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A circus act consists of

2024

bamboo sticks of pairwise different heights placed in some order, with a monkey standing atop one of them. The circus master can then give commands to the monkey as follows:
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Left! : When given this command, the monkey locates the closest bamboo stick to the left taller than the one it is currently atop, and jumps to it. If there is no such stick, the monkey stays put. [color=#FFFFFF]___

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Right! : When given this command, the monkey locates the closest bamboo stick to the right taller than the one it is currently atop, and jumps to it. If there is no such stick, the monkey stays put.
The circus master claims that given any two bamboo sticks, if the monkey is originally atop the shorter stick, then after giving at most

c

commands he can reposition the monkey atop the taller stick. What is the smallest possible value of

c

?
Proposed by Archit Manas

20

Problems(1)