# Dice sums

I have 4 (distinct) dice, each with 6 faces labelled $$1,2,3,4,5,6$$, and I roll all 4 simultaneously. Let $$d_{1}$$ be the number that comes up on the first dice, $$d_{2}$$ be the number that comes up on the second dice, $$d_{3}$$ be the number that comes up on the third dice and $$d_{4}$$ be the number that comes up on the fourth dice. In how many ways can I roll the 4 dice in this way so that 3 divides $$d_{1} + d_{2} + d_{3} + d_{4}$$?

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