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
If you could help me out I would really appreciate this.
Sep 9th 2007, 02:43 PM
This takes simple reasoning ... but a lot of it!
Solve the alphametic:
A N N
B E L
Consider the possible values for
; the product would be zero.
; the product would be
; the product would be a four-digit number.
. . Hence,
Then we have:
3 N N
- - -
9 E L
In the leftmost multiplication, we have: . . . There is no "carry" from the second multiplication,
But none of these will work. . . If , we have: . . . If , we have: . . . If , we have: .
In all cases, . . . which is not allowed.
And we have:
2 N N
- - -
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: .
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.