tough one very tough one?

Question

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

This requires a little bit of trial and error and some thinking about the possible ranges of values. If gh gets too big, then it isn't possible. So try keeping that small. The smallest solution for GH = 14. Next (d - e) needs to be relatively small, probably a difference of 2 and f also needs to be small. You want the item in the brackets to be a multiple of 10. Trying f = 2, didn't work out, but f = 3 gives 81... to get a multiple of 10, we need (b + c)^(d - e) to be 91, 101, 111, 121, 131, 141, 151, 161, 171, 181. Finally 121 looks promising... with a little more massaging you get to an answer:

ABCDEFGHJ
256973148

a * [ (b + c) ^ (d - e) - f ^(g * h) ] / j = 10
2 * [ (5 + 6) ^ (9 - 7) - 3^(1 * 4) ] / 8
2 * ( 11² - 3^4 ) / 8
2 * ( 121 - 81 ) / 8
2 * 40 / 8
2 * 5
10

Answer 2

256973148

2 * [ (5 + 6) ^ ( 9 - 7 ) - 3 ^ ( 1 * 4 ) ] / 8
= 2 * [ 11 ^ 2 - 3 ^ 4 ] / 8
= 2 * [ 121 - 81 ] / 8
= 2 * 40 / 8
= 80 / 8
= 10

Edit------------->
It appears that my solution is copied from Puzzlings!
Originally, Puzzling had a different solution due to mistaking "^" to mean "*". The wonders of editing :(

Answer 3

Are you saying that you can't have to Variables with the same number?