Filling Up A Grid - 3 * 3 Ring

Probability Level 2

Is it possible to fill the squares of the above grid with the integers from 1 to 8 (using each only once) so that no two adjacent squares (sharing a side or a corner) contain consecutive integers?

Yes No

Chung Kevin by Chung Kevin , 45, Australia

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1 solution

Starting at the top left box and going around clockwise, four valid "rings" are

( 1 , 4 , 2 , 7 , 5 , 3 , 8 , 6 ) , ( 1 , 4 , 7 , 2 , 5 , 8 , 3 , 6 ) , ( 4 , 1 , 6 , 3 , 8 , 5 , 2 , 7 ) (1,4,2,7,5,3,8,6), (1,4,7,2,5,8,3,6), (4,1,6,3,8,5,2,7) and ( 3 , 1 , 7 , 5 , 8 , 2 , 4 , 6 ) (3,1,7,5,8,2,4,6) .

The next challenge would be to determine the total number of valid rings, independent of rotation, and thus also what percentage of the 8 ! / 4 = 10080 8!/4 = 10080 possible rotation-independent fill-ins are valid rings.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice follow up question.

There's a nice way to restate the question, but it don't know if that helps with counting the number of ways easily.

Chung Kevin - 4 years, 4 months ago

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