Auto:: Shapovesov A.B.

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

![](https://cdn.mathpix.com/cropped/2024_05_06_eab8c6bbe58aee0b55b3g-10.jpg?height=889&width=807&top_left_y=1442&top_left_x=111)

Traversing half a circle clockwise from the 3rd red seat to the 7th blue seat, we pass (excluding these two) (100-2):2=49 seats. Six of these 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.