Sorting pennies in the dark

I am recurrently amazed at the wonderful logic and math puzzles posted at Futility Closet.   Here's a recent one:

You’re in a pitch-dark room. On a table before you are 12 pennies. You know that 5 are heads up and 7 are tails up, but you don’t know which are which. By moving and flipping the coins you must produce two piles with an equal number of heads in each pile. How can you do this without seeing the coins?

I was not able to solve this on my own and had to peek at the answer.  Even after seeing the answer, it took me a long time to comprehend why it works.

I'll add some thoughts in the Comments section, but for the answer, go to Futility Closet.

Fiendishly tricky geometry puzzle

Start with a piece of paper 8" x 8", as shown on the left.  Make the two cuts shown.

Then shift the big lower-left piece up and to the left and move the triangle from the upper left corner to the lower right one.

The area that used to be 8x8 = 64 square inches now appears to be 9x7 = 63 square inches.  Where is the fallacy?

I pondered this for way too long, and finally had to cut some physical pieces of paper to solve the paradox.

The puzzle was originally created by or published by the famous Sam Loyd; I found it in the Futility Closet.

"En passant" chess puzzle

Futility Closet posts some very interesting chess puzzles, and the one above is one of best I have seen.

White plays B-g2+.  Black responds with pawn to d5, which (he says) blocks the check and uncovers a checkmate by the black bishop at c8.   White responds that the black pawn never got to/can't go to d5, because the white pawn takes it "en passant" at d6. 

More at the link (puzzle from Heinrich Fraenkel, Adventure in Chess, 1951.)

A simple math puzzle

A ball 13 inches in diameter has a 5-inch hole drilled through the center. How deep is the hole?

You can do this one in your head.  The answer is in the comment section.

Found at Futility Closet, where it was credited to Henry Dudeny.