NR
+ RN
_______
ABC

The addition problem above is correct. If N, R, A, B, and C are different digits, what is the greatest possible value of B+C?

2. Originally Posted by Judi
NR
+ RN
_______
ABC

The addition problem above is correct. If N, R, A, B, and C are different digits, what is the greatest possible value of B+C?
A is clearly 1
N+R is a two digit number.
B=C+1
We have to find max. value of C
since N and R are different
N=9, R=8
C=7,B=8,A=1

Keep Smiling
Malay

3. ## Sorry, Malay . . .

Hello, Judi!

Code:
  1 2 3

N R
+ R N
-----
A B C
The addition problem above is correct.
If N, R, A, B, and C are different digits,
what is the greatest possible value of $\displaystyle B+C$?

In column-1, we see that $\displaystyle A = 1.$
Code:
  1 2 3

N R
+ R N
-----
1 B C

In column-3, we see that $\displaystyle R + N$ ends in $\displaystyle C.$
In column-2, we see that $\displaystyle N + R$ ends in $\displaystyle B.$

Then $\displaystyle R + N \geq 10$ and there is a "carry" to column-2
. . where we have: $\displaystyle N + R + 1 \:=\:10 + B$

For maximum $\displaystyle B + C$, let $\displaystyle \{R,N\} = \{8,9\}$
. . But we find that this results in duplicated digits.

For $\displaystyle R = 9$ we have:
Code:
    N 9
+ 9 N
-----
A B C

But we get: $\displaystyle B = N.$
. . (If $\displaystyle N = 9$, then $\displaystyle B = R.$)

Hence, neither $\displaystyle R$ nor $\displaystyle N$ can be $\displaystyle 9.$

The next largest sum occurs for: $\displaystyle \{R,N\} = \{7,8\}$ and we have:
Code:
    8 7
+ 7 8
-----
1 6 5
Therefore: $\displaystyle B + C \,= \,11$

4. I made a mistake: Duplicate Values....Sorry

Keep Smiling
Malay

5. thanks...