MathDB
Heaps of stones

Source: All-Russian MO 2023 Final stage 9.5

April 23, 2023
combinatorics

Problem Statement

If there are several heaps of stones on the table, it is said that there are <spanclass=latexitalic>many</span><span class='latex-italic'>many</span> stones on the table, if we can find 5050 piles and number them with the numbers from 11 to 5050 so that the first pile contains at least one stone, the second - at least two stones,..., the 5050-th has at least 5050 stones. Let the table be initially contain 100100 piles of 100100 stones each. Find the largest n10000n \leq 10 000 such that after removing any nn stones, there will still be <spanclass=latexitalic>many</span><span class='latex-italic'>many</span> stones left on the table.