Absolutely Christmas Crackers Puzzle - Solution
The Puzzle:
Three colours of hat: Red, Yellow and Blue
Four types of novelty: toy car, spinning top, magnifying glass and miniature hair brush
Four different types of joke slip
All the other parts were the same type. The kit contained enough bits for 50 crackers. Can I make each cracker different from all the others?
Our Solution:3 x 4 x 4 = 48. Sadly at least two crackers must be exact duplicates of ones already made.
BUT if you could handle the sad look on people's faces, you could consider a missing item as a possible combination. This gives 4 x 5 x 5 = 100 different crackers. 40 crackers would be missing one item, 11 will be missing two, and one cracker with nothing in at all! (This solution by Eric Chen, modified by Spacklick and Nehustan.)
BUT if you could handle the sad look on people's faces, you could consider a missing item as a possible combination. This gives 4 x 5 x 5 = 100 different crackers. 40 crackers would be missing one item, 11 will be missing two, and one cracker with nothing in at all! (This solution by Eric Chen, modified by Spacklick and Nehustan.)
Puzzle Author: Stephen Froggatt