bonanova

I think the puzzle has become something of a Rorschach test. Interesting.

You are on the right track. The logic can be tightened up, but you basically have the correct information.

Clue: six-fold symmetry.

k-man and TSLF agree on an answer that differs slightly from mine. So as it stands I am outvoted. But I invite a critique of my solution.

Clue: There is an algebraic solution (closed form) and a trigonometric solution (numerical.)

Are there others?

Sorry, but in my homeland the game is played only with corner pockets. I've given this one some thought. I have not come up with what I imagine would be an adequate approach. I'm open to a clue of some sort.

This is partially solved, but there are four questions to answer. What can be known about Bob's and Charlie's number and type?

I'll be a smart a** and say it's seven minus the expected value of the lowest valued die. Seriously, I'll work on it.

Take this answer a bit farther. Is there a dropping off place that will not result in their arriving simultaneously?

Sorry, I think I am wrong... Not far off, but it's more complex than that.

A dying man, knowing his wife was pregnant, left a will that divided his estate between his child and his wife, giving 1/3 to the wife if she gave birth to a son, and 2/3 to the wife if she birthed a daughter. As it turned out, she birthed fraternal twins: a son and a daughter. You are executor of the will. Wishing to adhere as closely as possible to the man's wishes, how will you divide the estate among the three heirs? If you desire more guidance than what has been provided, the situation is clear: there is no more guidance than what has been provided. You are the law.

An old Sam Lloyd classic that has to be dusted off every now and again. It's deceptively simple, and more fun to solve than to Google. Enjoy. A square phalanx of soldiers, 100 feet on a side, marches forward at a constant speed. The company mascot, a small terrier, trots along with them, starting at the center of the rear rank. Since he moves more quickly than the soldiers, he is able to trot at constant speed around the outside of the square, keeping as close as possible to the soldiers at all times. When he returns to his starting position at the rear of the formation, the soldiers have moved forward a distance of 50 feet. How long is the dog's path?

Doris and Forrest start out on a bike trip, but on the way Doris' bicycle breaks down. They agree to share the remaining bicycle. They begin simultaneously, Forrest on foot, Doris riding the good bike. After a certain distance, Doris dismounts, leaves the bicycle behind and continues on foot. When Forrest reaches the waiting bicycle, he mounts it and rides until he catches up with Doris. He then dismounts, and the process repeats until they reach their goal. How far from their destination should the the bicycle be left behind the final time to ensure they reach their destination at precisely the same moment? The distance from the breakdown to the destination is 60 miles, and they both walk at a constant rate of 5 mph and ride at a constant rate of 15 mph.

Every day at noon a ship leaves New York for London, and at that moment a ship also leaves London for New York. It's a leisurely trip that takes seven days and seven nights. How many London-bound ships will the ship leaving London today meet during its trip to New York?