Difference between revisions of "2022 IMO Problems/Problem 1"
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==Solution== | ==Solution== | ||
https://www.youtube.com/watch?v=nYD-qIOdi_c [Video contains solutions to all day 1 problems] | https://www.youtube.com/watch?v=nYD-qIOdi_c [Video contains solutions to all day 1 problems] | ||
| + | https://youtu.be/KHn3xD6wS3A | ||
| + | [Video contains problem 1 discussion] | ||
Revision as of 10:41, 16 August 2022
Problem
The Bank of Oslo issues two types of coin: aluminium (denoted A) and bronze (denoted B). Marianne has 
aluminium coins and bronze coins, arranged in a row in some arbitrary initial order. A chain is any subsequence of consecutive coins of the same type. Given a fixed positive integer 
, Marianne repeatedly performs the following operation: she identifies the longest chain containing the 
coin from the left, and moves all coins in that chain to the left end of the row. For example, if 
and 
, the process starting from the ordering AABBBABA would be
AABBBABA → BBBAAABA → AAABBBBA → BBBBAAAA → BBBBAAAA → ...
Find all pairs 
with 
such that for every initial ordering, at some moment during the process, the leftmost coins will all be of the same type.
Solution
https://www.youtube.com/watch?v=nYD-qIOdi_c [Video contains solutions to all day 1 problems] https://youtu.be/KHn3xD6wS3A [Video contains problem 1 discussion]
