Thursday, July 7, 2011

Rigged card game solutions

I am considering reducing the rate of puzzles on this blog.  I haven't been inspired to write many lately.

See the original puzzle

The three triplets are like rock paper and scissors.  If you pick the rock triplet, I'll pick the paper triplet.  If you pick paper, I'll pick scissors.  And so on.  The hard part is figuring out what card combinations will create the rock-paper-scissors structure.

Rock: 3, 4, 8
Paper: 1, 5, 9
Scissors: 2, 6, 7

If I pick the right one, then I have a 5/9 chance of beating you.

How did I get those numbers, you ask?  Each triplet contains a card from the set {1, 2, 3}, from {4, 5, 6}, and {7, 8, 9}.  If I pick a number from {1, 2, 3} and you pick one from {4, 5, 6}, then it's a lost cause for me.  But if we both pick one from the same set, notice that I will win 2/3 of the time.