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#228 A knight on the tiles

set by Colin Beveridge

My latest artistic commission is to create a pattern using two kinds of “Truchet” tiles, one with a black diagonal, the other with a white diagonal, like this:

My client, Sir Mo Sayik, is being incredibly fussy. He wants the tiles to be set on the specific 3 x 3 grid shown below.

He also wants the artwork to follow three rules. Firstly, wherever tiles join, the colours must match. Secondly, the black dots shown on the grid must have exactly three black diagonals touching them, and the white dot must have exactly three white diagonals touching it. And thirdly, the finished pattern can’t have any “islands” of black or white – all shapes formed must connect to an edge. Tiles can be rotated of course. Can you help?

Solution next week

#227 A great deal of magic

Solution

When Max flips over his own pile of cards at the end of the trick, he mathematically guarantees there will be an equal number of face-up cards in each hand.

Imagine that Max didn’t flip over his stack. His volunteer’s hand would have X face-up cards and 26 – X face down. Max would have the rest of the face-up cards, again totalling 26 – X, and the remainder of his hand would be face down. The number of these face-down cards would be 26 – (26 – X), or simply X. Once Max flips over his pile, the face-up and face-down cards would switch places, giving him X face-up cards, the same as the volunteer.

The rest of Max’s trick, which involved tapping and sliding piles of cards, was just showmanship.