The five owners of Plexus and Co. are voting on a very important decision (Top secret!). Each must vote for or against the decision. They don't necessarily own equal shares of the company, so they don't necessarily have equal voting power. For example, one person might have 5 votes and the other four have 1 vote each. However, it is distributed in a way that a tie is impossible. Obviously, everyone has positive voting power.

There are 2^5=32 different ways that the five people can vote (such as YYNNY, YNNYY, NNNNN, ...). Each way will result in favor or against the decision, depending on how the voting power is distributed.

There are 2^32 different combinations of the 32 outcomes, but not every combination is possible. For example, it is impossible for YYYNN to be in favor of the decision while YYYYN is against the decision, no matter how the voting power is distributed.

Out of the 2^32 different combinations, how many are possible, remembering that combinations where a tie is possible are not allowed?

In Christmas crackers, you sometimes get a set of 6 cards with numbers ranging from 1 to 63 on them, and you have to guess the number thought of by someone by being told what cards it is on - done by looking at the numbers in the top left hand corner and adding them - 1, 2, 4, 8, 16, 32.

So surely using this logic (where each number requires a unique set of cards), with 5 voters their power of voting would be 1, 2, 4, 8 and 16, with no tie possible, as all the numbers preceding number X will equal X-1.

I'm not going to work out how many combinations are possible, I'll leave that for someone else.

Posted by sassy on 2005-01-26 17:34:44