Lenny Conundrum 211

[Jerch]

The Brightvale Institute of Technology needed new Maths books, so they ordered a new set from Brightvale Books.

When they got the books back from the printers, however, they discovered that there had been a horrible mistake. Apparently the printer scrambled up all the digits in the printing press, so all the numbers reflected wrong digits. Yet somehow, these mistakes were consistent throughout the book. (For example, all instances of the digit "2" would instead use the digit "7"... but that's just an example! Don't assume that that is a clue for this puzzle!)

Some examples that were printed in the book were:

518 x 70 = 6270

6481 + 3294 = 32847

7221 x ( 3334 + 3666 ) = ?

Using this numbering system, what would this book list as the answer to the problem 7221 x ( 3334 + 3666 )?

Hmm...

I would suggest using alphabetical variables to avoid confusion...
ie. 0=a, 1=b, etc.

...and writing a program that would cough up an answer to the question.

btw, 'example' might not be the most appropriate word for their case. I always like the word 'hint' more than 'clue' anyway... Glad that I'm not alone


The sum of all the digits of my answer is an odd number.

[AySz88]

Hmm, the sum of the digits to my (final) answer is an even number. The sum of the digits of the answer to the math problem (in everyday numbers) is an odd number, though.

And yes, brute force is the way to go here. I can't think of any analytical approach - the only approach I thought of ended up being a red herring. Of course, I took everything at face value...maybe there is an analytical way to do it if you didn't take the statement at face value. (At first glance, it at least reduces the brute force work by a factor of about 50.)

[edit: fixed first sentence]

Last edited by AySz88 on Thu Apr 12, 2007 7:18 pm, edited 1 time in total.

[Jerch]

To be fair though, you can use the analytical approach and find out the real value of some digits...

There are at least 3 digits that can be found in this way...

[yvonne_l_d]

I have the value of the 3 and the value of the 6, and I got that just by analysing. I don't really have the skills to build a program, so that's out of the question for me. I think I might be able to get them all, just by analysis.

[AySz88]

To be fair though, you can use the analytical approach and find out the real value of some digits...

There are at least 3 digits that can be found in this way...

If I'm seeing the same thing as you are, that needs a certain assumption, though it's probably safe to assume it. To make an analogy, I remember a puzzle that required you to assume "males don't live in pink houses" - the author might want you to assume it but that sort of thing just doesn't feel valid to me.

(I don't feel comfortable revealing requisite the assumption yet... maybe during the weekend.)

[Jerch]

To be fair though, you can use the analytical approach and find out the real value of some digits...

There are at least 3 digits that can be found in this way...

If I'm seeing the same thing as you are, that needs a certain assumption, though it's probably safe to assume it. To make an analogy, I remember a puzzle that required you to assume "males don't live in pink houses" - the author might want you to assume it but that sort of thing just doesn't feel valid to me.

(I don't feel comfortable revealing requisite the assumption yet... maybe during the weekend.)

As in the leftmost digit cannot be a 0?

Now that I think of it.... I treated "7221 x ( 3334 + 3666 )" literally.

[AySz88]

...Yeah. But isn't it reasonable for a basic arithmetic textbook to include some questions about leading zeros not mattering?