Dice sums

Discrete Mathematics Level 3

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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Dice sums

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.