Maths Olympiad Prep

Track / Stage 4 / 147 of 340 #407 of 1964

Problem 407

AMC 12 late, AIME early
Number theory Difficulty 4.8 Find the answer

Write 7 consecutive natural numbers such that among the digits in their notation there are exactly 16 twos. (Consecutive numbers differ by 1.)

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

Answer. Any of the following two sequences will do:

2229, 2230, 2231, 2232, 2233, 2234, 2235

2215, 2216, 2217, 2218, 2219, 2220, 2221

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.