Problem-solving is an art and it can be learned. Below is Edward De Bono’s useful five-step process for problem-solving. There are however different types of problem and they require different thinking styles in order to crack them.
Here are some problems to give you a bit of practice. The retrograde chess problems do not require you to be a chess expert; just a logical thinker (though you need to know how the pieces move). The Lateral Thinking problems require a different approach – you have to think of the answer first, and then figure out why it fits the facts.
Edward DeBono’s Model
- To – Where do you want to get To? (Definition)
- Lo – Look at the Problem. (Logical Analysis)
- Po – Possible Solutions (Generate Possibilities)
- So – So what shall we Do? (Make your Decision)
- Go – Get Going (The Implementation Phase)
The above model is very useful when it comes to real-life problems; the sort of problems that have many possible solutions. Certain problems really have a single solution and therefore will yield to analysis (LO phase). The retrograde chess problems below are designed to stimulate your ability to analyse problems logically.
With many problems, we tend to get stuck at the PO phase – we call this lack of inspiration. Lateral thinking is a technique designed to help us improve our ability to creatively access solutions we might normally discount as possibilities – often because the possibility seems absurd. The lateral thinking problems are designed to stimulate your ability to come up with possibilities – there can be many different solutions but there will generally be a single possibility that seems most plausible.
Retrograde Chess Problems
Problem Number #1 by Raymond Smullyan
This is an excellent problem for getting you started on Retrograde Analysis.
There are at least three possible answers to the problem
Black moved last. What was Black’s last move & what was White’s?
Problem Number #2 by W. F. von Holzhausen
(Akademische Schachblater, 1901)
A bit more of a traditional problem; however you do have to figure out who’s move it is, so some Retrograde Analysis is required.
This problem is a Checkmate-in-One. (One move is considered to be one move by each player!)
Who checkmates whom and how?
Problem Number #3 by Raymond Smullyan
(Composed in 1925 when he was 16 only years old)
What is the missing piece?
What can I say about this problem? I had it all set up on my chess board & worked with it for about three weeks, on and off, before I finally solved it. A brilliant puzzle.