# The Logical Puzzle - 20 Oct 2005

### SOLUTION TO NOVEMBER'S PUZZLE: CUTTING A STICK TO MAKE A TRIANGLE

In last month's puzzle, you cut a stick in two random places, then had to figure out the probability that you could form a triangle out of the three pieces.

In order for the three pieces to form a triangle, all pieces must be shorter than half the length of the original stick. In a triangle, the sum of the lengths of any two sides is always longer than the length of the remaining side. If a piece ends up being longer than half the stick's size, the sum of the other two pieces will be shorter and you will not be able to form a triangle.

To avoid having a piece that is at least half the length of the stick, the two cuts must be on opposite sides of the middle point. The probability of this occurring is ½ (either both cuts end up on the same half or not). Now assume that the first cut is made on point p (where p is a percentage of the full length of the stick). In addition, the second cut must fall below the p + ½ point.The probability for this is of course ½ . Now multiply the two probabilities and you get the final answer: ½ × ½ = ¼ .

### DECEMBER'S PUZZLE: RECTANGLE WITHIN A CIRCLE

This month's logical puzzle is a geometrical one. Examine Figure A and see whether you can calculate the length of the circle's radius.