Question

An equation is written where the sum of two 3-digit numbers is a 3-digit number N. Each digit, 1 through 9, is used exactly once. What is the largest possible value of N?

I have an idea of how to carry this out, I just need a more mathematical procedure to use. Thanks :)

Answer 1

Hello there.

An equation is written where the sum of two 3-digit numbers is a 3-digit number N. Each digit, 1 through 9, is used exactly once. What is the largest possible value of N?

1839

Answer 2

We can start with:
x + y = N
where
x is the first 3 digit number
y is the second 3 digit number

In order to get the maximum value of N, the digits used must 9,8,7,6,5,4
To maximize, 9 and 8 must be added. This can only happen if 9 is the first digit of the first number and 8 is the first digit of the second number. The same idea is applied to the other digits. So
x must be 975 and
y must be 864
N = 975 + 864 = 1839