Red-Dog's Last Theorem

[kinboshi]

We all know Tom is a deep thinker, and recently a mathematical problem has been his major concern.  It's caused him sleepless nights, and prompted hours of debate over the felt at the poker tables at DTD.

Basically what Tom wants needs to know is if there's a mathematical formula (which there will be) that can tell you how many times you have to riffle two different coloured stacks of chips so that the stacks are back to all the same colours, according to how many chips are in the stacks?

For example, if you have 3 chips in each stack, you need to do three riffles to achieve this.  The same if you have 4 in each stack.   But if you have 5 in each stack, you need to do 5 riffles.  6 -takes 6 riffles.

We went down the empirical evidence route, riffling larger and larger stacks:

Chips	Riffles
2	2
3	3
4	3
5	5
6	6
7	4
8	4
9	9
10	6

Our problem was that we couldn't riffle beyond stacks of 10.  Also Tom (being a mathematician), didn't want it based on experimental data but on a mathematical proof.

So can any maths geniuses work out a formula so we can predict the number of riffles when the stacks are n chips high?

[tikay]

Fermat will know.

I'm not entirely sure, but he may have passed away by now.

[EvilPie]

Lol

I thought I was the only saddo that wanted to work this out.

Are you sure about you 7 and 8? They look a bit low to me.

Looking at this sequence there will be no mathematical formulae available. UL

[kinboshi]

Lol

I thought I was the only saddo that wanted to work this out.

Are you sure about you 7 and 8? They look a bit low to me.

Looking at this sequence there will be no mathematical formulae available. UL

As a scientist, I'm appalled by your lack of trust in the accuracy of my scientific method.  I find it an insult that you question my findings.


(I just checked and they are right).

[tikay]

Lol

I thought I was the only saddo that wanted to work this out.

Are you sure about you 7 and 8? They look a bit low to me.

Looking at this sequence there will be no mathematical formulae available. UL

Matt, don't be silly! Of COURSE there is a formula.

[kinboshi]

Lol

I thought I was the only saddo that wanted to work this out.

Are you sure about you 7 and 8? They look a bit low to me.

Looking at this sequence there will be no mathematical formulae available. UL

Matt, don't be silly! Of COURSE there is a formula.

Agreed.  There HAS to be a formula. 

I'm waiting for Jon MW to see this...he's the man for this one.  He's probably out on his horse at the moment though.

[Jon MW]

Lol

I thought I was the only saddo that wanted to work this out.

Are you sure about you 7 and 8? They look a bit low to me.

Looking at this sequence there will be no mathematical formulae available. UL

Matt, don't be silly! Of COURSE there is a formula.

Agreed.  There HAS to be a formula. 

I'm waiting for Jon MW to see this...he's the man for this one.  He's probably out on his horse at the moment though.

tl;ds

[Pawprint]

Looking at this sequence there will be no mathematical formulae available. UL

+1

[EvilPie]

Lol

I thought I was the only saddo that wanted to work this out.

Are you sure about you 7 and 8? They look a bit low to me.

Looking at this sequence there will be no mathematical formulae available. UL

Matt, don't be silly! Of COURSE there is a formula.

Well if there is it's going to have lots of log's, ln's, <'s, >'s and upside down i's (haven't got a factorial button on here).

I honestly don't see how this sequence can have a mathematical formula to it. I agree it should have but the sequence looks too awkward.

What formula can possibly make both 7 and 8 = 4?

I'll be thinking on this for a while.

It's interesting that 3, 6 and 9 lead to 3, 6 and 9. Could be a starting point me thinks.

[tikay]

Lol

I thought I was the only saddo that wanted to work this out.

Are you sure about you 7 and 8? They look a bit low to me.

Looking at this sequence there will be no mathematical formulae available. UL

Matt, don't be silly! Of COURSE there is a formula.

Well if there is it's going to have lots of log's, ln's, <'s, >'s and upside down i's (haven't got a factorial button on here).

I honestly don't see how this sequence can have a mathematical formula to it. I agree it should have but the sequence looks too awkward.

What formula can possibly make both 7 and 8 = 4?

I'll be thinking on this for a while.

It's interesting that 3, 6 and 9 lead to 3, 6 and 9. Could be a starting point me thinks.

There will be a formula for it, 100% guaranteed. If it can happen, there's a formula.

If chance permits, Matt, try & get a copy of, & read, "Fermat's Lost Theorem", upon which this Thread title is based. You'd absolutely love it. And you'd learn the mathematical formula for working out the true (actual) length of the bendiest of rivers on earth, simply by using pye.

[AndrewT]

This is more complex than you could ever possibly imagine and, to my knowledge, is unsolved.

[Cf]

Lol

I thought I was the only saddo that wanted to work this out.

Are you sure about you 7 and 8? They look a bit low to me.

Looking at this sequence there will be no mathematical formulae available. UL

Matt, don't be silly! Of COURSE there is a formula.

Well if there is it's going to have lots of log's, ln's, <'s, >'s and upside down i's (haven't got a factorial button on here).

I honestly don't see how this sequence can have a mathematical formula to it. I agree it should have but the sequence looks too awkward.

What formula can possibly make both 7 and 8 = 4?

I'll be thinking on this for a while.

It's interesting that 3, 6 and 9 lead to 3, 6 and 9. Could be a starting point me thinks.

Really trivial example, but:

4 + (floor (n/9))

[marcro]

Hmmm, does the title of this thread mean that he will never have another theorem?

[Grier78]

Its not simple problem, although some of the results are easy.

2 stacks of 2 chips = 2 Riffles
2 stacks of 4 chips = 3 Riffles
2 stacks of 8 chips = 4 Riffles
2 stacks of 16 chips = 5 Riffles
2 stacks of 32 chips = 6 Riffles
2 stacks of 64 chips = 7 Riffles
etc...

You will also get different results if you don't always riffle in exactly the same way, i.e. when the stack cut off the top has its lowest chip at the bottom of the riffle or if the bottom stack has its lowest chip at the bottom.

[Robert HM]

This is more complex than you could ever possibly imagine and, to my knowledge, is unsolved.
Who cares, I don't, I have a life

FYP