When the number of colors increases, the problem stops being a simple game of immediate deduction and begins to require a much finer form of coordination. His interest is in how a single intervention can order what comes next.
The executioner and the hats (3 colors)
Riddle statement
There are 10 people in a row, numbered 1 to 10, where 10 is behind everyone.
Each hat can be red, blue or green. Person 10 speaks first and sees the hats of the 9 people in front of him; the 9 sees 8; and so on. No one sees their own hat or those behind them.
Take turns, each person must say a single word out loud: “red”, “blue” or “green”. They cannot add anything else.
If someone guesses the color of his hat correctly, he survives; If you fail, you die. Before starting they can agree on a strategy.
How many lives can they guarantee at least?