# No 3's Allowed!

Discrete Mathematics Level 4

Let $$P = (p_1, p_2, \ldots, p_7)$$ be a permutation of the integers $$1, 2, \ldots 7$$. For how many permutations $$P$$ are all seven sums $$S_1 = p_1$$, $$S_2 = p_1 + p_2$$, $$\ldots$$ and $$S_7 = p_1 + p_2 + \cdots + p_7$$ not multiples of 3?

Details and assumptions

A permutation is a rearrangement of the entire set of objects.

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