4B. Around are placed 10 children. Ivo needs to join them. They will all play the elimination game in the following way: they start counting from the number 1 in the direction of the clock's hands, and the one on whom the number 13 falls is eliminated from the game. The counting continues with the remaining children where it was interrupted, and the thirteenth one is again eliminated from the game, etc. At which position (between which two of the ten marked numbers, see image) should Ivo stand to be the last one in the game?

![](https://cdn.mathpix.com/cropped/2024_06_05_a6c2bf676fcc39861820g-03.jpg?height=377&width=360&top_left_y=840&top_left_x=666)
Solution. When Ivica enters the circle, there will be 11 children in it. By crossing out every 13th number (not counting the already crossed out ones) and marking them with

![](https://cdn.mathpix.com/cropped/2024_06_05_a6c2bf676fcc39861820g-03.jpg?height=416&width=411&top_left_y=1311&top_left_x=669)

Roman numerals according to the order in which they fall out, we get the image above.

This means that the number 7 remains. According to this, to win, i.e., to be the last one standing in the counting, Ivica needs to stand between the numbers 6 and 7.

## II year