He figures if by Friday morning he has not been told, then he will immediately know his execution is on Saturday, thus violating the Judge's order; therefore he cannot be executed on Saturday.
Knowing he can't be executed on Saturday, if on Thursday morning he has not been told, he knows he must be executed on Friday, thus violating the Judge's order. By induction it would violate the Judge's order to execute him on any day of the next week.
The following Tuesday he was thus completely surprised to be taken out to be executed.
7397: Digits 4-8 of the sequence "sum of iterated phi(n)".
1074: Sorry, that's digits 4-8 of log_21(8). Please try again.
6235: Sorry, that's digits 10-14 of an irregular triangle read by row's squarefree quadratic non-residues. Please try again.
2099: Sorry, that's digits 4-8 of the decimal expansion of the x-intercept of the shortest segment from the positive x axis through (2,1) to the line y=x.
Clearly, these are all way too easy to guess for an attacker for you to use them as a PIN number.
https://blog.xkcd.com/2008/01/14/robot9000-and-xkcd-signal-a...
1. Input "0531" on another iPhone's setup screen.
2. Try "0531" and the other suggested PINs, based on distance from thumb to the option.