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Switch statistics pazzle.

There are 2 sets of 4 switches A,B,C,D for 2 people.  The "second person" can set on any of follows 2 pairs ( AB, BC, CD, AD)  Then "the first" will switch one of the switches on.  If both set on the same switch "the first" loose.
So simple strategy for first person when you set only A and C guarantee you 50% chance.
What will be you odds if you use more then just 2 opposite switches?

Vladimir Sakharuk
Monday, June 2, 2003

I'm not sure I'm clear about the problem. Can you check I've got this right?

The first player turns on one of his switches, A B C or D. The second player does not see what the first player does.The second player then turns on two of his switches, but only four choices are allowed: AB, BC, CD or DA. The first player wins if the switch he turned on is not the same as one of the two switches the second player turns on.

If this is what you meant, then I think the game is one of pure luck. There is a 50% chance that the two players will turn on the same switch, whatever strategy they follow.

David Clayworth
Wednesday, June 18, 2003

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