By W. Timbrell Pierce. White to mate in two moves.

# Puzzles

# Black and White

Tim Krabbé calls this “one of the funniest chess problems I ever saw.” Its composer, M. Kirtley, won first prize with it in a *Problemist* tourney in 1986.

It’s a selfmate in 8, which means that White must force Black to checkmate him 8 moves, despite Black’s best efforts to avoid doing so.

The solution is a single line — all of Black’s moves are forced:

1. Nb1+ Kb3 2. Qd1+ Rc2 3. Bc1 axb6 4. Ra1 b5 5. Rh1 bxc4 6. Ke1 c3 7. Ng1 f3 8. Bf1 f2#

All of White’s pieces have returned to their starting squares!

# Gear Trouble

A problem from the U.S.S.R. mathematical olympiad:

You’re given 13 gears. Each weighs an integral number of grams. Any 12 of them can be placed on a pan balance, with 6 in each pan, so that the scale is in equilibrium. Prove that all the gears must be of equal weight.

# Coming and Going

A puzzle by Pierre Berloquin:

In my house are a number of rooms. (A hall separated from the rest of the house by one or more doors counts as a room.) Each room has an even number of doors, including doors that lead outside. Is the total number of outside doors even or odd?

# Forewarned

From *The Booke of Meery Riddles*, 1629:

A soldier that to Black-heath-field went,

Prayed an astronomer of his judgment,

Which wrote these words to him plainly,–

Thou shalt goe thither well and safely

And from thence come home alive againe

Never at that field shalt thou be slaine.

The soldier was slaine there at that field,

And yet the astronomer his promise held.

How?

# Black and White

By Alexander Yarosh. The position above was reached in a legal game, except that one piece has been knocked off the board. What was it?

# Two-Toned

A problem from the 2004 Moscow Mathematical Olympiad:

An arithmetic progression consists of integers. The sum of its first *n* terms is a power of two. Prove that *n* is also a power of two.

# Moving Up

My wife and I walk up an ascending escalator. I climb 20 steps and reach the top in 60 seconds. My wife climbs 16 steps and reaches the top in 72 seconds. If the escalator broke tomorrow, how many steps would we have to climb?

# Black and White

By Rudolf L’hermet. White to mate in two moves.

# Pointing Fingers

Only one of these statements is true. Which is it?

A. All of the below

B. None of the below

C. One of the above

D. All of the above

E. None of the above

F. None of the above