This is hard! Can you do it?

Question

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.

Answer 1

ABCDEFGHJ = 256973148


Firstly...
C - B = 1.......C = B + 1
H - G = 3.......H = G + 3

The equation can be simplified as:

A * [ (2B + 1)^(D - E) - F^(G(G+3)) ] / J = 10

1. The difference between the numbers within the square brackets cannot be more than 100 since dividing by J, which is a single digit will not give 10 (assuming that A was 1). Therefore both numbers are supposed to be weighted similarly.

2. Consider the value of 'A'. If the difference were even, then it must be multiplied by 5 before dividing in order to get 10. If it were 5, then 'A/J' has to scale it down accordingly. If it were odd, there are no possible values 'A' can take. Thus the difference can be either be even or a multiple of 5.

3. I assume F is an odd number! The reasoning behind this is that the difference between the 2 numbers can be even [Exception is if the difference were an odd multiple of 5. If it doesn't work then consider the other alternative]. Since (2B + 1) raised to any power is odd, then F must be odd to obtain an even difference.

4. Look at all powers that have values in the range of 1 - 256, since I assume that the values are small and close in value. I consider 1^2 to 15^2, 1^3 to 6^3, 1^4 to 4^4 and 1^5 to 3^5. Look at those with odd bases [also easier to start off with since trial and error must take place now].

5. I obtain and test 11^2 - 3^4 = 121 - 81 = 40. From this, (2B+1) = 11-->B = 5, D-E=2, F = 3 and G^2 + 3G = 4 --> G=1

using 40...A = 2 and J = 8 in order to get a solution of 10

If G = 1 then H = 4 from original equation
If B = 5 then C = 6 from original equation

The remaining numbers are 7 and 9, which allows D = 9 and E = 7 to satisfy the final equation of unknowns [D-E=2]

I hope you understand and it helps!

Answer 2

This is the fourth time this has been asked in a couple of days now. And *everybody* is missing out the power signs when they copy and paste it.. sigh.

Anyway, the answer is 256973148.