IKMC 2023 - Grades 9-10 - Self-study Question 30

Question 30

Pia places the integers 1 to 9 in nine boxes in a row, one in each, so any three adjacent boxes have a sum divisible by 3. How many arrangements are possible?

Question illustration

$6^4$
$6^3$
$2^9$
6 × 5 × 4 × 3 × 2 × 1
9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1