4. There are 2019 penguins waddling towards their favourite restaurant. As
the penguins arrive, they are handed tickets numbered in ascending order
from 1 to 2019, and told to join the queue. The first penguin starts the queue.
For each n > 1 the penguin holding ticket number n finds the greatest m < n
which divides n and enters the queue directly behind the penguin holding
ticket number m. This continues until all 2019 penguins are in the queue.
(a) How many penguins are in front of the penguin with ticket number 2?
(b) What numbers are on the tickets held by the penguins just in front of
and just behind the penguin holding ticket 33?
Bạn đang xem 4. - ĐỀ THI OLYMPIC TOÁN HỌC QUỐC TẾ BMO NĂM 2020
