2023 IMO Problems/Problem 5
Problem
Let be a positive integer. A Japanese triangle consists of circles arranged in an equilateral triangular shape such that for each , , , , the row contains exactly circles, exactly one of which is coloured red. A ninja path in a Japanese triangle is a sequence of 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 , along with a ninja path in that triangle containing two red circles.
In terms of , find the greatest such that in each Japanese triangle there is a ninja path containing at least red circles.
Solution
https://www.youtube.com/watch?v=jZNIpapyGJQ [Video contains solutions to all day 2 problems]
See Also
2023 IMO (Problems) • Resources | ||
Preceded by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 6 |
All IMO Problems and Solutions |