Logic Puzzle

Author: mistertfy64

Find the amount of permutations of {1, 2, 3, 4, 5, 6, 7, 8, 9} that satisfy these conditions:

• The first number from the left is divisible by the fifth number from the left.
• The second number from the left is divisible by the sixth number from the left.
• The product of the third number from the left and the fourth number from the left is equal to or greater than 15.
• The rightmost number, that is, the ninth number from the left, is even.

Formally, find the number of permutations p of {1, 2, 3, 4, 5, 6, 7, 8, 9} such that:

• p₁ mod p₅ = 0, that is, there exists an integer a that ap₅ = p₁.
• p₂ mod p₆ = 0, that is, there exists an integer b that bp₆ = p₂.
• p₃p₄ ≥ 15
• p₉ mod 2 = 0, that is, there exists an integer c that 2c = p₉.

Two such permutations to include are {4, 3, 5, 9, 2, 1, 8, 7, 6} and {7, 4, 3, 9, 1, 2, 5, 8, 6}.

Correct Answers