快猫短视频

#173 Knight moves

My son is obsessed with chess, and has been acting out the game鈥檚 moves everywhere we go, running like a bishop and jumping like a knight on tiled floors. He was tickled to see that on the number pad of my keyboard he could type 27 using a knight鈥檚 move, because the move from 2 to 7 is an L-shape, like a knight moves on a chessboard.

Alas, he can鈥檛 make 27 using a bishop move. Bishops move diagonally any number of spaces, so a bishop, using multiple moves, could make a number like 484 or 9157. In a similar fashion, a knight could make numbers such as 167 or 8349.

Yesterday, he made a happy discovery: a three-digit knight number that is exactly 27 more than a three-digit bishop number. (Actually, I found I could put another digit, call it 鈥淴鈥�, at the front of my son鈥檚 numbers, and still have a knight number that is exactly 27 more than a bishop number.) What numbers did my son find?

Solution next week

#172 Four got it

Solution

The house code is 8712, and the car code is 2178. We need a 4-digit number that, when multiplied by 4, equals the reverse of the original number. It would need to be less than 2500 or it would result in a 5-digit number. The number can鈥檛 start with 1, since a whole number multiplied by four can鈥檛 end in 1. If it starts with 0, it has to be 0000 (a number that wouldn鈥檛 need any memory prompt!) or 0 x x 5, but that couldn鈥檛 be multiplied by four to get a number in the 5000s. So, it must start with 2 and end with 8. From that it emerges that the car code must be 2178, with the house code being the reverse.