Olympiad Maths Prep

Track / Stage 4 / 248 of 340 #508 of 2000

Problem 508

AMC 12 late, AIME early
Combinatorics Difficulty 4.9 Find the answer

2. On the table lie sticks of lengths 1,2,3,,n1,2,3, \ldots, n centimeters. It is known that from them, 50 triangles can be formed, using each stick no more than once, but 51 cannot. Find nn (the length of the longest stick)? If there are multiple possible answers, list them in ascending order separated by a semicolon.

Official solution

Answer: 151,152,153151;152;153151,152,153 \mid 151 ; 152 ; 153

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.