[Mathematical logic (miscellaneous).] $[$ Arithmetic. Mental arithmetic, etc. ]

In the room, there are 85 balloons — red and blue. It is known that: 1) at least one of the balloons is red; 2) in every arbitrarily chosen pair of balloons, at least one is blue. How many red balloons are in the room?
Think about whether there can be two red balls in the room.

## Solution

Since among any two balls, one is blue, there cannot be two red balls in the room. Therefore, there are 84 blue balloons and 1 red balloon in the room.

## Answer

1 ball.