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 [quote="Chuck"]I guess this has been around long enough. The answer, invisible, is: Multiply the last two numbers and subtract the largest square that won't cause the result to go negative. Example: The starting numbers 7 and 11 when multiplied give 77. The largest square equal to or less than 77 is 64, so subtract 64. The result, and third number of the sequence, is 13. Then multiply 11 and 13 giving 143. Subtract 121 giving 22 as the fourth number of the sequence. Continue until bored or zero is reached.[/quote]
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Chuck
Posted: Thu Apr 04, 2002 2:21 am    Post subject: 1

I tried lots of numbers, some with hundreds of digits. None ran off to overflow my 2600 digit limit. Most dropped to zero quickly. I don't know if any pair of numbers start a series that runs off to infinity.

If I subtract the highest cube instead of highest square the series usually gets very high very quickly and doesn't come back down.
CrystyB
Posted: Thu Apr 04, 2002 1:44 am    Post subject: 0

Chuck, i meant can it be transcedental? (going into no loops, 0's or no 0's)

It sometimes rises, but i think in general it should not be possible, b/c of a finite number of values.
Chuck
Posted: Sun Mar 31, 2002 10:14 pm    Post subject: -1

Ok, ten points.
ctrlaltdel
Posted: Sun Mar 31, 2002 10:07 pm    Post subject: -2

oh, why didnt i think of that.... but hey, don't i get points for solving the question whether chuck is evil?
Chuck
Posted: Sun Mar 31, 2002 4:19 am    Post subject: -3

CrystyB
Posted: Sun Mar 31, 2002 2:38 am    Post subject: -4

this has a second "thoeretically possible" question: can it not repeat itself?
Chuck
Posted: Sat Mar 30, 2002 12:30 am    Post subject: -5

I've posted worse series puzzles.

Yes, I'm evil, but it's a lighthearted, funloving evil.
SaberKitty
Posted: Fri Mar 29, 2002 11:39 pm    Post subject: -6

How would you describe that as easy?
I agree with Lepton, you are evil, or maybe just crazy-with a warped perception of the world of math.
edit: spelling

[This message has been edited by SaberKitty (edited 03-29-2002 06:39 PM).]
Chuck
Posted: Fri Mar 29, 2002 11:29 pm    Post subject: -7

I guess this has been around long enough. The answer, invisible, is:

Multiply the last two numbers and subtract the largest square that won't cause the result to go negative.

Example: The starting numbers 7 and 11 when multiplied give 77. The largest square equal to or less than 77 is 64, so subtract 64. The result, and third number of the sequence, is 13. Then multiply 11 and 13 giving 143. Subtract 121 giving 22 as the fourth number of the sequence. Continue until bored or zero is reached.
The Hint Fairy
Posted: Wed Mar 27, 2002 9:44 pm    Post subject: -8

This just in: My "1057" was a typo for 1078. I got DOurk's correct, but the first number was typoed!

1057
853
1020
1436
620
1071
1424
2348
1968
2663
1263
3480
2024
5111
2008
3679
5343
5408
4319
8928
8351
11772
747
2459
848
96
183
144
108
176
239
39
105
126
5
5
0

The SCYTHER sequence:
10325
208518
26909
102026
76818
49427
105362
84678
96411
45342
9873
602
4577
3073
2621
89
945
5
101
21
5
5
0

The VULPIX sequence:

212012
16924
80188
1287
14031
3896
8327
8967
1328
5676
2703
7172
8312
15264
19199
27612
18212
33968
8832
22976
4007
807
845
1290
114
371
269
574
742
804
584
311
148
232
111
152
231
143
272
87
255
281
366
446
20
84
80
159
176
95
79
109
147
147
0
mathgrant
Posted: Wed Mar 27, 2002 8:50 pm    Post subject: -9

Yes, they arrived only three days after I sent the e-mail with my address, and they were great! I loved that one with the curious and interesting numbers, I actually read the whole thing in one day.
Jingle47
Posted: Wed Mar 27, 2002 5:55 pm    Post subject: -10

If you will permit me Chuck....

17
18
17
17
0

And the other one looks like this...
28
6
24
0

And all I will say about 1078 and 853 is that it does not end in 0.......

[This message has been edited by Jingle47 (edited 03-27-2002 12:56 PM).]
CrystyB
Posted: Wed Mar 27, 2002 4:59 pm    Post subject: -11

Courk asked for 1078 and 853... And may i request 17&18 and 28&6? TY!

Is there a reason you're still unregistered, Hint Fairy? What if your loop is wrong? Shouldn't you be able to edit/delete your posts?

[This message has been edited by CrystyB (edited 03-27-2002 12:02 PM).]
Chuck
Posted: Wed Mar 27, 2002 3:25 pm    Post subject: -12

You obviously know the rules. The prize list is in the second post on page 1 here: http://www.greylabyrinth.com/Forums/Forum7/HTML/002929-6.html

Choose any three and email me a postal mailing address at Chuck1863@msn.com

Mathgrant took all the good stuff, but there's plently left. I'm now reading Flatterland by Ian Stewart. You can have that as one of your choices if you're willing to wait a few days.

Mathgrant, did the box of books arrive?
Jingle47
Posted: Wed Mar 27, 2002 1:11 pm    Post subject: -13

Well I believe these examples may show that I have figured it out....
Are there any prizes left? Prizes for me? How do I get them?
1111
4747
2301
6431
6015
6504
9044
8615
15784
239
1012
787
780
771
755
1461
555
855
1181
1739
270
305
554
49
250
150
251
14
33
21
17
33
32
32
0

Wow that was longer than I thought, but I strarted so I must finish....
Here is a shorter one...

2002
47
458
210
80
159
176
98
79
109
147
147
0

And here is my birthday sequence....

910
1976
2560
559
624
716
560
271
439
633
158
158
0
The Hint Fairy
Posted: Wed Mar 27, 2002 5:37 am    Post subject: -14

1057
853
1770
1826
2811
2661

5315
5615
10281
13406
22965
6674
4010
2811
2661

Hey! A loop! So the answer is no, it doesn't always give 0!

100
36
0

I think Jingle knows it. . .

100
37
100
100
0

I think Jingle may know it! If you do, don't forget the prizes!
Jingle47
Posted: Wed Mar 27, 2002 3:54 am    Post subject: -15

What about 100 and 36? They should return zero right?
Courk
Posted: Wed Mar 27, 2002 3:11 am    Post subject: -16

ctrlaltdel
Posted: Sun Mar 24, 2002 1:08 pm    Post subject: -17

thousand apologies o jen the merciful!!! what can i say to defend your wrath? erm.. btw psyduck conflicts also with poliwrath the obviously inadequate knowledge of english is my only excuse - and this of course is but my shame and blame. i hereby proclaim that i will (try to) not be picky with you again.

[This message has been edited by ctrlaltdel (edited 03-24-2002 08:09 AM).]
Jen Aside
Posted: Fri Mar 22, 2002 12:48 pm    Post subject: -18

any = one

It does not conflict with at least ONE, STOP BEING PICKY!!!!!!!111

Muk, in my boredom, I seem to have skipped in subconscious realization of its inconsequence, on several levels. However, I like Mew, so Mew is on the list.
The Hint Fairy
Posted: Thu Mar 21, 2002 8:17 pm    Post subject: -19

Infernal Series Error
The Hint Fairy
Posted: Thu Mar 21, 2002 8:16 pm    Post subject: -20

This puzzle is too hard, obviously. We need a vacation!

Let's go on down to Squaresville!
Mendoza
Posted: Thu Mar 21, 2002 8:00 pm    Post subject: -21

~newbie tiptoes in, clears throat~

Well, some days ago I noticed that

if a chuck b = c (which we know to be equivalent to b chuck a = c) with a>b then
1/if a-b is even, then c=2b-(((a-b)/2)-1)^2 (if positive); and
2/if a-b is odd then c=b-((a-b-1)/2))^2 (if positive).

Unfortunately as soon as a-b is large enough compared to b, these expressions give negative quantities and then I don't know what's going on anymore!! Clearly a by-product of the actual rule which is simpler and more elegant...

Like most people here I'm sure, I reckon that as a 14-year old I would have cracked this in minutes.

ctrlaltdel
Posted: Wed Mar 20, 2002 11:55 pm    Post subject: -22

5 chuck 8 = 4
5 chuck 6 = 5 (and also 6 chuck 5 = 5)
5 chuck 5 = 0
5 chuck 1 = 1

it can't be that hard!!
Chuck
Posted: Wed Mar 20, 2002 8:20 pm    Post subject: -23

I wouldn't consider zero to be no data. It's just that applying the rule to zero and any other number always results in zero. The sequence continues. It's just not very interesting any more.

I was thinking of replacing you with Mathgrant in the next universe design team anyway.
ChienFou
Posted: Wed Mar 20, 2002 7:47 pm    Post subject: -24

The fact that you are losing data as the sequence progresss (ie you can't backtrack) suggests to me that finally you will have no data. Hence the series will always end with zero. Is this a valid postulate? Alternatively can you construct a starting position in which no data is ever lost? Then if you can, there will be a series which does not converge on zero.

I am of course no nearer to solving the problem, and I'm very tempted to break up my partnership with Chuck in "Design-a-Universe Corp" because anyone who is this malevolent can't design a benign universe
The Hint Fairy
Posted: Wed Mar 20, 2002 5:56 pm    Post subject: -25

Speaking of missing stuff, you missed Muk.
The Hint Fairy
Posted: Wed Mar 20, 2002 5:52 pm    Post subject: -26

I can't believe I missed Flareon!
Chuck
Posted: Wed Mar 20, 2002 5:42 pm    Post subject: -27

You wouldn't get a unique series by working backward. When working forward, different starting numbers can fall into the same ending sequence.
ctrlaltdel
Posted: Wed Mar 20, 2002 5:28 pm    Post subject: -28

can the sequence be worked the other way??

if you know the last digits are:

5
6
5
5
0

can you work your way back up the list? going up to infinity?
ctrlaltdel
Posted: Wed Mar 20, 2002 12:04 pm    Post subject: -29

what do you mean it does not conflict?

it does conflict with Dunsparce, Cyndaquil, and Dragonite

[This message has been edited by ctrlaltdel (edited 03-20-2002 07:05 AM).]
Jen Aside
Posted: Wed Mar 20, 2002 11:02 am    Post subject: -30

I feel so silly but here are all the non-repeating Pokémon names I found, in order from highest number of letters to lowest, then alphabetized by letter content... problem letters seem to be A (mostly A), O, R, and sometimes I.

code:

Dunsparce ACDENPRSU
Cyndaquil ACDILNQUY
Poliwrath AHILOPRTW
Growlithe EGHILORTW

Kabutops ABKOPSTU
Clefairy ACEFILRY
Articuno ACINORTU
Quagsire AEGIQRSU
Sunflora AFLNORSU
Cloyster CELORSTY
Squirtle EILQRSTU
Slowking GIKLNOSW

Machoke ACEHKMO
Chansey ACEHNSY
Pikachu ACHIKPU
Flareon AEFLNOR
Seaking AEGIKNS
Haunter AEHNRTU
Starmie AEIMRST
Persian AEINPRS
Omanyte AEMNOTY
Spearow AEOPRSW
Poliwag AGILOPW
Miltank AIKLMNT
Ivysaur AIRSUVY
Snorlax ALNORSX
Umbreon BEMNORU
Golduck CDGKLOU
Psyduck CDKPSUY
Shuckle CEHKLSU
Scyther CEHRSTY
Pidgeot DEGIOPT
Dugtrio DGIORTU
Kingler EGIKLNR
Tyrogue EGORTUY
Moltres ELMORST

Ledyba ABDELY
Crobat ABCORT
Golbat ABGLOT
Kabuto ABKOTU
Raichu ACHIRU
Machop ACHMOP
Fearow AEFORW
Horsea AEHORS
Mankey AEKMNY
Slugma AGLMSU
Gastly AGLSTY
Raikou AIKORU
Ponyta ANOPTY
Tauros AORSTU
Staryu ARSTUY
Cubone BCENOU
Swinub BINSUW
Pineco CEINOP
Scizor CIORSZ
Pidgey DEGIPY
Rhydon DHNORY
Togepi EGIOPT
Meowth EHMOTW
Vulpix ILPUVX

Magby ABGMY
Arbok ABKOR
Zubat ABTUZ
Ekans AEKNS
Lugia AGILU
Aipom AIMOP
Pichu CHIPU
Golem EGLMO
Hypno HNOPY

Natu ANTU
Xatu ATUX
Onix INOX
Jynx JNXY

Mew EMW

I came across a puzzle idea (or three, actually) in doing this... but I haven't decided whether to bother formally posting anything... but no, Psyduck is the only one that doesn't conflict with any of the top five...

The Hint Fairy
Posted: Tue Mar 19, 2002 5:10 pm    Post subject: -31

I looked at Nintendo's Official Pokedex, and found these 7's with no repeats:

Ivysaur
Metapod
Pidgeot
Spearow
Pikachu
Dugtrio
Persian
Psyduck
Golduck
Poliwag
Machoke
Haunter
Kingler
Chansey
Seaking
Starmie
Scyther
Omanyte
Snorlax
Moltres
Umbreon
Shuckle
Kingdra
Tyrogue
Miltank

How many was that? 25? We need a 7 and a 9 to tie with Psyduck and Growlithe. That's 125 possibilities.
mathgrant
Posted: Tue Mar 19, 2002 3:35 pm    Post subject: -32

Well duh! I'm a Pokemon fan, and I'm The Hint Fairy, so The Hint Fairy is a Pokemon fan!

------------------
Sometimes life gives you a deck without any aces. Deal with it.
Chuck
Posted: Tue Mar 19, 2002 3:29 pm    Post subject: -33

Factoring the numbers isn't necessary. I don't know if it will help. Doing so might cause you to notice things, I suppose.
ctrlaltdel
Posted: Tue Mar 19, 2002 12:20 pm    Post subject: -34

im still clueless, im messing around with dividing each number with all of its primes... am i on the right track even...?
Jen Aside
Posted: Tue Mar 19, 2002 11:12 am    Post subject: -35

Considering:

Dunsparce, Cyndaquil, Dragonite, Poliwrath, and Growlithe all have nine letters each,

and

Kabutops, Clefairy, Articuno, Quagsire, Sunflora, Cloyster, Squirtle, and Slowking all have eight letters each,

and

any two pairs of Pokémon listed above share at least one letter,

and

there are no other Pokémon with more than seven letters in its name (non-repeating),

Growlithe and Psyduck have the most non-repeating letters between them of any pair (although other pairs might tie--I haven't bothered to check).

Is the Hint Fairy a Pokémon fan, or is it just a ready puzzle source?

...this seems unrelated, but only invisibly so
The Hint Fairy
Posted: Mon Mar 18, 2002 3:01 pm    Post subject: -36

It does in this case. Can you find the logic behind thestarters for that sequence?
cubestudent
Posted: Mon Mar 18, 2002 9:29 am    Post subject: -37

my mind has slowed too far with age.

i think if i were 14, i could get it too.

remarkable puzzle, chuck
ctrlaltdel
Posted: Mon Mar 18, 2002 9:12 am    Post subject: -38

8100 ->modChuck-> 2916 = 0???

insane...

does the fact that 8100 = 81x4x5^2
and 2916 = 81x4x3^2 (or 3^6x4) mean anything?

[This message has been edited by ctrlaltdel (edited 03-18-2002 04:18 AM).]