2023 IMO Problems/Problem 5

Problem

Let $n$ be a positive integer. A Japanese triangle consists of $1 + 2 + \dots + n$ circles arranged in an equilateral triangular shape such that for each $i = 1$ , $2$ , $\dots$ , $n$ , the $i^{th}$ row contains exactly $i$ circles, exactly one of which is coloured red. A ninja path in a Japanese triangle is a sequence of $n$ circles obtained by starting in the top row, then repeatedly going from a circle to one of the two circles immediately below it and finishing in the bottom row. Here is an example of a Japanese triangle with $n = 6$ , along with a ninja path in that triangle containing two red circles.

[Image to be inserted; also available in solution video]

Solution

$k=\floor(\log_2(n))+1$ (Error compiling LaTeX. Unknown error_msg) https://www.youtube.com/watch?v=jZNIpapyGJQ [Video contains solutions to all day 2 problems]

2023 IMO (Problems) • Resources
Preceded by Problem 4	1 • 2 • 3 • 4 • 5 • 6	Followed by Problem 6
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2023 IMO Problems/Problem 5

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