How to Solve It?

Solve. (Halmos) Every man in a village knows instantly when another’s wife is unfaithful, but never when his own is. Each man is completely intelligent and knows that every other man is. The law of the village demands that when a man can PROVE that his wife has been unfaithful, he must shoot her before sundown the same day. Every man is completely law-abiding. One day the mayor announces that there is at least one unfaithful wife in the village. The mayor always tells the truth, and every man believes him. If in fact there are exactly forty unfaithful wives in the village (but that fact is not known to the men,) what will happen after the mayor’s announcement?

See here.


  1. 1 3 5 horizontal
    2 3 4 vertically. And vice versa

    3 is common and sum is rest two is same both ways.

  2. If x1,x2,x3,x4 &x5 are 5 numbers ;
    If Any xi comes in center i=1,2,3,4,5;
    Then sum of two is sum of remaining two excluding xi;
    If xi=1 remainings are 2,3,4 &5 :- 2+1+5( let it be Horizontal)=3+1+4(let it be vertical);
    3+1+4 ( let it be Horizontal)=2+1+5(let it be vertical);

    If xi=2 remainings are 1,3,4 & 5:- Solution not possible;
    If xi=3 remainings are 1,2,4 &5 :- 1+3+5(H)=2+3+4(V);
    If xi=4 remainings are 1,2,3 & 5:- Solution not possible;
    If xi=5 remainings are 1,2,3,4 – (1+5+4)(H)=(2+5+3)(V);

  3. There are two possibilities in adding the five numbers to equal eight: 1,2,5 and 1,3,4. The number common to both permutations is 1. Therefore, the number in middle can only be 1.

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