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#245 Three men’s morris

Set by Rob Eastaway

The game of three men’s morris was invented hundreds of years ago. It was eventually superseded by noughts and crosses, or tic-tac-toe.

To play, you draw a grid. Each player has three counters, and the aim is to get three of your colour in a row, column or diagonal. The players take it in turn to place a piece on a junction. If there isn’t a winner after all the pieces have been placed, you can slide one of your pieces to an adjacent empty junction on your next move. So, in the game shown on the left below, white could move the bottom-left piece up or the piece in the centre in one of three directions.

Alpha and Zoe are playing a game, shown above right. Alpha is first and puts her piece in the centre. Zoe goes for a corner. Alpha smiles. She thinks she can guarantee a win in… how many more moves? And should Zoe have gone for middle top instead?

Solution next week

#244 Wheel-to-reel

Solution

The coach was going at 8 yards per second. The back wheels are 4 yards in circumference with 24 spokes, and the front wheels are 3 yd in circumference with 12 spokes (3/4 the diameter means 3/4 the circumference as well). As the back wheels rotate, they will appear the same every 1/6 yd (4 yd/24 spokes). The front ones appear identical every 1/4 yd (3 yd/12 spokes). The shortest distance that both sets of wheels will appear the same together is every 1/2 yd. So, if every frame represents 1/2 yd of travel, then the wheels would appear not to move. At 16 frames a second, this translates to 8 yd/s of stagecoach speed, just over 16 miles per hour. In theory, it could have also gone 1 yard per frame, but this would be 32 mph, faster than Usain Bolt.