• Jul 17th 2006, 09:31 PM
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?
• Jul 17th 2006, 09:39 PM
malaygoel
Quote:

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
• Jul 18th 2006, 07:23 AM
Soroban
Sorry, Malay . . .
Hello, Judi!

Quote:

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: $B + C \,= \,11$

• Jul 18th 2006, 08:20 AM
malaygoel
I made a mistake: Duplicate Values....Sorry

Keep Smiling
Malay
• Jul 18th 2006, 08:31 AM
Judi
thanks...