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 $B+C$?

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

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

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

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

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

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

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

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

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

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

Keep Smiling
Malay

5. thanks...