# Multiplication problem

• May 15th 2006, 07:42 AM
ferdo
Multiplication problem
Ann was a bright mathematics student, she discovered something interesting about her first 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.
ANN
X A
_____
BEL

Be sure to explain your work.

Thanks Im stumped
• May 15th 2006, 08:33 AM
CaptainBlack
Quote:

Originally Posted by ferdo
Ann was a bright mathematics student, she discovered something interesting about her first 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.
ANN
X A
_____
BEL

Be sure to explain your work.

Thanks Im stumped

Since BEL has only 3 digits A cannot be greater than 3, in fact it cannot
even be 3 (since the last two digits of BEL are different AxN>9, and so
there ill be a carry and ANNxA would have four digits).

Also A cannot be 1, since then AxANN=ANN, so we may conclude that A=2.

Finnaly trial and error will alow us to find that:

288
X 2
_____
576

RonL
• May 16th 2006, 09:23 AM
ferdo
Thanks for your quick response