I took the following assumptions: 1) The women can't tell each other anything 2) Every woman knows the following fact: "every woman knows when a husband other

I took the following assumptions: 1) The women can't tell each other anything 2) Every woman knows the following fact: "every woman knows when a husband other than her own cheated". Now, let's simplify the problem and say that there are only 3 women as opposed to 100, and assign numbers to them and their respective husbands. Woman #3 thinks "I know that husband #1 and husband #2 cheated. Woman #2 knows that husband #1 cheated. Woman #1 sees that woman #2 and I (woman #3) are not killing our husbands, which logically would mean that her husband is the cheater. However, she (Woman #1) is capable of going through this thought process, and is yet not killing her husband. That means that she is thinking of either husband #2 or my husband (#3) as the cheater. Yet, woman #2 is capable of going through this thought process as well, and if my (#3) husband was not a cheater, then woman #2 would've killed her husband. Yet she hasn't, which means that my husband (#3) is the cheater. So, I have to go kill him". Now, there was nothing special about woman #3 - every woman goes through this thought process simultaneously, and all arrive at the same conclusion. Now, expand to 100. Maybe my explanation is a little muddy, and I am not giving enough justification to the last step of "simultaneous thought process", but I am pretty sure that this is the right method for solving the problem.