How to add within elements of a list?

Question

I'm trying to show the possible combinations of rolling 3 dice and taking the sum of the two highest numbers

dice = {1, 2, 3, 4, 5, 6}
j = Flatten[Outer[List, dice, dice, dice], 2]
j1 = Table[Extract[j, {i, 2}], {i, 1, 216}];
j2 = Table[Extract[j, {i, 3}], {i, 1, 216}];
Transpose[{j1, j2}];

How can I add the two elements up of each part of the last line (Transpose...) to give the sums ranging from 2 to 12? Thank you

Answer 1

You can simply add your j1 and j2:

rowtotals  = j1 + j2;

Total[Transpose[{j1, j2}], {2}] == rowtotals

True

Note that you can use {2} in the second argument of Total to get row totals.

You can get the same result using a combination of Tuples and Total as suggested by J.M. in comments:

Total[Tuples[Range @ 6, 3][[All, 2 ;;]], {2}] == rowtotals

True

ListLinePlot[rowtotals]