Dictator a is planning to slaughter the people of province q and province q anticipates the attack. Dictator a can either attack by air or by sea. Province q can either prepare for an aerial defense or a defense againt an assault by sea. Both sides must choose either an all air or all sea strategy, and they can't divide their armed forces. Given:

* If Dictator a attacks by sea and q defends by sea, the probability of massive slaughter is 80%.
* If Dictator a attacks by sea and q defends by land, the probability of massive slaughter is 100%.
* If Dictator a attacks by land and q defends by land, the probability of massive slaughter is 60%.
* If Dictator a attacks by land and q defends by sea, the probability of massive slaughter is 100%.

What should the strategy of Dictator a be, assuming the goal is to slaughter as many people of Province q as possible? Assume the goal of Province q to be to minimize the probability of mass slaughter. What is the final probability of mass slaughter assuming both utilize an the best strategy?

Suppose that you have two jars, one with 50 red marbles and the other containing 50 blue marbles. First, a jar is picked at random, and then a marble will be picked from the corresponding jar. Placing all of the marbles in the jars, how can you maximize the chances of a red marble being picked? What are the exact odds of getting a red marble using your scheme?

If yesterday was Wednesday's tomorrow and tomorrow is Sunday's yesterday, what day would today be?

A cardplayer is dealt a poker hand (five cards) from an ordinary playing deck with the standard 52 cards. Find the number x of ways the player could be dealt a diamond flush (five diamonds).

If seven people meet each other and each shakes hands only once with each of the other, how many handshakes will have taken place?

The Beatles have a concert that starts in 17 minutes and they must all cross a bridge to get there. All four men begin on the same side of the bridge. It is nightfall, and there is only one flashlight. A maximum of two people can cross at one time. Any party who crosses, either 1 or 2 people, must have the flashlight with them, and the flashlight must be walked back and forth. Each band member walks at a different speed. A pair must walk together at the rate of the slower man's pace:

*Ringo: - 1 minute crossing
*George: - 2 minutes crossing
*Paul:- 5 minutes crossing
*John: - 10 minutes crossing

Example: If Ringo and John go first, 10 minutes have elapsed when they get to the other side of the bridge. If John then returns with the flashlight, a total of 20 minutes have passed and they have missed the concert.

There are two known answers to this problem.