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Problem 356

AMC 12 late, AIME early

Combinatorics Difficulty 4.8 Find the answer

1. Carolina has a box of 30 matches. She begins to make the number 2022 using matchsticks. The diagram shows the first two digits. How many matchsticks will be left in the box when she has finished?
A 20
B 19
C 10
D 9
E 5

Your answer

Official solution

Solution
D

Each of the twos in " 2022 " requires 5 matches, so 15 altogether. And she needs six matches for the zero, which leaves $30-15-6=9$ matches.

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