Solving Really Big Formula: Find ABCDEFGHJ

[kappcity06]

You are confronted with the following formula:

A * [(B + C)(D - E) - F(G*H) ] / J = 10

Knowing that each variable is a unique, single-digit, nonzero number, and that C - B = 1, and H - G = 3, what is the number ABCDEFGHJ, where each letter is a digit? For example, if A = 4, B = 2, and C = 7, ABC would equal 427.

I tried to set up some rwalsionship but I cannot elimante enough variblies to move on with the proplem. can anyone help please.

 

[interested_learner]

This would be easy to solve by computer. There is a very finite list of numbers to check.

 

[KoGs]

Haha I like your teacher. This is my kind of problem. Give me a moment.

 

[KoGs]

Right off the bat it tells you C - B = 1. This tells you something about C + B. In particular it tells you C + B = odd number. This becomes very important as you are asked to multiply (B + C) (D - E).

 

[KoGs]

Actually I guess it's not that important. But if you separate the equation to be:

(A/J) * [(B + C)(D - E) - F(G*H) ] = 10

This tells you A/J either = 2 or = 5, as there is no way to get a fraction from what's left. Now we know A/J must = 2. Because in order for A/J to = 5, A must be 10 and J must be 2. This violates our condition that all letters are single digits.

And there are only a few possibilities for A/J. 4/2, 6/3, or 8/4.

 

[KoGs]

Ok I guess it is important that B + C is odd afterall.

We have an equation H - G = 3. This tells us H - G is odd. Because either H must be odd and G even, or H must be even and G odd. An odd number * an even number gives an even number. So GH is an even number, likewise FGH must be an even number.

This tells us (B+C)(D-E) must be odd, because (B + C)(D - E) - F(G*H) = 5.

 

[KoGs]

A = 6, J = 3.

 

[KoGs]

Ok I lied. A could also be = 2, and J = 1.

 

[kappcity06]

i am still not understanding where you want be to go from here. I realize what you are talking about with the odd numbers. How do i figure out which numbers are the correct ones to use. with A and j having 3 different possiblies

 

[kappcity06]

anyone else know anything else?

 

[Number2Pencil]

The reason you didn't get a straight answer is because you didn't copy the problem down correctly.

A * [(B + C)^(D - E) - F^(G*H) ] / J = 10

they were exponents not products. I've seen this problem before is how I know.

now you can get the right answer:

256973148