Example Problems
Ernest Clement Mortimer (version by A. Frolkin),Shortest Proof Games, 1991
| a | b | c | d | e | f | g | h | ||
| 8 | 8 | ||||||||
| 7 | 7 | ||||||||
| 6 | 6 | ||||||||
| 5 | 5 | ||||||||
| 4 | 4 | ||||||||
| 3 | 3 | ||||||||
| 2 | 2 | ||||||||
| 1 | 1 | ||||||||
| a | b | c | d | e | f | g | h |
Probleemblad, May/June 1999
| a | b | c | d | e | f | g | h | ||
| 8 | 8 | ||||||||
| 7 | 7 | ||||||||
| 6 | 6 | ||||||||
| 5 | 5 | ||||||||
| 4 | 4 | ||||||||
| 3 | 3 | ||||||||
| 2 | 2 | ||||||||
| 1 | 1 | ||||||||
| a | b | c | d | e | f | g | h |
A relatively simple example is given to the right. It is a version by Andrei Frolkin of a problem by Ernest Clement Mortimer, and was published in Shortest Proof Games (1991). It is an SPG in 4.0. It is natural to assume that the solution will involve the white knight leaving g1, capturing the d7 and e7 pawns and the g8 knight, and then being captured itself, but in fact the solution carries an element of paradox quite common in SPGs: it is the knight that started on b8 that has been captured and the knight now on that square has come from g8. The solution (the only possible way to reach the position after four moves) is 1. Nf3 e5 2. Nxe5 Ne7 3. Nxd7 Nec6 4. Nxb8 Nxb8.
A more complex proofgame, with more solutions, can be seen in the second diagram. The solutions are: 1. b4 h5 2. b5 Rh6 3. b6 Rc6 4. bxc7 Rxc2 5. cxb8=Q Rxd2 6. Qd6 Rxd1 7. Qxd1 and 3. ... Rd6 4. bxc7 Rxd2 5. cxb8=B Rxc2 6. Bbf4 Rxc1 7. Bxc1, showing the Pronkin theme in both solutions (in the first solution with a queen, in the second solution with a bishop).
Read more about this topic: Proof Game
Famous quotes containing the word problems:
“...I have wanted to believe people could make their dreams come true ... that problems could be solved. However, this is a national illness. As Americans, we believe all problems can be solved, that all questions have answers.”
—Kristin Hunter (b. 1931)
“In many ways, life becomes simpler [for young adults]. . . . We are expected to solve only a finite number of problems within a limited range of possible solutions. . . . It’s a mental vacation compared with figuring out who we are, what we believe, what we’re going to do with our talents, how we’re going to solve the social problems of the globe . . .and what the perfect way to raise our children will be.”
—Roger Gould (20th century)