1996 AMC 12 Problem 14

Attempt Problem 14 of the 1996 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1996 AMC 12 solutions, or check the answer key.

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14.

Let

E(n)

denote the sum of the even digits of

n.

For example,

E(5681)=6+8=14.

Find

\begin{gathered} E(1)+E(2)+E(3)+\cdots\\ {}+E(100). \end{gathered}

200

360

400

900

2250

Include leading zeros and consider the integers from

00

through

99

In each digit position, every digit occurs equally often

From

00

through

99,

each digit occurs

10

times in each of the two positions. The positive even digits sum to

2+4+6+8=20,

so the total contribution is

2\cdot10\cdot20=400.

The number

100

contributes no even positive digit, so the correct answer is C.

Problem 14 in other years