If there is one cheating husband
, his wife knows that no one else's husband is cheating, so hers must be because there is at least
one cheating husband. She brings him to the public square
on day one.
If there are two cheating husbands, each wife sees the other cheated-on wife not bring her husband to the public square on day one, and therefore concludes that her own husband is cheating
. (The other wife would only bring her husband to the public square if she knew that no other husbands were cheating. Because she doesn't bring him, at least one other husband must be cheating. Because the only unknown value
for the first wife is her own husband, she concludes that he must be cheating.) Both wives bring their husbands to the public square
on day two.
If there are three cheating husbands, each wife
sees the other cheated-on wives not bring her husband to the public square on day one, or day two. Therefore, she concludes that her own husband
is cheating. (The other wives must know someone else is cheating, and that someone else must be her husband.) All three bring their husbands to the public town on day three
Thus, given k
cheating husbands, they will all be brought to town on day k
. Assuming, of course, that the wives are inclined toward reasoning things out rather than beating their husbands with a frying pan
until they 'fess up.