this is my kids math problem 4th grade and i have no idea
Answers (1)
Well, if you imply that has to be more than one cube to make it a row, the most rows you can have is six rows of two. Beyond that, some of the rows are going to have to have three or more cubes. If you have a row with three, then you can't use up all the cubes unless you have another odd number (say another three). If you carry on with this thinking, you get:
2 2 2 2 2 2
2 2 2 3 3
3 3 3 3
4 2 2 2 2
4 2 3 3
4 4 2
5 3 2 2
5 4 3
6 2 2 2
6 3 3
6 4 2
7 3 2
7 5
8 2 2
8 4
9 3
10 2
That's all the possible numbers of sets of rows. Seventeen! The question involve permutations too, though (i.e. 10 2 is a different answer than 2 10). If that's the case:
2 2 2 2 2 2 (only one combination of this because they're all 2's)
2 2 2 3 3 (ten combinations)
3 3 3 3 (one combination again)
4 2 2 2 2 (five combos as the 4 can be in one of five positions)
4 2 3 3 (twelve combinations)
4 4 2 (three combos)
5 3 2 2 (twelve)
5 4 3 (six)
6 2 2 2 (four)
6 3 3 (three)
6 4 2 (six)
7 3 2 (six)
7 5 (two)
8 2 2 (three)
8 4 (two)
9 3 (two)
10 2 (two)
Eighty combinations in total! This still assumes all the cubes are the same. If all the cubes are different colours and can be arranged in different groups of colours in their rows, then the number really ramps up. I'm guessing they wouldn't spring that on a fourth grader, though. The first answer is probably the one they meant.