In the image, there is a number line with marked numbers 10 and 30 and other unnamed points representing whole numbers. Janek marked his favorite number and four other numbers on this line, about which we know that:

- one is half of Janek's number,
- one is 6 greater than Janek's number,
- one is 10 less than Janek's number,
- one is twice as large as Janek's number.

Determine which number is Janek's favorite.

(S. Bednářová)

![](https://cdn.mathpix.com/cropped/2024_04_17_f467490caffab06dae3cg-4.jpg?height=83&width=1100&top_left_y=852&top_left_x=478)
Between the numbers 10 and 30, there are 10 segments. Thus, one segment has a length of 2, and the numbers marked by dots are in sequence $6, 8, 16, 22$, and 32.

![](https://cdn.mathpix.com/cropped/2024_04_17_f467490caffab06dae3cg-4.jpg?height=91&width=1100&top_left_y=1154&top_left_x=478)

From the problem statement, it follows that among these five numbers, there are two smaller and two larger than Jan's favorite number. Therefore, Jan's number must be 16:

- 8 is half of 16,
- 22 is 6 more than 16,
- 6 is 10 less than 16,
- 32 is twice as large as 16.

Scoring. 3 points for determining the numbers marked by dots; 3 points for determining Jan's favorite number (1 point for verifying all conditions in the problem statement).