Department of Mathematics, Statistics
and Computer Science
Wim Ruitenburg's Spring 2006 MATH025.1001
Mathematical puzzles are more than just recreation, just as children playing is
more than just fun.
Mathematical puzzles are excellent training for problem solving skills.
Mathematical puzzles
We use the book, pages 28-32, as a start for the following list of
illustrations about mathematical puzles.
- Problem 6 on the 3 switches and the light, is not really a mathematics
problem; its solution needs extra principles from physics.
It is usual for a solution to a puzzle, to need scientific principles from
outside the ones stated in the problem, but they should be kept to a bare
minimum, and be obvious from the context of the problem.
- Problem 3 on buying and selling, is a mathematical puzzle.
It is not too exciting; it looks like a beginning business math textbook
exercise.
- Problem 13 on the cup with tea and the pitcher with cream, is a
mathematical puzzle in the full sense.
Its solution is mathematical, with minimal assumptions from physics.
In fact, its best solution requires almost no mathematics either.
- Problem 8 on the cannibals and missionaries is a classic mathematical
problem.
Its solution is usually found through a simple trial and error.
The only trick is that some step may be perceived as counterintuitive.
- The following problem is not in the book.
Consider the two pieces of paper below, outlined by solid lines.
The dotted lines are only an auxiliary grid by which we can see that the
first piece of paper is a 4 by 6 rectangle, and the second is a 5 by 5 piece
with two opposite corners clipped.
Problem: Show how to cut one piece into two parts by cutting with a scissors,
so that the other paper can be obtained by putting the two parts together in
another way.
- We seem to make the puzzle above harder by asking to solve the same clip
and paste question for the following two pieces of paper:
Did we really make it harder?
The more complicated picture on the right leaves so few possibilities to try,
that it should be be easier.
Last updated: February 2006
Comments & suggestions:
wimr@mscs.mu.edu