快猫短视频

#238 Knight shift

Set by Sam Hartburn

鈥淚鈥檝e heard that whatever square I start from, and no matter what path I take, I can always make at least 10 moves without landing on a square I鈥檝e already been on,鈥� said the white knight.

The black knight tested it out. After jumping onto a particular black square somewhere in the top left-hand quarter of the chess board, she made three hops, but there were now no squares she could move to that she hadn鈥檛 already visited. 鈥淭hat wasn鈥檛 10!鈥� she said.

鈥淢aybe you were unlucky,鈥� said the white knight. The black knight set off from where she had finished before. Her first three hops retraced her earlier moves, then she made another six hops, visiting at least one square in every column and making exactly one hop into the lower half of the board. After these nine moves, she was stuck once more. 鈥淪till one short. So much for your theory!鈥� she said.

Can you retrace her path? Knights can move three squares in an L shape in any direction.

Solution next week

#237 Golden oldie

Solution

The padlock code was 1089, regardless of which year Rumpelschtumpel was born.

The difference between a three-digit number (ABC) and its reverse (CBA) is 99(A 鈥� C), i.e. it is a multiple of 99. The multiples (XYZ) are 198, 297, 396 and so on, and each of these when added to its reverse is 1089 (e.g. 198 + 891 = 1089).

Note that if A and C are the same digit, then XYZ is 000. So, if 1089 doesn鈥檛 work, Prince Hopeful should try 0000 on the padlock.