# A day at the circus (pay attention)

When I went to a circus show I saw the following:

• Exactly x red balloons
• Exactly half as many green balloons than red balloons
• Exactly one fifth blue balloons than green balloons.

These were the only balloons at the show (none others). And they were either small, medium or large. I noticed that there were just as many red as green large balloons. There were nine large balloons in total. Two of the balloons were small and with different colors. And the rest of the balloons were medium.

Question:

How was the different sizes distributed among the red, green, blue balloons? (how many red were small/medium/large? how many green, how many blue)

Note: I'm looking for specific numbers!

I think the balloon sizes are distributed as follows

Blue: 1 large.
Green: 4 large, 1 small.
Red: 4 large, 5 medium, 1 small

Reasoning

So on the face of it, there doesn't seem to be enough information but if we read the first line again: "Exactly x red balloons" and interpret the x as being the lowercase Roman numeral representing 10 then we see there are 10 red balloons, 5 green balloons and 1 blue balloon.

Since the number of large balloons is odd and there are as many red large as green large, the number of blue large balloons must be odd (i.e, 1) and the other eight large balloons are split equally between red and green. The two small balloons must then be red and green (as there are no more blue balloons) and the rest can be filled in as medium.

• This is correct :) Commented Jul 15, 2020 at 9:36
• @Prim3numbah Ah, okay, nice puzzle! Commented Jul 15, 2020 at 9:37