Math Is Fun Forum

23998
2+3+9-9+8=13

23946
(2*3)+9+(4-6) = 13

Sorry for the late reply.
Great work. If you feel like it, you may try to combine, for your own fun, the different problems (reverse, noise, 1-2 or 1-3 digits for a first split) but you already solved my problems (I will finish the rest later).

And take a look @ the game (Mean Sumurai @ Google Play). If you don't have an Android, the iOS version will be out this month. I want this "number splitting" thing to have some visibility.

It's been great interacting with you guys. Very gifted guys, that's what you are.  Thanks again.

... ... this post is starting to sound like I'm going away. I'm still a member of this forum, darn it :-D
I'm sticking around :-). If you have any questions, follow-ups, suggestions, I'll be happy to hear them.

Best,

Terrific.
Congrats to both of you. The formula I had looked like the one from the post #27 but used intermediate variables for (1+sqrt(5))/2 and (1-sqrt(5))/2 so confirming post #27 could not be done by a quick look.

And yeah, anonimnystefy, your new formula does look much nicer than the previous one.

I don't know bobbym's education but both of you are obviously gifted people. There's still V-b to solve but truth is I'm mighty busy these times so if you have an answer, don't expect a quick confirmation. I also have one (may be 2) related problems. I will present it (them) straight away after an answer for V-b

One last point: I presented this number splitting formulation on the math section of Reddit (don't trust Reddit caricature in the media, many of the guys in that forum are maths Ph.D.s) and it may turn out that you guys, along with a few other people close to me, have been working on a new and possibly research-worthy problem. Now, if one of us could spot an interesting link with any sort of existing concept or phenomenon, the whole thing could become very exciting. Keep your eyes open.

Best,

Congrats bobbym for the splittings. Only one left.
I think you'll enjoy the game. Go get it :-)

oh sorry. probably a lack of sleep.
Great Job bobbym! I'm definitely impressed by this forum. You're serious about your fun :-)
Well, I'll get some rest, go out a bit and probably post Parts V and VI
by this evening or tomorrow morning.
Best,

Congrats anonimnystefy
You're really skilled :-). I'll let some time (may be a day or 2) for others to possibly come with an answer.
Then I will continue the series with some even harder challenges (formulas + games) on the same theme.
Meanwhile, you can get hints about what's coming by taking a look at MEAN SUMurai (@ Google Play).

Also, don't forget this part of the challenge

"
34 as a mean for 691795
35 as a mean for 59458531

with a least one split to read from right to left.
"
Yeah, I know it's less cool than finding formulas but it requires different skills and qualities.

Best

PS: Latest, more clear version of the challenge below for people who want to try

[CHALLENGE]
Consider that you are given a sequence of n=4 digits
Assign to these digits numbers from 1 to 4.
Below, an enumeration of the all different combinations.

1234

1 2 3 4
1 2 34 -- 1 2 43
1 23 4 -- 1 32 4
12 3 4 -- 21 3 4
12 23 -- 12 32 -- 21 23 -- 21 32

so 11 different splittings for n = 4

Find a formula for the number of combinations, given n.

No, you can't count 21 1 2 and 12 1 2 as one splitting. 2->1 is definitely different from 1->2.
hehe, this is a perfect case-study of why anticipating questions is not always a good thing.
I just confused you guys. Forget totally about same digits stuff and just focus on the following

Consider that you are given a sequence of 4 digits
Assign these digits numbers from 1 to 4.
Below, an enumeration of the all different combinations.

1234

1 2 3 4
1 2 34 -- 1 2 43
1 23 4 -- 1 32 4
12 3 4 -- 21 3 4
12 23 -- 12 32 -- 21 23 -- 21 32

so 11 different splittings for n = 4

*You don't need to care about whether digit 1 is equal or not to digit 2.
*Order is irrelevant. While looking for a formula, you may write 1 2 4 3 instead of
1 2 3 4. It is the same splitting but I highly suggest you stick with the order in
which the digits appear. Otherwise, you may get unnecessarily confused.
[If you want to introduce order, you can do so and it could be interesting
but it is outside the scope of the challenge]

Now, if you really want to see the context of all this, go download the game
Mean Sumurai @ Google Play. This could sound like another shameless plug.
It may well be one :-) but I sincerely think it could help you guys.

Also, don't think this is an easy problem. It is pretty hard and though it has a clean answer
it is not something like Fn+1. It is slightly messier.

You can see it that way, as long as you don't forget that you're looking for the number of combinations.
So, as you probably already know, if you have n pairs in a splitting, it does not mean that it counts for 2*n.

Edit: Just in case: "pair" in what I wrote above refers to 2-digit groups

Congrats anonimnystefy and bobbym
Your quick answers are impressive, considering that:
- I posted Part II for days in the Mathematics community (~70k) of Google+ and only the first 2 got solved.
- I also posted Part I yesterday before posting it here. still waiting for an answer.

Let's continue this.

__Part III__ (tougher cookie than Part I but I have even tougher ones in case someone manages to solve this.)
You are given a sequence of n digits and allowed to split it by grouping at most 2 consecutive digits together.
Example: 796421 may give the splitting 7 96 4 21

Difference with Part I is that
An orientation is attached to 2-digit splits, meaning they can be read either from left to right or right to left
So 7 96 4 21 (in the above example) may correspond to 7 96 4 21 or 7 96 4 12 or 7 69 4 21 or 7 69 4 12
Whether the two different orientations give the same number or not is not taken into account:
a split 33 (left to right) is different from a split 33 (right to left) because the pairs [2 consecutive number][orientation]
are different

***Find a formula for the number of possible splittings.***

__Part IV__
You are given a number X and a sequence of digits.
Your task is to split the sequence so that the obtained groups
(of at most 2 digits) add up (or average to) X.
You can define your splits from left to right

Examples
24 as a sum for 3381           3 3 81[right to left] --> 3 3 18 --> 24
15 as a mean for 9423         9 4 23[right to left] --> 9 4 32 --> 45/3 = 15

Solve the following:

177 as a sum for 3534477
204 as a sum for 944949165

34 as a mean for 691795
35 as a mean for 59458531

Constraint: Use at least one backward orientation.

In this series, parts with odd numbers will be about formulas
while parts with even numbers will propose some (more and more) challenging
puzzles based on number splitting.

[To the moderator, let me try to convince you not to cut the following :-)
The challenges are taken from the game, which is a free (without any in-app purchases) maths game that may interest people who try to
solve the challenges. I'm a (hobby) app developer but I'm also a computer science Ph.D. with a good day-job. So this is not about money.]

More (diverse and randomly generated) puzzles await you in the Android game
MEAN SUMurai. The game includes an online versus mode, achievements and leaderboards.
If you take a look, you will know that very serious math challenges await you
in the next parts.

Best