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Problem 421

Combinatorics Difficulty 2.0 Find the answer UKMT Grey Kangaroo · United Kingdom · 2024

A group of 50 girls sit in a circle. They throw a ball around the circle. Each girl who gets the ball throws it to the girl sitting six places anticlockwise from her, who catches it. Freda catches the ball 100 times. In that time, how many girls never get to catch the ball?

(A) $0$ (B) $8$ (C) $10$ (D) $25$ (E) $40$

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