This puzzle, by F. Abdurahmanovic, won first prize in a 1959 Yugoslav tourney. It’s a helpmate — how can Black, moving first, cooperate with White to get himself checkmated in two moves?

# Puzzles

# The Four Points, Two Distances Problem

Alex Bellos set a pleasingly simple puzzle in Monday’s *Guardian*: How many ways are there to arrange four points in the plane so that only two distances occur between any two points? He gives one solution, which helps to illustrate the problem: In a square, any two vertices are separated by either the length of a side or the length of a diagonal — no matter which two points are chosen, the distance between them will be one of two values. Besides the square, how many other configurations have this property?

The puzzle comes originally from Dartmouth mathematician Peter Winkler, who writes, “Nearly everyone misses at least one [solution], and for each possible solution, it’s been missed by at least one person.”

# Black and White

“A fairly good two-mover” from Benjamin Glover Laws’ *The Two-Move Chess Problem*, 1890. What’s the key move?

# Quickie

Is 94,271,013 the sum of 12 consecutive integers?

# Black and White

By G.E. Rottigni. White to mate in two moves.

# Podcast Episode 266: Lateral Thinking Puzzles

Here are seven new lateral thinking puzzles — play along with us as we try to untangle some perplexing situations using yes-or-no questions.

# The Two Squares Puzzle

Lee Sallows just sent me this — the puzzle is difficult, but the solution is stunning:

# Query

What’s remarkable about this set of words?

BIOLOGY DEATHLY SLOSHED BASTARD SELVAGE FISSILE DALLIES FLAVORS

# Keeping Distance

For which values of *n* can *n* points be placed on a sphere so that all of them are equidistant from each other?

# Some Two

Given 52 integers, prove that it’s always possible to find some two of them whose sum or difference is evenly divisible by 100.