IKMC 2006 - Grades 11-12 - Self-study Question 28

Question 28

Place 1, …, 6 once each in the six squares shown. How many ways avoid edge-adjacent numbers differing by 3? Corner contact is not adjacency.

Question illustration

$3\times2^5$
$3^6$
$6^3$
$2\times3^5$
$3\times5^2$