Maths Olympiad Prep

Track / Stage 4 / 131 of 340 #391 of 1964

Problem 391

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

5. 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.

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 and solution reproduced as published; topic, difficulty and ordering added by this site.