Perfect Ten - a new FOFC numeric puzzle

[QuikSand]

Back in the good old days, we used to do lots of these... I thought this would be a fairly harmless renewal. Perhaps it might turn out to be worth doing more than once.


Here's the concept:

Take each of the digits from zero through nine.

You must use all ten digits exactly once in each calculation.

Use them, along with any combination of these operations:
-addition
-subtraction
-multiplication
-division
-exponent

You may use unlimited perentheses to establish the order or operations in your calculation.

You may not simply concatenate digits together to make multi-digit numbers for use in the calculation.

Your goal, for each of ten rounds, is to create a calculation that gets as close as possible to the listed target value.

Your score will be one point for each consecutive digit, starting at the leftmost nonzero digit in the given target number. Decimals beyond those shown are to be ignored. Up to ten points may be awarded per round.

Scoring example:

Target = 2,390.021772
Result = 2,390.023770
Score = 6 points (no points awarded for getting the digits correct after the missed one)

Ten rounds, ten target numbers, ten digits each. Perfect score is 100.



If you have questions about the rules, post them below -- I will clarify as needed. (Historically, it seems that some prefer the location of loopholes in the wording of rules to the actual intended contest)


I am finishing up an automated target generator... and I'll post the first set of target numbers momentarily. They will start with a ten-digit integer, and progress down to a nine-digit decimal. I'm not certain that this will maximize the challenge, but it seems like a fair starting point.

[QuikSand]

Okay, here's the list of target numbers:

A 4,742,071,038
B 843,341,983.6
C 36,850,939.37
D 3,141,624.332
E 843,212.5512
F 25,099.81518
G 4,295.799897
H 418.5108209
I 76.01053674
J 9.328924151

Have at it...

[cuervo72]

concatenate digits together to make multi-digit numbers

Yep...concatenate.

[QuikSand]

I knew the title would lure you in, at the very least.

[John Galt]

All correct answers must divide 2 by 3.

[cuervo72]

I knew the title would lure you in, at the very least.

Oh, you bet - that was the first thing that came to mind.

[MIJB#19]

I'm understanding correctly that 12 (twelve) (the concatenate rule) is no legal number, but is 0.5 (half)? I'm a little bit confused about why we'd use the 0 in the puzzle then. (aside from x ^ 0 = 1)

[Passacaglia]

Can a digit be used more than once?

[QuikSand]

Can a digit be used more than once?

No, edited to clarify above.

[Pumpy Tudors]

This one looks like a lot of fun. Thanks for the puzzle, Quik!

[SirFozzie]

I'm understanding correctly that 12 (twelve) (the concatenate rule) is no legal number, but is 0.5 (half)? I'm a little bit confused about why we'd use the 0 in the puzzle then. (aside from x ^ 0 = 1)

If the target is a reallllly small number, you may want to divide by zero early.

[QuikSand]

I'm understanding correctly that 12 (twelve) (the concatenate rule) is no legal number, but is 0.5 (half)? I'm a little bit confused about why we'd use the 0 in the puzzle then. (aside from x ^ 0 = 1)

Without the zero, we'd only have nine digits, and the puzzle name wouldn't make sense.


Well, more fairly, I had originally though that I'd allow concatenation, which would make the zero plenty useful... and only after some thought, decided to disallow it. Dropping the zero would make plenty of sense, really.

I have no problems with submitted formulas that skip the perfunctory +0 at the end and just leave out the zero.

[cuervo72]

No, actually the '0' could have a good deal of utility, if you wanted to negate one or more of the numbers. Throwing a 0/7 in there to get rid of an extra '7', for example.

[Passacaglia]

When do we need results by?

[QuikSand]

No, actually the '0' could have a good deal of utility, if you wanted to negate one or more of the numbers. Throwing a 0/7 in there to get rid of an extra '7', for example.

That all amounts to the same thing, in my view -- you can take any number of unused digts and convert them into zero or one, as needed, to essentially drop them out of the picture. But the zero doesn't seem to have any other use, that I can see.

[QuikSand]

When do we need results by?

Honestly, I don't know how difficult this wil be. I spent about 10 minutes with the first number, and found it to be excruciatingly difficult by my brute force method.

My best guess is that this might turn into a collective enterprise, rather than a competitive one.

I would welcome a post to the extent of "I got up to six points on A" if that serves to advance the cause.

If people would rather work on it independently, and submit their final answers in more of a contest format... post that as your preference, and I'll gladly turn this into that sort of contest.

[Pumpy Tudors]

If the target is a reallllly small number, you may want to divide by zero early.
*head explodes*

[sabotai]

If people would rather work on it independently, and submit their final answers in more of a contest format... post that as your preference, and I'll gladly turn this into that sort of contest.

I'd prefer the contest format, at least for now. If it turns out to be rather difficult (read: In a few days, most people still have rather small scores) then it'd be good to try to work them out together to see how high we can collectively go.

EDIT: Hmm. I spent about 10-15 minutes on the first one and got a few points out of it. The second one....for me at least, has been a lot harder.

[sabotai]

dola,

After an hour and a handful of points to show for it, maybe it's best if this was just a collective thing. (Maybe others are having much more luck/skill with this than I am...)

[QuikSand]

Anything?

[Eaglesfan27]

Just started working on this as I'm catching up on the board. Certainly an interesting exercise.

[sabotai]

Tried the first few (then got caught up in other things and forgot about it. :) ). Only really got anywhere with the first one.

Here's what I have for the first one. Need to get 4,742,071,038

(( 5*4*7*8*9)^3) / (6^(2+1)) (obligatory + 0 at the end)

That gets me 4,741,632,000 for 3 points.


The second one, all I could get was the first digit. Need to get 843,341,986.6

(((9^(7)) * (8+2+1+6+3))) * (5+4) (obligatory +0 at the end)

That gets me 860,934,420.0 for 1 point

[Eaglesfan27]

With a few minutes of working on it, only able to get 4 points on A so far. I'm going to try more tonight, but I wonder how many points anyone has on A so far.

[cuervo72]

A 4,742,071,038

Closest I've come so far on this is:

((5*9-4)^2)^3 - (7+8-1)^6 = 4,742,574,705

I'm sure there's something closer than that, but it's at least in the ballpark.

[Daimyo]

I've can get four digits to A, but in working for something better I'm currently looking at the following

7^4 * 2^8 = 614,656 which only needs to be multiplied by 7,715 to get 8 points. I can't figure out a way to get to 7715 (or close for less points) with 1,3,5,6,9. 6^5 = 7776, but then you'd have to be able to get 60 from 1,3,9.

[Brillig]

The most annoying thing about these is that there isn't really any clever way of attacking the problem other than brute-forcing it. And there's no progression, either, there's no logical way to improve a 6 point solution to a 7 point solution...

I got to 6 points on A before I got tired of it.

(8 + (1 / ((9^6) / 4)))) ^ ((( 5^2) * 3) / 7) = 4742076154

[QuikSand]

I made a grid of exponents (pretty obvious) but it really doesn't serve to offer any kind of precision at all... just gets close tothe bigger numbers. I haven't had any real luck with brute forcing either... I don't even have six points anywhere yet, on my own.

[SplitPersonality1]

I made a grid of exponents as well but have yet to do better than 5 points. I like this puzzle but as Brillig said, there doesn't seem to be any systematic way of improving any of the solutions.

Despite that, I am still going to work on this. I like a challenge. It may take me quite a bit of time to get a decent score. (I am targeting 70 or higher)

[BrianD]

Were the numbers generated in such a way as to make 100 points possible, or are they just a random 10-digit number?

[Bee]

I'm pretty sure the plane would take off.

[Pumpy Tudors]

I'm pretty sure the plane would take off.
BRILLIG SAYS THAT THIS DISCUSSION IS OVER.

[QuikSand]

Were the numbers generated in such a way as to make 100 points possible, or are they just a random 10-digit number?

B

[gstelmack]

The problem with a simple table of exponents is you also need to consider things like:

8 ^ (1/5)

You need a whopping big table of exponents.

[Brillig]

Here's a 6 point solution for F (25,099.81518) :

(Yes, I know I said it was annoying, but sometimes it's like picking a scab...)

(((3^5)+8)*((6+4)^2))-(1/7) = 25099.85714

there's still 0 and 9 left over, if anyone wants to do something with them.

*for simplicity, since any number of left over digits can be dealt with by adding a 0 ^ (A + B + ...) term, I'm omitting non-essentials.