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AIMO 2021 Secondary 1 — Preliminary (Open Trial 1) Question 16

AIMO · AIMO 2021 Secondary 1 — Preliminary (Open Trial 1)

Question 16

Jane has 9 identical pieces of bite-size chocolate. She takes at least 1 piece each day. In how many ways can she finish the chocolate?

Original printed choices: A: $2^{10}$; B: $2^9$; C: 18; D: 20.

Editorial response format: give the exact answer; the original choices are retained for reference.

Convention: Count ordered sequences of positive daily amounts, ending on the day the last piece is taken.