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Odd Determinants of a Square Array (Posted on 2024-05-29)

Find the number of ways in which the nine digits 1,2,3,...,9 can be arranged in a 3*3 square array such that the determinant of this square is an odd integer. Each digit to be used only once.

No Solution Yet Submitted by Danish Ahmed Khan

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A different answer

| Comment 3 of 7 |

aSet=perms(1:9);

oddCt=0;

for i=1:length(aSet)

a=reshape(aSet(i,:),[3 3]);

if mod(det(a),2)==1

oddCt=oddCt+1;

end

oddCt

finds

oddCt =

108585

showing 108585 of the 9! = 362880 determinants are odd.

Posted by Charlie on 2024-05-29 15:17:01

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