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Problem 514

AMC 12 late, AIME early

Number theory Difficulty 4.9 Find the answer

1. [3] Several natural numbers are written in a row with a sum of 20. No number and no sum of several consecutive numbers equals 3. Could there be more than 10 numbers written?

A. Shapovalov

Your answer

Official solution

Answer: could.

Solution. An example with 11 numbers: $1,1,4,1,1,4,1,1,4,1,1$ . It can be proven that more than 11 numbers could not have been written down. See also the more general problem 5 for higher grades.

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