Help needed for a certain type of puzzle

[+Vexidus]

I've been caching for a little while now, and am getting into puzzle caches. However, I'm very stuck with a certain type of puzzle, and can't even find information about what type of puzzle it is. Here's an example:

 

You must solve the following. The NINE letters represent the digits from 1 to 9

 

AB - CD > AD - CB

 

EC - FG > EG - FC

 

FH - AE > FE - AH

 

J > B

 

What in the world? I don't even know where to begin with that. I'd like to know what this type of puzzle is, and perhaps get a link to a tutorial about them, or something.

 

Thanks!

[+medwardl]

It's an algebraic problem I'll mull it over a bit I have done these in ages and this is a tougher one.

 

I think it's Boolean algebra I'm not certain yet Its been about 10 years since I've done anything this complex.

 

forgot to ask is that an actual problem or is that a random equation you came up with?

Edited May 11, 2011 by medwardl

[+medwardl]

My brain hurts If that is the actual equations then I'm not sure how to simplify it enough to solve it. It's been too long since I've done that kind of thing.

 

Basically one you simplify each expression to something like D>f you can then figure out the order of the letters and then assign numbers to them which I'm guessing the cache puzzle gives you a set of letters so once you figure out what number corresponds with what letter you can get your cords.

[+niraD]

I don't even know where to begin with that. I'd like to know what this type of puzzle is, and perhaps get a link to a tutorial about them, or something.

It's basically a type of logic puzzle. I haven't worked out this one, but I've solved others. They all work basically the same way.

 

In this case, you've got 9 letters that represent the digits 1-9. (Some puzzles use 10 letters that represent the digits 0-9 instead.) You need to work out which digit corresponds to each letter.

 

The equations provide some of the information you need. Sometimes, when multiple letters represent multi-digit numbers, it can be helpful to convert the equations to use single digits, multiplied by powers of 10. For example:

 

ABC + DEF = GHJK

 

could be converted to:

 

A*100 + B*10 + C + D*100 + E*10 + F = G*1000 + H*100 + J*10 + K

 

But that may or may not help, depending on the puzzle.

 

Also, don't forget to carry/borrow when you're doing the math. In the above example, it's tempting to assume that C+F=K. However, it is also possible that C+F=K+10.

 

One key to keep in mind is that the 9 (or 10) letters represent the 9 (or 10) digits. That means that each letter represents a different digit (otherwise, there wouldn't be enough letters to represent all the digits). This is usually an important key to solving the puzzle.

[+dfx]

Ah, good old inequalities. Basically you can solve those the same way you'd solve equations, but there's a few additional rules you have to pay attention to. If you google for solving inequalities, you can find the basic rules.

 

The rest of it is a logical problem. Note that on both sides of the inequalities, the first digits (tens) of the given numbers are always the same. This should help you get started.

[+Vexidus]

Thank you all for the helpful replies! I now have enough information to do some good research.

 

For those of you wondering if that was a real puzzle or not, it was indeed copied straight from a cache description. There is a series of over 80 of these exact types of puzzles, but in different variations. GC258ER