: 010 and 101.
The updated possible configurations:
001
012
021
022
102
110
120
122
201
202
210
212
220
221
222
Now, C says “I don’t know”. So, we need to remove: 001, 012, 102, and 110.
The updated possible configurations:
021
022
120
122
201
202
210
212
220
221
222
Now, A says “I don’t know”. So, we remove: 201, 202, 210, and 212.
The updated possible configurations:
021
022
120
122
220
221
222
Obviously, at this point, B can answer that his stamps is mixed: 1 red and 1 blue.
QED.
Posted by turuthok on October 27, 2010 at 5:40 am
Exactly, Felix … thanks for stopping by. BTW, I need a copy of your book
… congrats and great job.