MathDB

A four-digit number

n

is said to be literally 1434 if, when every digit is replaced by its remainder when divided by

5

, the result is

1434

. For example,

1984

is literally 1434 because

1

mod

5

1

9

mod

5

4

8

mod

5

3

, and

4

mod

5

4

. Find the sum of all four-digit positive integers that are literally 1434.
Proposed by Evin Liang
Solution.

\boxed{67384}

The possible numbers are

\overline{abcd}

where

a

1

6

b

4

9

c

3

8

, and

d

4

9

. There are

16

such numbers and the average is

\dfrac{8423}{2}

, so the total in this case is

\boxed{67384}

Problem Statement