A “grid-chess” problem by E. Visserman, from *Fairy Chess Review*, 1954. A grid divides the board into 16 large squares, and each move by each side must cross at least one line of the grid. For example, in this position it would be illegal for the black king to move to f3. How can White mate in two moves?

# Puzzles

# Line Work

A problem proposed by C. Gebhardt in the Fall 1966 issue of *Pi Mu Epsilon Journal*:

A particular set of dominoes has 21 tiles: (1, 1), (1, 2), … (1, 6), (2, 2), … (6,6). Is it possible to lay all 21 tiles in a line so that each adjacent pair of tile ends matches (that is, each 1 abuts a 1, and so on)?

# A Bureaucracy Maze

At a Mensa gathering in 2003, Robert Abbott tried out a new type of maze — five bureaucrats sit at desks, and solvers carry forms among them:

When you enter the maze you are given a form that says, ‘Take this to the desk labeled Human Resources.’ You look for the desk with the nameplate Human Resources, you hand in your form to the bureaucrat at that desk, and he gives you another form. This one says, ‘Take this form to Information Management or Marketing.’ Hmm, there is now a choice. Let’s say you decide to go to Information Management. You hand in your form and receive one that says, ‘Take this form to Employee Benefits or Marketing.’ You decide on Employee Benefits where you receive a form saying, ‘Take this form to Corporate Compliance or Human Resources.’

Of the 30 participants, half gave up fairly soon, but the rest kept going until they’d solved it, taking 45 minutes on average. Here’s an online version with four desks, and here’s a fuller description of the project and its variants, including a Kafkaesque 2005 version by Wei-Hwa Huang in which the participants don’t know they’re in a maze.

# Black and White

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?

# 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: