In a garden there are three kind of roses-red, yellow and white. No matter which 9 roses are selected at least 2 of them are white; and no matter which 10 roses are selected at least 2 of them are yellow and o matter which 11 roses are selected at least 2 of them are red. Find out how many roses were there in the garden.
2026-03-29 17:31:34.1774805494
counting of numbers
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Hint: how many non-white roses can there be? If there are $r$ red roses and $y$ yellow ones, the sum must be less than or equal to this. You also need at least $2$ roses of each color and $11$ total. I find four solutions, but there is one that could be argued for as the "correct answer".