This is a listing of hopefully-original puzzles. All of these have appeared at one time or another on the newsgroup rec.puzzles. The puzzles are given in order of my estimation of difficulty - and even the first couple are IMHO non-trivial.

#1 The Pool Shot: A cue ball is on a pool table, a distance X away from a pocket. Somewhere
on the line from the cue ball to the pocket an object ball is placed.

What is the object ball placement that maximizes the difficulty of the
shot?

What is the placement that minimizes the difficulty of the shot?

Assumptions:
* This is a "physics" pool table, collisions are perfectly elastic, etc.
* The difficulty of the shot scales with the angular accuracy necessary
to make the shot

Cool things to notice for pool players:

* Notice how flat the accuracy-requirement is in the middle

* This formula breaks down when the object ball is very close to the cue
ball, because pool table collisions are *not* perfectly elastic.

* Note how close the object ball has to be to the pocket in order to
be twice as easy of a shot (compared to the most difficult one).

* What is the human response to the angular accuracy requirement? I'm
a decent pool player, and I'd say it's reasonably linear up to a
point, and then anything past that point is automatic.

2) When is Venus at its maximum brightness?

Assumptions:

* The orbits of Venus and Earth are coplanar, concentric, and circular.

* Radius(Earth's orbit)=1.0 Radius(Venus' Orbit)=.72

* The brightness of Venus as seen from Earth is directly proportional to the area subtended by the sunlit portion of Venus.

3) Hiking: I am hiking on a path with many other hikers, going both ways. I hike at 5 km/hr. The average hiker on the path hikes at 5 km/hr, with a standard deviation of 1 km/hr. What is the ratio of hikers I pass going my way, to hikers that I meet coming the other way?

4) Baseball: A baseball team consists of 8 .300 hitters, and one hitter whose batting average is X. All hitters either get a hit or get called out on strikes during an at-bat. When they hit, they hit singles, doubles, triples, and homers with equal probability. Baserunners advance the same # of bases that the hitter does.

Warm-up question: How high does X have to be for the opposing team to rationally intentionally walk Mr. X, if they are trying to minimize the chances of Mr. X's team scoring in this inning?

Harder question: How high does X have to be for the opposing team to rationally intentionally walk Mr. X, if they are trying to minimize Mr X's team's run expectation in this inning?

5) Jumping Off Of A Swing: What is the optimal release angle to maximize distance jumping off of a swing? (this problem is significantly harder than it looks!)

6) How many ways are there to bowl a 150?

American 10-pin bowling: 2 shots per frame, 10 frames, strike = 10+next
2 balls, spare=10+next ball, the 10th frame can consist of 3 tosses if the first one is a strike, or if the first two are a spare.