Lenny Conundrum 194

[pipsqueeek]

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.

Gah. I've been working on this for ages and can't get anywhere. I've been doing a sorta trial and error approach. I keep thinking I'm getting somewhere and then... not. Any ideas?

Edit// Gah. Superscripts.

Last edited by pipsqueeek on Thu Nov 30, 2006 4:23 am, edited 1 time in total.

[sily_sicily]

Woah woah woah! *calls in my maths teacher*

[Mongrel]

Okay, here's what I've got so far:
Each letter represents a different nonzero digit, and there are 9 letters, so they're 1-9.
C is 1 more than B. So if B is 4, C is 5.
H is 3 more than G. So if G is 1, H is 4. H also can't be less than 4, because that would make G less than 1.

No, I don't have the answer yet. I'm just trying to state facts a different way in hopes that it'll help someone.

[mazil]

I think I got it... surprisingly quickly, since I haven't done much maths in a while!

Firstly, I simplified the question as much as I could. I moved A and J over to the right hand side, and converted "C" and "H" into "B" and "G" values, with the help of the given equations. I'm not sure how much it helped, though.

I did a lot of "guessing and checking", but I also tried to keep the "power of" numbers as small as possible.

---

For my answer, the first two numbers have a difference of 3... has anyone else gotten that too? (I can't think how else to compare answers without completely giving it away!)

[pipsqueeek]

The fist two numbers meaning A and B or meaning (B + C)^(D - E) and F^(G*H)?

[mazil]

Oops, sorry! I meant A and B

[Mongrel]

Once I realized that (D-E) and (G*H) were exponents, it took me about ten minutes to solve with random number-filling-in. I decided to try to keep the total of the exponents(like the difference of D and E) small, which kept it simple.
Once I confirm with someone else, if I'm still on, I'll try to post another hint.
EDIT: confirmed with mazil, so here's another hint--A+E=9

Last edited by Mongrel on Thu Nov 30, 2006 5:32 am, edited 1 time in total.

[pipsqueeek]

I wish I could program. I've gotten the number of possibilities down to a managable amount, but it's still taking me a long time to work through them all. It'd be so much easier if I could just tell the computer to do it. I'm only about a third of the way through, and I'm going to have to do the rest tomorrow, as it's already way too late and I haven't done my homework yet. *stupid conundrum getting in the way of my sleep*

[kentieness]

Woooo! Thank you so much for helping me (and my brother) out, mazil! I'd been trying to work it out for hours, and I was just going around in circles

[mazil]

I thought about my hint above ... and for those of you doing it by hand, moving A and J to the right side is definitely helpful. Especially the A, move that first It cuts down its possible values a bit (we'll have no fractions here!)

Both the final calculated values of the "power of" numbers are under 5, by the way (ie. "D-E" is less than 5, and "G*H" is less than 5). Just to save you guys from playing with big numbers.

Edit: That's quite okay, kentieness! Glad I could help out

[AySz88]

Blargh, I started implementing a way-too-complicated algorithm (it involves linked lists and virtual nodes), and of course it doesn't work right. Oh well, I'll give it another shot tomorrow...

[lemonberri]

This one wasn't as bad as it seemed... With my educated guessing I managed to figure it out on the second try.

[BananaLee]

Did it the raw way - using nested for loops and a computer.
After 4.87million iterations (that's 9^7), I got the answer.

[May]

Yay! I finally got it! I doubt I got a trophy or anything though

[pipsqueeek]

Finally got it! Glad that's over with.

maz, thank you so much for your help.