Number splitting

bobbym · 2013-08-04 07:10:35

For VI)

7 + 2 + 99 + 2 = 110

4 + 9 + 71 + 2 + 6 = 92

(9 + 7 + 53) / 3 = 23

( 59 + 95 + 2 ) / 3 = 52

anonimnystefy · 2013-08-04 07:25:19

Hi meanmaths

Last edited by anonimnystefy (2013-08-04 07:26:34)

meanmaths · 2013-08-05 11:58:43

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

meanmaths · 2013-08-05 11:59:59

anonimnystefy,
that was super-fast. Much faster than expected.
Truth is I can't even say right now whether your answer is correct or not.
Do you have a recursive form? It would be easier for me to check.

My gut feeling tells me that your formula is right.
I'm quite busy right now so give me 1-2 days to get back to you.
Sorry :-(

I have to ask: What is your educational background?

anonimnystefy · 2013-08-05 14:07:32

Hi

That's okay, take your time.

This one I did with the help of the Mathematica package.

In September I'm starting 4th year of high school, which would be 12th grade, I guess.

Last edited by anonimnystefy (2013-08-05 19:53:05)

bobbym · 2013-08-05 22:51:14

Use this for a recurrence.

Do you have a recursive form? It would be easier for me to check.

last solution for VI)

( 71+13+3+8+4+3 ) / 6 = 17

anonimnystefy · 2013-08-07 00:44:02

Hi meanmaths

I have been able to greatly simplify my formula from post #27.

It does look much nicer than before and it agrees with bobbym's recursion.

Last edited by anonimnystefy (2013-08-07 01:01:08)

meanmaths · 2013-08-07 14:10:50

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,

bobbym · 2013-08-07 21:06:57

Hi;

I don't know bobbym's education but both of you are obviously gifted people.

He is gifted, I am a bumpkin .

anonimnystefy · 2013-08-07 21:52:24

Bobbym's gifted as much as he denies it.

anonimnystefy · 2013-08-08 01:06:35

Hi

I found the generating function for V in the case that m digits are not considered for the splitting:

EDIT: Found a formula for V b):

Last edited by anonimnystefy (2013-08-08 01:45:22)

bobbym · 2013-08-08 06:34:00

Hi;

For convenience the recurrence is:

a[n] = 3 a[n - 1] - 5 a[n - 3] + 3 a[n - 5] + a[n - 6]

with

a[0] = 0, a[1] = 0, a[2] = 1, a[3] = 3, a[4] = 9, a[5] = 22

anonimnystefy · 2013-08-08 08:45:22

I wonder if a general formula is achievable for k unused numbers.

meanmaths · 2013-08-08 09:55:39

A quick post to present the (probably) last parts.
I'll come back to your previous answers later today or tomorrow

____Part VII____
I no longer think it is that hard, compared to the "noise" digits.
It now strikes me as relatively easy (at least the simplest versions)

Anyway, here it is
Given the sequence, there is now some order involved because we want
to tag the first split (it will be the X of previous parts). You can see it as if any
split now has a boolean/binary attribute indicating whether it is the first or not.
Only one of the split can have this boolean at true.

For instance, with a sequence of length 3 and positions 123
1 2 3 --> 1 or 2 or 3 could be the first split
1 23 --> 1 or 23 could be the first split
12 3 --> 12 or 3 could be the first split

For now, let's keep it that simple
(actually, if the first split has to be the X, there are some
obvious constraints on the lengths of the splits)

The first split can be of length
(a) 1 or 2
(b) 1 or 2 or 3 (all the other splits would still be made of 2 digits at most)

___Part VIII__

Example: 32017 --> The first split defines X=20,
the sequence becomes 3[20]17 --> the splits 3 and 17 complete the splitting.
Note that 31 cannot be a valid split: 20 is in the way

The first split defines the target sum

8995383
115161845

The first split defines the target mean
369792
195457

There are much more difficult instances in Mean Sumurai but
these will be fine for a text-version (plus, I have to hurry)

later

Last edited by meanmaths (2013-08-08 09:57:30)

anonimnystefy · 2013-08-08 11:38:48

Hi

For the first part 1 of VII the recurence is the same as for part 1 of V, but the initial conditions a[0]=0,a[1]=1,a[2]=3,a[3]=7.

bobbym · 2013-08-08 11:54:05

8 + [99] + 5 + 3 + 83 = 99

[115] 1 + 61 + 8 + 45 = 115

[36]9792 -> ( 9 + 7 + 92 ) / 3 = 36

[19]5457-> (5 + 45 + 7) / 3 = 19

anonimnystefy · 2013-08-08 11:56:40

Formula:

Last edited by anonimnystefy (2013-08-08 13:11:24)

bobbym · 2013-08-08 13:03:42

Hi anonimnystefy;

I am not always getting integers for that when I use n = 0,1,2,3,4...

anonimnystefy · 2013-08-08 13:12:30

I have edited my post. Apparently F[n-1]+F[n]=F[n+2], according to me.

bobbym · 2013-08-08 13:49:31

Hi;

I meant post #42.

anonimnystefy · 2013-08-08 14:31:07

Good, we are talking about the same post. Have you seen the edited version of it?

bobbym · 2013-08-08 14:37:44

Edited?

Looks the same.

anonimnystefy · 2013-08-08 14:42:11

Nope. The index of F changed. It was n+2 before.

Last edited by anonimnystefy (2013-08-08 14:42:57)

bobbym · 2013-08-08 14:47:58

Okay, it is working fine now.

anonimnystefy · 2013-08-08 14:49:32

Great then. Still need to get the second part.

Math Is Fun Forum

#26 2013-08-04 07:10:35

Re: Number splitting

#27 2013-08-04 07:25:19

Re: Number splitting

#28 2013-08-05 11:58:43

Re: Number splitting

#29 2013-08-05 11:59:59

Re: Number splitting

#30 2013-08-05 14:07:32

Re: Number splitting

#31 2013-08-05 22:51:14

Re: Number splitting

#32 2013-08-07 00:44:02

Re: Number splitting

#33 2013-08-07 14:10:50

Re: Number splitting

#34 2013-08-07 21:06:57

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#35 2013-08-07 21:52:24

Re: Number splitting

#36 2013-08-08 01:06:35

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#39 2013-08-08 09:55:39

Re: Number splitting

#40 2013-08-08 11:38:48

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#41 2013-08-08 11:54:05

Re: Number splitting

#42 2013-08-08 11:56:40

Re: Number splitting

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Re: Number splitting

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