One hundred people know almost everything: they see other people's numbers, but not their own. Without communicating after knowing the numbers, each one must predict theirs. The group wins if at least one guesses correctly.
Can the group guarantee victory, regardless of the number assignment?
The modular oracle
Riddle statement
There are 100 people numbered from 0 to 99. An integer between 0 and 99 is written on each person's forehead. There may be repetitions.
Each person sees the others' 99 numbers, but not their own.
Before the numbers are written, the 100 people can agree on a strategy. Then, without communicating, each person must write a single prediction for their own number.
The group wins if at least one person is correct.
Is there a strategy that guarantees victory, regardless of the 100 numbers written?