Peegue's Puzzle Page Welcome to the sixth edition of Peegue's Puzzle Page. As you know, Peegue is the mayor of Wondertown and, as such, comes across all sorts of problems that need to be solved. Can you help?

Nine Rainbow Coins

This time Peegue has dug up several puzzles based on nine rainbow coins arranged in a 3x3 grid.

Puzzle #1: First, without moving any coins, find all six squares that can be drawn using exactly four coins as corners. Got them all? Good! Now, can you figure out how many circles can be drawn that go through exactly four coins?

Puzzle #2: Again, without moving any coins, can you draw four straight lines that go through all nine coins, without lifting your pen? This puzzle will require you to think "outside the box".

Puzzle #3: Right now, the nine coins form exactly eight lines of three coins each (three horizontal, three vertical, and two diagonals). Can you move two of the coins to a new position, so that the resulting figure forms exactly ten lines of three coins each?

Puzzle #4: Peegue knows that one of the coins is actually a fake. It looks just like the other eight, but it weighs a tiny bit less. Peegue has a very sensitive balance scale on which to place the coins. Clearly Peegue could weigh two coins at a time until the scale tips toward the heavier one, identifying the other coin as the fake. Can you devise a method that would allow you to identify the the fake coin with certainty, using the scale only twice?

If you think you have the answer (or you -gulp!- give up), you can send Peegue an e-mail at peegue@midnightsynergy.com. You will receive an automated reply with the link to the solutions. (Make sure that you add Peegue to your address-book if you use a spamfilter, so that the reply doesn't land in your junk folder).