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?

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- Jul 17th 2006, 09:31 PMJudiaddition
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 PMmalaygoelQuote:

Originally Posted by**Judi**

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

Answer is 15

Keep Smiling

Malay - Jul 18th 2006, 07:23 AMSorobanSorry, Malay . . .
Hello, Judi!

Quote:

Code:`1 2 3`

N R

+ R N

-----

A B C

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

- Jul 18th 2006, 08:20 AMmalaygoel
I made a mistake: Duplicate Values....Sorry

Keep Smiling

Malay - Jul 18th 2006, 08:31 AMJudi
thanks...