Puzzles collated by David MacKay

1. Tiling a big rectangle with small rectangles.
   Problem statement: (pdf) (postscript)]
   Solutions: rectangles.ps.gz. rectangles.pdf. html. abstract
2. Funky dice for Monopoly. postscript (one page) | pdf (one page)
   (Thanks to Alan Beardon).
   solution
3. The Transatlantic Cable. postscript (one page) | pdf (one page)
   From p173 of Information Theory, Inference, and Learning Algorithms by David J.C. MacKay (C.U.P. 2003), available free online. A solution is on page 174.]
4. Sort five objects, all different in weight, using a balance - in as few comparisons as possible. (Thanks to Frank King.)
5. The Hat puzzle.
6. The Best Trick.
7. Conway's Soldiers
   Conway's soldiers, also known as the "solitaire army" game (Berlekamp et al. 1982) or "checker-jumping problem" (Honsberger 1976) is a one-player game played on an infinite checkerboard in which every square below a certain horizontal line is occupied by a piece (or "soldier"). Play proceeds by jumping horizontally or vertically over other pieces onto an empty space, where jumped-over pieces are then removed. Puzzle 1: Get a soldier to the fourth row. Puzzle 2: Is it possible to get a soldier to the fifth row? For a nice applet that can help you play with Conway's soldiers go here [] and click on the phrase "Conway's soldiers" (near the bottom-left of the page).