Chessametics

keith chessametic

Mike Keith published this remarkable invention in the Journal of Recreational Mathematics in 1975. Suppose a chess game goes:

P-K4   P-K4 
B-B4   P-R4 
Q-B3   P-R4 
QxP 

This is checkmate, so White says “I win!” Now if the game score is written out in one column, including White’s exclamation:

P-K4
P-K4
B-B4
P-R4
Q-B3
P-R4
 QxP
----
IWIN

… we get a solvable alphametic — replace each letter (and the symbols x and -) with a unique digit and you get a valid sum. (The digits already shown count as numbers, and those numbers also remain available to replace letters.)

This example isn’t quite perfect — the two moves P-R4 are ambiguous, as is the final pawn capture. Keith’s Alphametics Page has an even better specimen, a pretty variation from a real 1912 game by Siegbert Tarrasch. It’s 13 moves long and forms a perfect alphametic with a unique solution.

Slitherlink

https://commons.wikimedia.org/wiki/File:SurizaL%C3%B6sung.png
Image: Wikimedia Commons

In this original logic puzzle by the Japanese publisher Nikoli, the goal is to connect lattice points to draw a closed loop so that each number in the grid denotes the number of sides on which the finished loop bounds its cell, as above: Each cell bearing a “1” is bounded on 1 side, a “2” on 2 sides, and so on.

Here’s a moderately difficult puzzle. Can you solve it? (A loop that merely touches a cell’s corner point without passing along any side is not considered to bound it.)

https://commons.wikimedia.org/wiki/File:Slitherlink-example.png
Image: Wikimedia Commons

The Roving Princess

A puzzle by University College London mathematician Matthew Scroggs: A princess lives in a row of 17 rooms. Each day she moves to a new room adjacent to the last one (e.g., if she sleeps in Room 5 on one night, then she’ll sleep in Room 4 or Room 6 the following night). You can open one door each night. If you find her you’ll become her prince. Can you find her in a finite number of moves?

Click for Answer

Sanity Check

https://pixabay.com/en/beach-island-palm-trees-nature-1844962/

From Raymond Smullyan: Every inhabitant of this island either a knight or a knave. Knights always tell the truth, and knaves always lie. Further, every inhabitant is either mad or sane. Sane inhabitants always answer questions correctly, and mad ones always answer incorrectly. You meet an inhabitant of the island and want to know whether he’s sane or mad. How can you determine this with a single yes-or-no question?

Click for Answer

For Pi Day

https://mobile.twitter.com/Cshearer41/status/1054674051388661760

From the prolifically interesting Catriona Shearer: The red line is perpendicular to the bases of the three semicircles. What’s the total area shaded in yellow?

Click for Answer

E Pluribus Unum

Replace each * with a different digit 1-9 to make this equation true:

\displaystyle \frac{*}{**} + \frac{*}{**} + \frac{*}{**} = 1

Click for Answer