Combinatorics › Pigeonhole and extremal problems › Coloured beads and balloons
Distinct candy flavors by percent red
High school · ●●○○○ 20 pts
Four red candies and three green candies can be combined to make many different flavors. Two flavors are different if their percent red is different, so 3 red / 0 green is the same flavor as 2 red / 0 green, and 4 red / 2 green is the same flavor as 2 red / 1 green. If a flavor is made using some or all of the seven candies (at least one candy), how many different flavors are possible?