MathDB
Springs are fired inXMO

Source: 16thXMO

June 22, 2024
contestscombinatorics

Problem Statement

Given an integer nn ,For a sequence of XX with the number of nn and YY with the number of 100n100n , we call it a spring . We have two following rules \blacksquare Choose four adjacent character , if it is YXXYYXXY , than it can be changed into XYYXXYYX \blacksquare Choose. four adjacent character , if it is XYYXXYYX , than it can be changed into YXXYYXXY If spring AA can become BB using the rules , than we call they are [color=#3D85C6]similar Thy to find the maximum of CC such that there exists CC distinct springs and they are [color=#3D85C6]similar