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 \( d_{1} + d_{2} + d_{3} + d_{4} \)?
by
Josh Rowley