[mqpippin]

 Frustrated, but in Sum Other Way

[Albedo]

This is encouraging - my programming skills have atrophied over the last decade or so and I never got beyond BASIC so my chances of coming up with a program are fairly slim. However I have been trying to narrow it down and your spoiler above supports my theory that:

Spoiler (Rollover to View):

there are just so many possible combinations of two, three and/or four digit numbers in the sum, any number up to 9999 could almost certainly be generated. Conversely once you get up to using a 6,7, 8 or 9 digit number you don't have many digits left over to 'modify' it with so I was guessing the solution was between five and six digits long. There's hope for me yet!

[jwo]

classyguy86 wrote:

I just have a few questions for those of you who have figured this one out. (not looking for the answer... yet ) Spoiler (Rollover to View): 1. Did any of you do this one without using a computer program? if no: 2. Now that you have the answer, do you think it would be possible to figure it out without a program? So far, my lowest guess (using only a calculator, because I'm worthless programming) is 113,575, which is very wrong. So either there's something lower (probably) or I'm completely off.

No answer given below, but responses to your questions and a hint about the order of magnitude of the answer:

Spoiler (Rollover to View):

1. Yes I used a computer. 2. I would have had trouble getting the answer without a computer. However, there may be some mathematical shortcuts that direct you towards the correct answer (my maths isn't good enough to find any though). 113575 can be calculated by the way (120359-6784). You are correct in assuming there is something lower that can't be calculated and you're not completely off.

[classyguy86]

I just have a few questions for those of you who have figured this one out. (not looking for the answer... yet )

Spoiler (Rollover to View):

1. Did any of you do this one without using a computer program? if no: 2. Now that you have the answer, do you think it would be possible to figure it out without a program? So far, my lowest guess (using only a calculator, because I'm worthless programming) is 113,575, which is very wrong. So either there's something lower (probably) or I'm completely off.

[jwo]

KingOfWrong wrote:

As for the number of possible sums, they took my code about three hours to work through.

You should be able to get it down to much less than that (not that it really matters once you have the answer).

Coding hint (not the actual answer):

Spoiler (Rollover to View):

I managed to get my code to get to the solution in under 5 minutes by going for random combinations of digits and operators rather than systematic calculation of all combinations. As the potential solution gets higher and higher, you can weight the random combinations to favour concatenation over +-. This homes in on the answer pretty quickly.

[GasparLewis]

KingOfWrong wrote:

Rand0m wrote: Nope, it ain't that, alas. It is within an order of magnitude, though

Spoiler (Rollover to View):

That's what I meant; of course I didn't think it was within, like, 10 up or down from that. I just figured that the square root of all possibilities minus the square root of the highest possible answer, rounded out, would make for a good shot in the dark, just on probabilistic principle and the brain lint left over from AP Statistics last year. And, apparently, my idea of scope wasn't too far off.

[KingOfWrong]

Rand0m wrote:

Nope, it ain't that, alas.

It is within an order of magnitude, though

As for the number of possible sums, they took my code about three hours to work through.

I'd have solved it at 6pm on day 1 except I made two mistakes in the problem definition,

Spoiler (Rollover to View):

first assuming that it was 0..9 in order, with the first digit on its own (i.e 0+... or 0-...), with the answer 211; then any ordering of the digits but still separating the first... oops!

[Rand0m]

GasparLewis wrote:

If I were going to guess, I would say in the neighborhood of...

Nope, it ain't that, alas.

[GasparLewis]

This is what I get for not reading everything intently.


Ah well, the principles aren't totally off.

Spoiler (Rollover to View):

And yeah, Classy, you had the idea right, but since I gave the wrong number (it's really 19683, not 19863), it's 71,425,670,400 possibilities, with an answer value lower than 9,876,543,210. Since the number positions ARE dependent on one another, there's 10 options, then 9, then 8... or 10 x 9 x 8..., or 10 factorial. Maybe not as happy as my incorrect reading, but still not miserable. 10^19683 would just be downright unfair. If I were going to guess, I would say in the neighborhood of... 167,875. Not that I can verify anything, but I have my reasons for that number.

[X9Tim]

GasparLewis wrote:

Well, think about this. Not an answer, but something notable. Spoiler (Rollover to View): You have 9 spaces between the numbers, with three possibilities: +, -, or nothing (null, which I'll call N). So, since none of the places depend on one another, you get 3^9 = 27^3 = 19,863 possibilities.

Yes, but you've missed something...

Spoiler (Rollover to View):

The digits can be in any order, so the number of possibilities = 10^(3^9) = a HUGE number!!

[classyguy86]

GasparLewis wrote:

Well, think about this. Not an answer, but something notable. Spoiler (Rollover to View): You have 9 spaces between the numbers, with three possibilities: +, -, or nothing (null, which I'll call N). So, since none of the places depend on one another, you get 3^9 = 27^3 = 19,863 possibilities.

But the card also says that the digits can be placed in any order. This would add a few possibilities, since concatenating digits in a different order, would definitely change the results.

Spoiler (Rollover to View):

It's been forever since I took probability, but I think the amount of different orders for the 10 digits would be: (10!) = 3,628,800. This would make the total possibilities for the equation: 3,627,800*19,863 = 72,078,854,400 (Although some of the equations would be the same)

^^That's just what I remember from 4 years ago, so hopefully a probability guy could check over it.

Hopefully I'm wrong, but if not, this problem might have gotten a bit more difficult.

[GasparLewis]

Well, think about this.
Not an answer, but something notable.

Spoiler (Rollover to View):

You have 9 spaces between the numbers, with three possibilities: +, -, or nothing (null, which I'll call N). So, since none of the places depend on one another, you get 3^9 = 27^3 = 19,863 possibilities.

This gives two things which can help:

One:

Spoiler (Rollover to View):

The answer would have to be 19,864 or less, and considered repeats and negative results, it's likely far, far, far, far less.

Two:

Spoiler (Rollover to View):

you could make a quick program to run through them all possibilites with the syntax: 0 (+/-/N) 1 (+/-/N) 2 (+/-/N) 3 (+/-/N) 4 (+/-/N) 5 (+/-/N) 6 (+/-/N) 7 (+/-/N) 8 (+/-/N) 9 and see what comes up, then list in order of value to find the first gap in the line, or if you really didn't want to work at all, run a cross-check afterwards until a gap is hit. I don't know exactly what the code would entail, but I'm positive you could whip it up pretty quick, knowing what I know about Visual Basic.

The rest, probably in my own time, I could solve, but that's leagues off.

Besides, I'm never gonna own the card anyway.

EDIT of EDIT: Took first EDIT, made into a new post.

[Curlytek]

X9Tim wrote:

A few quick thoughts: 1. The wording of the question should make the answer any number of the form xE-∞ (that's meant to be an infinity symbol) But I think we can assume that the answer is an integer 2. The maximum possible answer must be less than 9876543210 Not very helpful, but a starting point i hope

I don't think that it does, because it doesn't condone the use of decimal points or division, therefore doesn't allow the formation of anything but integers.

Should there be a formula to work this out, or is it simply a "try it till it (really) doesn't work" type of problem?

[X9Tim]

A few quick thoughts:

1. The wording of the question should make the answer any number of the form xE-∞ (that's meant to be an infinity symbol)
But I think we can assume that the answer is an integer

2. The maximum possible answer must be less than 9876543210

Not very helpful, but a starting point i hope

[PuzzledPineapple]

[S2] [Dice Set] #230 Sum Other Way