[ Mathematical logic (other).]

Lilac. In a vase, there is a bouquet of 7 white and blue lilac branches. It is known that 1) at least one branch is white, 2) out of any two branches, at least one is blue. How many white branches and how many blue branches are in the bouquet?

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Think about how many white branches there can be.

## Solution

From the first condition, it follows that there is at least one white branch. From the second condition, it follows that there is only one such branch: indeed, if there were at least two, then taking these two branches, we would get a pair in which there is no blue branch, i.e., condition 2 would not be satisfied. From this, we immediately get that there is one white branch, and the other six are blue.