Maths Olympiad Prep

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Problem 349

Combinatorics Difficulty 2.0 Find the answer CEMC Gauss (Grade 7) · Canada · 2005

Chris and Pat are playing catch. Standing 11 m apart, Pat first throws the ball to Chris and then Chris throws the ball back to Pat. Next, standing 22 m apart, Pat throws to Chris and Chris throws back to Pat. After each pair of throws, Chris moves 11 m farther away from Pat. They stop playing when one of them misses the ball. If the game ends when the 2929th throw is missed, how far apart are they standing and who misses catching the ball?

(A) 1515 m, Chris (B) 1515 m, Pat (C) 1414 m, Chris (D) 1414 m, Pat (E) 1616 m, Pat

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