🦘 Math Kangaroo Grade All Felix 1-2 Ecolier 3-4 Benjamin 5-6 Kadett 7-8 Junior 9-10 Student 11-12 ⇄ switch contest
2022 Math Kangaroo

Problem 8

Problem 8 · 2022 Math Kangaroo Medium
Counting & Probability careful-counting

All integers from 2 to 2022 which can be written using only the digits 0 and 2 are written in ascending order in a list. Which number is the middle number on that list?

Show answer
Answer: B — 220
Show hints
Hint 1 of 2
List every number from 2 to 2022 using only the digits 0 and 2.
Still stuck? Show hint 2 →
Hint 2 of 2
There are 11 such numbers; the middle one is the 6th.
Show solution
Approach: list and pick the middle
  1. The numbers are 2, 20, 22, 200, 202, 220, 222, 2000, 2002, 2020, 2022 — eleven of them.
  2. The middle (6th) number is 220.
Mark: · log in to save