Pencils grouping question?

There are 20 red pencils, 13 green, 12 yellow and 15 blue. If they are evenly distributed into groups of 3 with different colors, how many groups will you have? This is not a combinations/permutations question, just a straight up how many groups of 3 can you create where the pencils in each group is a different color.

I had to do this by hand but I am wondering if there is a formula for this type of thing. Below is what I did, resulting in 20 groups. I used red all the way through since there were more red pencils than any other color. Then I kept the others colors balanced, rotating between them. Is there a more efficient way to tackle this, like a formula?

start with 20 red pencils, 13 green, 12 yellow and 15 blue

group #1 rgb

leaving 19 red pencils, 12 green, 12 yellow and 14 blue

group #2 rgb

leaving 18 red pencils, 11 green, 12 yellow and 13 blue

group #3 ryb

leaving 17 red pencils, 11 green, 11 yellow and 12 blue

group #4 rgb

leaving 16 red pencils, 10 green, 11 yellow and 11 blue

group #5 ryb

leaving 15 red pencils, 10 green, 10 yellow and 10 blue

group #6 rgy

leaving 14 red pencils, 9 green, 9 yellow and 10 blue

group #7 rgb

leaving 13 red pencils, 8 green, 9 yellow and 9 blue

group #8 ryb

leaving 12 red pencils, 8 green, 8 yellow and 8 blue

......... keep doing this.for a while.....

1 red pencils, 0 green, 1 yellow and 1 blue

group 20 ryb

leaving 0 red pencils, 0 green, 0 yellow and 0 blue

2 Answers

Relevance
  • 1 month ago

    You can only can do the green and yellow twice so you will have 50 groups but green has one green to many so it would be 49 for yellow control the green's count.......  

  • Anonymous
    1 month ago

    Wrong forum! This is a math question, not a drawing & illustration question 

    .

    Fail

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