Solving Really Big Formula: Find ABCDEFGHJ

• kappcity06
In summary, the problem asks for the number ABCDEFGHJ, where each letter is a unique, single-digit, nonzero number and C - B = 1 and H - G = 3. By setting up the equation and using the given conditions, it can be determined that A/J must equal 2 and that (B + C)(D - E) must be an odd number. After considering all possibilities, the correct answer is 2569731481.
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.

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

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

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).

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.

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.

A = 6, J = 3.

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

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

anyone else know anything else?

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

Last edited:

1. How can I solve a really big formula like ABCDEFGHJ?

To solve a really big formula like ABCDEFGHJ, you will need to use a combination of mathematical principles and techniques. This may include breaking the formula down into smaller parts, using algebraic manipulation, and applying the order of operations. It is also helpful to have a good understanding of the properties of numbers and mathematical symbols.

2. What is the importance of finding the values of ABCDEFGHJ?

The values of ABCDEFGHJ are important because they represent specific variables or constants within the formula. By finding the values, you can better understand the relationship between the variables and how they contribute to the overall result of the formula. Additionally, knowing the values can help you to make predictions and solve related problems.

3. How do I know if I have solved the formula correctly?

To ensure that you have solved the formula correctly, you can use the values you have found to substitute into the original formula. If the resulting equation is true, then you have solved the formula correctly. You can also check your work by using a calculator or asking a peer or instructor to review your solution.

4. Can I use a calculator to solve the formula?

Yes, you can use a calculator to solve the formula, but it is important to have a good understanding of the mathematical concepts and principles involved. Using a calculator can be helpful for checking your work or solving more complex formulas, but it is important to avoid relying on it too heavily and to always double check your solutions.

5. Are there any tips for solving a really big formula like ABCDEFGHJ?

Yes, there are a few tips that can help you when solving a really big formula like ABCDEFGHJ. First, make sure to carefully read and understand the formula before attempting to solve it. Then, try breaking it down into smaller parts and solving each part separately. It can also be helpful to write out your steps and show your work to avoid making mistakes. Lastly, practice and patience are key in mastering the skills needed to solve complex formulas.

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