IBM Ponder This #017 · September 1999

Five people visit a restaurant with nine unfamiliar dishes. Each person orders one dish, and orders need not be distinct. The waiter places the dishes in the middle of the table without saying which dish is which.

They return twice more under the same rules, though they may order differently. After three meals, they have eaten all nine dishes and can identify every one.

What pattern of ordering makes this possible?

Show that the story could not be true if the menu contained ten dishes instead of nine.

Solution

Best opened after a real attempt

Solution

To be added.