Logical Algebra

Solve the equation by replacing the alphabet with numbers.

MOM + MOM + NO = BOOK=




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A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

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Can you arrange all the 16 hats in a 4x4 grid in a fashion that no two rows and columns have a repetition of colour or sign?
We have arranged four hats in the below picture to assist you.

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In 2007, a puzzle was released and $2 million prizes were offered for the first complete solution. The competition ended at noon on 31 December 2010, with no solution being found. Wiki