The Current Puzzler:

Three individuals (A, B, and C) decide to dual with pistols until only one is left standing.  Out of fairness, the three decide to take turns shooting.  The person shooting may select where to aim, but irrespective of the choice, the next person in the rotation shoots next. The order is A, B, then C, selected because A is the worst marksman hitting his target 1 out of 3 times.   B hits his target 2 out of 3 times and C hits his target every time he shoots.  Assuming that everyone tries to maximize their probability of winning, where should A aim first?

Bonus … What are the expected probabilities of survival for each individual?

The following collection of problems should challenge you for a while, and give us a chance to come up with a really complicated, mind bending puzzle.

1) In a roomful of engineers the following observations are made: a) every person, except one, shakes someone's hand; b) at least one person shakes at least two other people's hands; c) no one shakes the same person's hand twice. Is the number of people that shake hands an odd number of times, even, odd or indeterminate?

2) What "information" could be added or removed to change this conclusion?

3) There are 10 one-dollar bills that are to be placed in N bags in such a manner that any (dollar) amount from $1 to $10 can be provided by simply selecting an appropriate set of bags, but without altering the contents of the bags. What is the smallest value of N and how many bills are in each bag?

4) In the above problem, replace the 10 one-dollar bills with 1000 one-dollar bills. What is the fewest number of bags to provide any amount from $1 to $1000 following the rules above?

5) The numbers from 1 to 10 can be placed into two groups according to a certain rule.

   Juan: 2, 6
   Tu: 1, 3, 4, 5, 7, 8, 9

   In which group does 10 go and why?

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