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The six ten total challenge have only 8 combinations.

1st combination: Blue=4 Red=6 Total=84

2nd combination: Blue=1 Red=3 Total=36

3rd combination: Blue=3 Red=5 Total=68

4th combination: Blue=2 Red=4 Total=52

5th combination: Blue=3 Red=1 Total=28

6th combination: Blue=6 Red=4 Total=76

7th combination: Blue=5 Red=3 Total=60

8th combination: Blue=4 Red=2 Total=44

These are all the combinations that apply to the rules of six ten total.

We also found out, if you put the totals in order: 28,36,44,52,60,68,76,84.
There is a difference of 8 in between them.

We only found one 42 total combination which doesn't apply all the rules.
The combination is: Blue=2 Red=3 Total=42