Shapovalov A.V.

One hundred seats of a carousel are arranged in a circle at equal intervals. Each is painted yellow, blue, or red. Seats of the same color are placed consecutively and numbered $1,2,3, \ldots$ clockwise. The blue seat № 7 is opposite the red seat № 3, and the yellow seat № 7 is opposite the red seat № 23. Find how many yellow, blue, and red seats there are on the carousel.
Between the 3rd and 23rd red seats, there are 19 seats, so there are also 19 seats between the 7th blue and the 7th yellow. These are the first six yellow seats, and thus, 19-6=13 blue seats with numbers greater than 7. From this, we find that the total number of blue seats is $7+13=20$.

![](https://cdn.mathpix.com/cropped/2024_05_06_73983c7cc26f0024f238g-08.jpg?height=895&width=807&top_left_y=499&top_left_x=111)

Traversing half a circle clockwise from the 3rd red seat to the 7th blue seat, we pass (not counting these two) (100-2):2=49 seats. Six of them are blue, and the remaining 49-6=43 are red. Therefore, the total number of red seats is $3+43=46$. The number of yellow seats is $100-20-46=34$.

## Answer

Yellow: 34, Blue: 20, Red: 46.