Olympiad Maths Prep

Track / Stage 5 / 50 of 400 #650 of 2000

Problem 650

AIME late
Number theory Difficulty 5.2 Find the answer

4. A string contains several even natural numbers. Each number, except the leftmost one, is obtained by subtracting the largest digit of its left neighbor from it. Can the string contain more than 12 numbers?

Official solution

4. Answer. Yes, it can. Solution: For example, the following sequence of 13 numbers works: 888, 880, 872, 864, 856, 848, 840, 832, 824, 816, 808, 800, 792. Note that other examples are not excluded, and it is necessary to carefully check the condition that all numbers are even.

Criteria: any correct example of a sequence - 7 points; in all other cases 0 points.

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