A row of 10 prisoners, each in a numbered cell from 1 to 10, are told the following rule:
“Tomorrow, each of you may either say nothing or announce a single-digit number (0–9). If the sequence of spoken digits — read left to right across occupied cells — forms a numeric palindrome, you will all be freed. Otherwise, you all remain imprisoned.”
The prisoners can plan beforehand but may not communicate after.
On the day, some prisoners may be missing, and no one knows who will be present.
What strategy guarantees freedom, no matter who shows up?
Random Walking on a Hyper-Torus
The short answers to this puzzle are: There is a 100% probability that the random walk will eventually return to the origin and the average number of steps until it first returns to the origin is 2,000. If starting at another point, return to the origin is only possible if the coordinates of that starting point are all even or all odd. That is true for 1/4 of all the points on the hyper-torus. Starting from one of these reachable points there is also a 100% probability of visiting the origin at some point in the future, and the average number of steps until first reaching the origin is also 2,000.
Solutions were submitted by Bob Conger, Natalie Mo, and Natalie Ramirez.
Note, Steve (Soon Cheol) Kim was left out of the list of solvers for the “How Many Liars?” puzzle in the May/June AR.
