Difference between revisions of "2023 IMO Problems/Problem 5"
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| − | <math>k= | + | <math>k=[log2(n)]+1</math> |
https://www.youtube.com/watch?v=jZNIpapyGJQ [Video contains solutions to all day 2 problems] | https://www.youtube.com/watch?v=jZNIpapyGJQ [Video contains solutions to all day 2 problems] | ||
Revision as of 16:36, 30 April 2024
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.
[Image to be inserted; also available in solution video]
Solution
![$k=[log2(n)]+1$](http://latex.artofproblemsolving.com/f/8/2/f82f1ca33f6eae2c37bbedd1da752d11a8f3bc1c.png)
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 | ||
