2024 AMC 10A Problem 4

Question

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?

20

21

22

23

24

The largest two-digit number is

99,

so

k

numbers sum to at most

99k

Find the least

k

with

99k \ge 2024,

then confirm that many two-digit numbers can reach

2024

Each two-digit number is at most

99,

so

k

of them sum to at most

99k.

We need

99k \ge 2024,

which forces

k \ge 20.4,

so

k \ge 21.

And

21

really works: twenty

99

s plus one

44

give

1980 + 44 = 2024.

Therefore, the answer is B.

Problem 4 in other years