[Guest]

Substitute each of the capital letters in bold by a different base ten digit from 0 to 9, to satisfy this alphametic equation. None of L and R is zero.

89 (LARGE) = REGION

Note: While a solution is trivial with the aid of a computer program, show how to derive it without one.

Edited June 20, 2009 by K Sengupta

[Guest]

Never did one of these before, but am I right in thinking that:

L=1 and

A=0

Because if either of them is a larger number, then multipling LARGE times 89 will result in a 7 digit number, instead of the six required to fit REGION?

It's not much, but I'm wondering if I'm on the right track.

[Guest]

Since large is a 5 digit number and region is only 6. The large must start with a 10 in order for it to be multiplied by 89 and not hit into the millions.

Just by process of elimination

10294 X 89 = 910826

10987 X 89 = 977843

so region is betweeen that 977826 and 910826

So R is 9

So now LARGE is now 109XX.

89 X 10987 = 977843

89 X 10923 = 972147

Now we know region is 97gion.

G can only be 2-8, exlcuding 7, and LARGE can only be 109G7.

So just process of counting up,

89 * 10947 = 974283

89 (LARGE) = REGION

Well this is my first "I completed this post, with my answer". I think I got it.

BTW, I like all the topics you've done K Sengupta, I'd like to see more.

Sorry if there are some grammatical errors.

Edited June 20, 2009 by JeRaph

[Guest]

BTW, I like all the topics you've done K Sengupta, I'd like to see more.

Sorry if there are some grammatical errors.

Since large is a 5 digit number and region is only 6. The large must start with a 10 in order for it to be multiplied by 89 and not hit into the millions.

Just by process of elimination

10294 X 89 = 910826

10987 X 89 = 977843

so region is betweeen that 977826 and 910826

So R is 9

So now LARGE is now 109XX.

89 X 10987 = 977843

89 X 10923 = 972147

Now we know region is 97gion.

G can only be 2-8, exlcuding 7, and LARGE can only be 109G7.

So just process of counting up,

89 * 10947 = 974283

89 (LARGE) = REGION

Well this is my first "I completed this post, with my answer". I think I got it.

Welcome to Brainden, JeRaph, and what a way for an entry!!!

You have hit the nail right on the head with this one. Indeed, the answer is:

89*(10947) = 974283

I will not post an official solution, since that would be a precise duplication of your methodology.