
need help please!!!
Ann A. Bel, a bright mathematices student, has discovered something interesting about her name. If the letters are arranged as they are below, it is possible to replace each different letter with a different digit and have the multiplication work out correctly. What digit should replace each letter? Be sure to expain your work
ANN
x A
BEL
If you could help me out I would really appreciate this.
Thanks

Hello, dlhenry!
This takes simple reasoning ... but a lot of it!
Quote:
Solve the alphametic: Code:
A N N
x A

B E L
Consider the possible values for
; the product would be zero.
; the product would be
; the product would be a fourdigit number.
. . Hence,
Suppose .
Then we have: Code:
3 N N
x 3
  
9 E L
In the leftmost multiplication, we have: .
. . There is no "carry" from the second multiplication,
Hence: .
But none of these will work.
. . If , we have: .
. . If , we have: .
. . If , we have: .
In all cases, . . . which is not allowed.
Therefore: .
And we have: Code:
2 N N
x 2
  
B E L
In the rightmost mutliplication: . ends in
In the second multiplication: . ends in , a different digit.
Hence, there must be a "carry" from the first multiplcation.
. . So,
Since the second multiplication will also have a "carry",
. . the leftmost multiplication is: .
Therefore: .
So: .
If , we have: .
. . which makes . . . and 2 is already used.
If , we have: .
. . which makes . . . and 5 is already used.
If , we have: .
. . which makes . . . and 9 is already used.
The only remaining choice is: .
Therefore, the solution is: Code:
2 8 8
x 2
  
5 7 6