My first pass at the puzzles:

**Q: List the 5000 largest known prime numbers.**
List the next 5000 too.

**You have four sticks...**
I like puzzles like this, where you have to think and keep track of stuff. Solution wasn't that much longer than the question though.

**Given an apple, a lemon...**
This was ...different. Not a very long answer, either.

**For what positive k is it possible to dissect a 1xk rectangle...**
The answer went right over my head.

**You are given nine identically looking balls and a balance scale...**
I went back and found that I didn't use the intended solution if neither weighing balanced.

Click here to view the secret text

×In the third case, you don't have to weigh three balls against each other in the third weighing, you just need to weigh 1 vs 2. If they balance, then one of 3,4 is light, and one of 5,6 is heavy. Weigh 3 vs 2 and 5 vs 2.

This shortens the answer significantly, but requires a fifth weighing. Good puzzle.

**You have to get 5 things across a river:...**
This was basically a slightly longer version of a well known existing puzzle. It actually felt a little like tedium solving it.

**How can you count the decimal numbers of finite length?**
Of course the answer is infinity, the point of the puzzle is to show that they're countably infinite instead of uncountably infinite. The way to prove them countably infinite is to demonstrate that they can be lined up against the integers 1:1 using a predefined method, and this puzzle was to find that method. Remember, the questions wasn't "

How many are there,"

the question was "

How can you count them?"

**A two foot tall man is found dead in his home...**
The place you've seen this puzzle before was by me, in the puzzle thread. I left part of it out there, and had to remove it. It's on one of the early pages. And the reason the answer is long is that you have to use your powers of deduction. You could give

*any* short answer to the puzzle, but without anything to back it up it's just theory.

**In a regular game of Hearts, what are the chances...**
When Noah PMed me for the answer to this, I gave him a pair of simple nCi formulas that I intended him to expand and combine as the actual answer. I was really quite surprised when he only changed a couple words and threw it up. As it is, the posted answer is incorrect due to its wording. This is a purely mathematical question.

**How would it be possible (regardless of the law) for a male person to be his own grandpa...**
My dad marries a twenty year old girl, and I marry her mom. That way, it's even legal. Again, I've seen this exact puzzle before.

**In a particular numerical code, 6-18-18-213-39-174-123...**
I feel like a cryptographer.

**I secretly pick four points. I then give you...**
I think the wording of the question was artificially shortened, which made it a little difficult to understand. I thought it was asking something entirely different at first. I had to play with both my questions a lot to avoid this, and it seems I too wasn't clear enough with the decimal numbers puzzle.

[Edited by DiMono on 09-18-2004 at 02:25 PM GMT]

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