2024 AMC 10A Problem 4

Problem 4 of 25EasierAlgebra

The number

2024

is written as the sum of not necessarily distinct two-digit numbers. What is the least number of two-digit numbers needed to write this sum?

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Solution

Each two-digit number is at most

99,

k

of them sum to at most

99k.

We need

99k \ge 2024,

which forces

k \ge 20.4,

k \ge 21.

And

21

really works: twenty

99

s plus one

44

give

1980 + 44 = 2024.

Therefore, the answer is B.

Concepts: inequality · bounding to limit cases · optimization

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.