Science Puzzle
The Gulp Bait Selection
There are five lure colours: red, blue, green, yellow and purple. Three fish each independently pick one colour. You cannot see their choices as they happen.
What is the minimum number of fish that must have chosen before you can guarantee that at least two of them picked the same colour?
The Answer
Six fish. With only three fish choosing from five colours, it is possible for all three to pick different colours, so no repeat is guaranteed. It is possible but not certain.
The Pigeonhole Principle says: if you distribute more items than there are containers, at least one container must hold more than one item. Here the five colours are the containers and the fish are the items.
In the worst case, the first five fish each pick a different colour, filling all five containers exactly once. The sixth fish must pick a colour that is already taken. So six fish choosing from five colours guarantees at least one repeated colour, whatever choices they make.
The principle: The Pigeonhole Principle. If more items are distributed than there are categories, at least one category must contain more than one item. Worst-case reasoning reveals the guaranteed threshold.