A “no-brainer” by Harvard mathematician (and chess master) Noam Elkies. White has choices as to how to play, but no matter how he proceeds, he’ll wind up mating Black on the seventh move.

(From Tim Krabbé’s chess diary.)

A “no-brainer” by Harvard mathematician (and chess master) Noam Elkies. White has choices as to how to play, but no matter how he proceeds, he’ll wind up mating Black on the seventh move.

(From Tim Krabbé’s chess diary.)

By Thomas Tarrant. White to mate in two moves.

A problem from the British Columbia Colleges Senior High School Contest for 2000:

If I place a 6 cm × 6 cm square on a triangle, I can cover up to 60% of the triangle. If I place the triangle on the square, I can cover up to 2/3 of the square. What is the area, in cm^{2}, of the triangle?

(a) 22 4/5

(b) 24

(c) 36

(d) 40

(e) 60

“We now give what is acknowledged to be the finest two-move problem extant,” wrote J.H. Blackburne in the *Strand* in 1908. “It is by the American expert, W.A. Shinkman, and is also claimed by G.E. Carpenter, a fellow countryman of his. Here we have not only a difficult key-move, but also beauty of theme and artistic construction, the three essential qualities necessary to a perfect problem.”

White to mate in two moves.

Charles W. Trigg offered this puzzle in the Fall 1977 issue of *Pi Mu Epsilon Journal* (PDF):

This square array contains the first 25 positive integers. Choose five, no two from the same row or column, so that the largest of the five elements is as small as possible, and justify your choice.

Dutch mathematician Hans Freudenthal proposed this puzzle in 1969 — at first it appears impossible because so little information is given.

X and Y are two different whole numbers greater than 1. Y is greater than X, and their sum is no greater than 100. S and P are two logicians; S knows the sum X + Y, and P knows the product X × Y. S and P both reason perfectly, and both know everything I’ve just told you.

- S says, “P does not know X and Y.”
- P says, “Now I know X and Y.”
- S says, “Now I also know X and Y.”

What are X and Y?

By Robert A. Lincoln. White to mate in two moves.

University of Ljubljana electrical engineer Izidor Hafner devised this maze on a tetrahedron, presented as an unfolded plane plan. Can you find a path from one dot to the other? To do so you’ll have to fold up the figure in your head:

By Augusto Piccinini. Imagine that the board is a vertical cylinder, that is, that the a-file and the h-file are joined so that pieces can move across the border. How can White mate Black in two moves?

What three digits are represented by X, Y, and Z in this addition problem?