#71 White lines
There are 32 white squares on a chessboard. Your task is to draw a line that passes through all of the white squares only once, moving via the corners where they touch without lifting your pen off the board. The diagram shows the kind of line that is required. Start from any square you like. Can you get through all the squares with a single line? If not, then what is the smallest number of separate lines that you need?
Answer next week
#70 Taking the biscuit
Solution
Alpha should grab one digestive biscuit, leaving seven and four in the two jars. The key to the game is ultimately to leave your opponent with two biscuits in one jar and one in the other. Whatever move they make, you can follow with a winning move. From seven and four, Betty鈥檚 next move can鈥檛 be three digestives because Alpha would win straight away.
Whatever other move Betty makes, Alpha will be able to follow it either by getting to five and three (and thereafter to two and one or zero), or to two and one. Whatever happens, she has a guaranteed path to win. This is formally known as Wythoff鈥檚 Game.
Quick quiz #63
1. What nugatory addition did Indian mathematician Brahmagupta apparently make to the number system in AD 628, enabling modern arithmetic?
2. In solid-state physics, what name is given to the absence of an electron?
3. Two mirrors placed opposite each other in a vacuum will move towards one another. What is this effect called?
4. Nitrogen 78 per cent, oxygen 21 per cent鈥� what comes next on this list?
5. What procedure did William Morton first demonstrate on Gilbert Abbott in front of a large audience in Boston in 1846?
Answers
1 The number zero, and rules for its manipulation
2 A hole. It is a convenient mathematical fiction sometimes to regard electric current as made of moving holes
3 The Casimir effect. It is due to a vacuum not being empty, but full of quantum fields
4 Argon 0.9 per cent, in the list of abundances of gases in Earth鈥檚 atmosphere
5 Anaesthesia by inhaling ether