World!Of
Numbers
HOME plate
WON |

EMBED
The Nine Digits Most Recent Page
with some Ten Digits (pandigital) exceptions
rood Page 4 rood Page 3 rood Page 2 rood Page 1 rood comments



Most Recent Page


[ April 27, 2014 ]
Order out of chaos using the ninedigits

Numberphile has released a video file that relates to the ninedigits.
Near the end of the video the zero comes in as well!
https://www.youtube.com/watch?v=CwIAfkuXc5A&feature=em-uploademail

And here is a video explaining the mysterious math from above
which is in fact the Erdös-Szekeres theorem.
https://www.youtube.com/watch?v=LBPj8E1JKaQ&feature=em-uploademail


[ December 15, 2013 ]
Nearing the end of the year 2013

There is a unique ninedigital number that when divided by the year 2013 delivers a palindrome.
Ain't that nice!

127495368 = 2013 * 63336

Who likes to do this exercise for the coming years 2014, 2015, ...
And what about the pandigital version of this topic ?


[ January 1, 2013 ]
The ninedigital primes version of WONplate 181

The following ninedigital numbers are all (probable (3-PRP!)) prime.
Note that the 5-digit displacements are also prime !
1325! + 87649
1462! + 59387
1475! + 96823
1547! + 68239
1685! + 29437
2351! + 74869
2354! + 86197
2468! + 75193
2486! + 15973
2615! + 84793
2876! + 15493
3218! + 45697
3845! + 76129
4618! + 32579
4895! + 76213
4981! + 62753
8153! + 72649
8573! + 41269
9625! + 34781
9824! + 61357
1438! - 57269
1478! - 52369
1486! - 59273
1576! - 28493
1849! - 67523
2471! - 63589
2536! - 84179
3469! - 28751
4285! - 71963
4562! - 93871
4691! - 52837
5239! - 16487
5417! - 86923
5462! - 98317
5743! - 68219
5749! - 26183
7948! - 23561
7982! - 45361
8123! - 47569
9836! - 25147


[ December 30, 2010 ]
From a posting to [SeqFan]
by Eric Angelini.

"As an afterthought, here's one I like (because of
the symmetry in the operations) that was appropriate
for the countdown on Friday night { can you find out the exact year? }:

10 + 9 * 8 * 7 / 6 * 5 * 4 + 321

Happy New Year! "


[ April 2008 ]
Fractions using the same digits as their decimal representation
A webpage by Christian Boyer.

An example using all the nine digits from
http://www.christianboyer.com/fractiondigits/ is

124983 / 576 = 216.984375

The above link came from a reply in the SeqFan mailing list where
Alexander R. Povolotsky's topic was about approximating Pi
using just nine- and pandigitals. Here is his *best* combination !

689725314(0) / 219546387(0) = 3.141592642...


[ March 31, 2008 ]
Blending palindromes with nine- & pandigitals using multiplication by 9
by B.S. Rangaswamy

This topic is a continuation from wonplate 173.

Pandigitals (Kmil = 1000 million) total = 559

Palindrome	Pandigital
P9 P9 * 9
Palindrome Ninedigital
P8 P8 * 9     
Palindrome	Pandigital
P9 P9 * 9
Palindrome Ninedigital
P8 P8 * 9     
Palindrome	Pandigital
P9 P9 * 9
Palindrome Ninedigital
P8 P8 * 9     
Palindrome	Pandigital
P9 P9 * 9
Palindrome Ninedigital
P8 P8 * 9     
1 Kmil  # 81
2 Kmil  # 46

134050431 1206453879 134060431 1206543879 136717631 1230458679 136727631 1230548679 137606731 1238460579 137626731 1238640579 137818731 1240368579 137848731 1240638579 138929831 1250368479 138959831 1250638479 139828931 1258460379 139848931 1258640379 143050341 1287453069 143060341 1287543069 145030541 1305274869 145080541 1305724869 145272541 1307452869 145282541 1307542869 146717641 1320458769 146727641 1320548769 148919841 1340278569 148969841 1340728569 152676251 1374086259 152898251 1376084259 154030451 1386274059 154080451 1386724059 156252651 1406273859 156303651 1406732859 156373651 1407362859 157818751 1420368759 157848751 1420638759 158707851 1428370659 158747851 1428730659 158919851 1430278659 158969851 1430728659 167030761 1503276849 167080761 1503726849 167363761 1506273849 167414761 1506732849 167484761 1507362849 168929861 1520368749 168959861 1520638749 169818961 1528370649 169858961 1528730649 174898471 1574086239 176030671 1584276039 176080671 1584726039 176252671 1586274039 178050871 1602457839 178060871 1602547839 178252871 1604275839 178363871 1605274839 182565281 1643087529 183676381 1653087429 187050781 1683457029 187060781 1683547029 187303781 1685734029 187494781 1687453029 189272981 1703456829 189282981 1703546829 189373981 1704365829 189484981 1705364829 189515981 1705643829 215030512 1935274608 215080512 1935724608 215272512 1937452608 215282512 1937542608 216252612 1946273508 216303612 1946732508 217030712 1953276408 217080712 1953726408 217414712 1956732408 217484712 1957362408 218050812 1962457308 218060812 1962547308 218363812 1965274308 219272912 1973456208 219282912 1973546208 219373912 1974365208 219484912 1975364208 219515912 1975643208
224050422 2016453798 224060422 2016543798 225717522 2031457698 225727522 2031547698 226404622 2037641598 226818622 2041367598 226848622 2041637598 227959722 2051637498 240545042 2164905378 240656042 2165904378 255717552 2301457968 255727552 2301547968 264010462 2376094158 264404462 2379640158 266818662 2401367958 266848662 2401637958 268121862 2413096758 268454862 2416093758 277929772 2501367948 277959772 2501637948 279232972 2513096748 279565972 2516093748 286010682 2574096138 286232682 2576094138 286606682 2579460138 286626682 2579640138 315010513 2835094617 315494513 [Obs] 2839450617 315595513 2840359617 315989513 2843905617 316595613 2849360517 317010713 2853096417 318232813 2864095317 318343813 2865094317 326020623 2934185607 326090623 2934815607 326131623 2935184607 326494623 2938451607 327020723 2943186507 327090723 2943816507 327353723 2946183507 327595723 2948361507 328464823 2956183407 329050923 2961458307 329060923 2961548307 329464923 2965184307
3 Kmil  # 74
4 Kmil  # 90

336020633 3024185697 336090633 3024815697 336131633 3025184697 336494633 3028451697 341050143 3069451287 341060143 3069541287 344717443 3102456987 344727443 3102546987 347121743 3124095687 347232743 3125094687 360121063 3241089567 360212063 3241908567 360989063 3248901567 361202163 3250819467 361232163 3251089467 361323163 3251908467 364505463 3280549167 364989463 3284905167 365101563 3285914067 365494563 3289451067 365717563 3291458067 365727563 3291548067 378101873 3402916857 378545873 3406912857 389212983 3502916847 389656983 3506912847 412050214 3708451926 412060214 3708541926 412676214 3714085926 412787214 3715084926 413272314 3719450826 413282314 3719540826 416454614 3748091526 416545614 3748910526 416575614 3749180526 417565714 3758091426 417656714 3758910426 417686714 3759180426 420545024 3784905216 420656024 3785904216 422050224 3798452016 422060224 3798542016 423050324 3807452916 423060324 3807542916 425010524 3825094716 425494524 3829450716 427454724 3847092516 427696724 3849270516 428010824 3852097416 428565824 3857092416 431050134 3879451206 431060134 3879541206 432505234 3892547106 432747234 3894725106 432808234 3895274106 432858234 3895724106 435030534 3915274806 435080534 3915724806 435272534 3917452806 435282534 3917542806 435717534 3921457806 435727534 3921547806 436020634 3924185706 436090634 3924815706 436131634 3925184706 436494634 3928451706 438020834 3942187506 438090834 3942817506 438575834 3947182506 438696834 3948271506 439030934 3951278406 439080934 3951728406 439131934 3952187406 439686934 3957182406
445919544 4013275896 446202644 4015823796 448020844 4032187596 448090844 4032817596 448575844 4037182596 448646844 4037821596 448696844 4038271596 451030154 4059271386 451080154 4059721386 452373254 4071359286 452393254 4071539286 455919554 4103275986 455969554 4103725986 459121954 4132097586 459676954 4137092586 462010264 4158092376 462202264 4159820376 467101764 4203915876 480212084 4321908756 480989084 4328901756 485676584 4371089256 485767584 4371908256 486454684 4378092156 486646684 4379820156 486989684 4382907156 487545784 4387912056 487919784 4391278056 487969784 4391728056 512030215 4608271935 512080215 4608721935 512303215 4610728935 513010315 4617092835 513252315 4619270835 513353315 4620179835 513545315 4621907835 514232415 4628091735 514323415 4628910735 514353415 4629180735 519010915 4671098235 519787915 4678091235 519878915 4678910235 521454125 4693087125 521898125 4697083125 523181325 4708631925 523404325 4710638925 523676325 4713086925 524010425 4716093825 524373425 4719360825 526454625 4738091625 526545625 4738910625 526575625 4739180625 529010925 4761098325 529787925 4768091325 529878925 4768910325 531545135 4783906215 531878135 4786903215 533151335 4798362015 533181335 4798632015 534030435 4806273915 534080435 4806723915 534151435 4807362915 534181435 4807632915 536232635 4826093715 536595635 4829360715 536696635 4830269715 536989635 4832906715 537454735 4837092615 537696735 4839270615 541030145 4869271305 541080145 4869721305 541252145 4871269305 541292145 4871629305 542151245 4879361205 542181245 4879631205 543626345 4892637105 543747345 4893726105 546252645 4916273805 546303645 4916732805 546373645 4917362805 546818645 4921367805 546848645 4921637805 547020745 4923186705 547090745 4923816705 547353745 4926183705 547595745 4928361705 548020845 4932187605 548090845 4932817605 548575845 4937182605 548646845 4937821605 548696845 4938271605
5 Kmil  # 64
6 Kmil  # 78

623020326 5607182934 623090326 5607812934 623141326 5608271934 623191326 5608721934 623414326 5610728934 623565326 5612087934 624121426 5617092834 624363426 5619270834 624464426 5620179834 624656426 5621907834 625343526 5628091734 625434526 5628910734 625464526 5629180734 630121036 5671089324 630212036 5671908324 630989036 5678901324 632565236 5693087124 633020336 5697183024 633090336 5697813024 634020436 5706183924 634090436 5706813924 634262436 5708361924 634292436 5708631924 634515436 5710638924 634787436 5713086924 635121536 5716093824 635484536 5719360824 637565736 5738091624 637656736 5738910624 637686736 5739180624 642656246 5783906214 642989246 5786903214 644262446 5798362014 644292446 5798632014 645141546 5806273914 645191546 5806723914 645262546 5807362914 645292546 5807632914 647010746 5823096714 647343746 5826093714 648010846 5832097614 648565846 5837092614 652141256 5869271304 652191256 5869721304 652363256 5871269304 653262356 5879361204 653292356 5879631204 654707456 5892367104 654737456 5892637104 654808456 5893276104 654858456 5893726104 657030756 5913276804 657080756 5913726804 657363756 5916273804 657414756 5916732804 657484756 5917362804 657929756 5921367804 657959756 5921637804 658131856 5923186704 658464856 5926183704 659030956 5931278604 659080956 5931728604 659131956 5932187604 659686956 5937182604
668202866 6013825794 668424866 6015823794 671030176 6039271584 671080176 6039721584 673101376 6057912384 673252376 6059271384 674595476 6071359284 682010286 6138092574 682202286 6139820574 684232486 6158092374 684424486 6159820374 689323986 6203915874 689545986 6205913874 712030217 6408271953 712080217 6408721953 712303217 6410728953 712454217 6412087953 713010317 6417092853 713252317 6419270853 713353317 6420179853 713545317 6421907853 714232417 6428091753 714323417 6428910753 714353417 6429180753 719010917 6471098253 719878917 6478910253 723020327 6507182943 723090327 6507812943 723141327 6508271943 723191327 6508721943 723414327 6510728943 723565327 6512087943 724121427 6517092843 724363427 6519270843 724464427 6520179843 724656427 6521907843 725343527 6528091743 725434527 6528910743 725464527 6529180743 745020547 6705184923 745090547 6705814923 745383547 6708451923 745393547 6708541923 745606547 6710458923 745616547 6710548923 746010647 6714095823 746121647 6715094823 749010947 6741098523 749787947 6748091523 749878947 6748910523 753878357 6784905213 753989357 6785904213 755383557 6798452013 755393557 6798542013 756030657 6804275913 756080657 6804725913 756141657 6805274913 756191657 6805724913 756383657 6807452913 756393657 6807542913 758232857 6824095713 758343857 6825094713 761030167 6849271503 761080167 6849721503 762141267 6859271403 762191267 6859721403 764383467 6879451203 764393467 6879541203 765828567 6892457103 765838567 6892547103 768050867 6912457803 768060867 6912547803 768252867 6914275803 768363867 6915274803 769050967 6921458703 769060967 6921548703 769353967 6924185703 769464967 6925184703
7 Kmil  # 69
8 Kmil  # 57

781050187 7029451683 781060187 7029541683 783474387 7051269483 785101587 7065914283 785494587 7069451283 812050218 7308451962 812060218 7308541962 812676218 7314085962 812787218 7315084962 816454618 7348091562 816575618 7349180562 817565718 7358091462 817656718 7358910462 821565128 7394086152 821787128 7396084152 823151328 7408361952 823181328 7408631952 824010428 7416093852 824373428 7419360852 826454628 7438091652 826545628 7438910652 826575628 7439180652 829010928 7461098352 829787928 7468091352 829878928 7468910352 834020438 7506183942 834090438 7506813942 834262438 7508361942 834292438 7508631942 834515438 7510638942 834787438 7513086942 835121538 7516093842 835484538 7519360842 837565738 7538091642 837656738 7538910642 837686738 7539180642 840121048 7561089432 840212048 7561908432 840989048 7568901432 843787348 7594086132 844020448 7596184032 844090448 7596814032 845020548 7605184932 845090548 7605814932 845383548 7608451932 845393548 7608541932 845606548 7610458932 845616548 7610548932 846010648 7614095832 846121648 7615094832 849010948 7641098532 849787948 7648091532 849878948 7648910532 867050768 7803456912 867060768 7803546912 867151768 7804365912 867181768 7804635912 867383768 7806453912 867393768 7806543912 871050178 7839451602 871060178 7839541602 871262178 7841359602 873262378 7859361402 873292378 7859631402 874383478 7869451302 874393478 7869541302 879272978 7913456802 879282978 7913546802 879515978 7915643802
915010519 8235094671 915595519 8240359671 915989519 8243905671 916595619 8249360571 917010719 8253096471 917343719 8256093471 918232819 8264095371 918343819 8265094371 923050329 8307452961 923060329 8307542961 925010529 8325094761 925494529 8329450761 927454729 8347092561 927696729 8349270561 928010829 8352097461 928565829 8357092461 934030439 8406273951 934080439 8406723951 934151439 8407362951 934181439 8407632951 936232639 8426093751 936595639 8429360751 936696639 8430269751 936989639 8432906751 937454739 8437092651 937696739 8439270651 945141549 8506273941 945191549 8506723941 945262549 8507362941 945292549 8507632941 947010749 8523096741 947343749 8526093741 948010849 8532097641 948565849 8537092641 951434159 8562907431 951989159 8567902431 955141559 8596274031 955191559 8596724031 956030659 8604275931 956080659 8604725931 956141659 8605274931 956383659 8607452931 956393659 8607542931 958232859 8624095731 958343859 8625094731 963878369 8674905321 963989369 8675904321 966383669 8697453021 966393669 8697543021 967050769 8703456921 967060769 8703546921 967151769 8704365921 967181769 8704635921 967262769 8705364921 967292769 8705634921 967383769 8706453921 967393769 8706543921

[ June 14, 2014 ]
Observation by Heine Wanderlust (email)

315494513 (a prime by the way) * 9 = the pandigital 2839450617.
But multiply by 18 and you get a pandigital with a nice permutation: 5678901234.
Also in both these pandigitals the differences between each
successive digit creates a palindrome: 656515656, 111191111


[ January 22, 2006 ]
Pandigital... throughout

A unique construction : start with multiplying these two
5-digit factors which taken together form a pandigital number :

54981 * 62037

equals

3410856297

as you can see the result of the multiplication is pandigital as well.
And now let us take the square of this pandigital 34108562972

11633940678784552209

... an order_2 pandigital emerges since all the digits from 0 to 9
occur exactly two times !

Discover more of these gems at wonplate 167 !


[ October 26, 2005 ]
From Palindromic Squares to Pandigitals

264 is a very interesting number since it is the 12th basenumber of a palindromic square.
The square itself is this nice palindrome 69696.
Note the presence of the number of the Beast ! 69696 .

Did you know that when we power up 264 with two exponents and add them up
that we arrive at a pandigital number... in two different ways !

2643 + 2644 = 4875932160
2644 + 2644 = 9715064832

The second equation can be written as a palindromic expression itself using
69696 squared and then doubled

 2 * 69696 ^ 2 
(There exists another 5-digit palindrome with this property. Can you discover it ?)

B.S. Rangaswamy [ August 11, 2006 ] was enthused by this presentation
and found the following solutions :

232322 *   8 = 4317806592 = 464642 * 2
232322 * 18 = 9715064832 = 696962 * 2
423242 *   4 = 7165283904

One can play along with other than our 264 number namely 2016.
I found the next equation of some interest.

20162 + 20163 = 8197604352

Or the next one with two consecutive integers

233 * 244 = 4036718592

Is there more to discover ?

Yes, see Claudio Meller's contribution at WONplate 183


[ October 2005 ]
Figure this out : 4-1-4

It is a four digit number multiplied by a one digit number to equal another four digit number
    and only the nine digits from 1 to 9 can be used once ?

Two solutions to this 9-digit problem can be found.

1738 * 4 = 6952
1963 * 4 = 7852


[ October 2006 ]
Figure this out : 4-1-5

It is a four digit number multiplied by a one digit number to equal a five digit number
    and only the ten digits from 0 to 9 can be used once ?

Thirteen solutions to this pandigital problem can be found.

3094 * 7 = 21658
3907 * 4 = 15628
4093 * 7 = 28651
5694 * 3 = 17082
5817 * 6 = 34902
6819 * 3 = 20457
6918 * 3 = 20754
7039 * 4 = 28156
8169 * 3 = 24507
9127 * 4 = 36508
9168 * 3 = 27504
9304 * 7 = 65128
9403 * 7 = 65821


[ September 4, 2005 ]
Generating Pandigitals from Palindromes through Fibonacci iteration
by B.S. Rangaswamy

" I got inspired by your presentation of the derivation of 68 ninedigit numbers (with all numerals from 1 to 9)
from palindromes through Fibonacci iteration. I have developed it further by arriving at a dozen 10 digit numbers
(with all numerals from 0 to 9) from 2 to 10 digit palindromes. Some of the 10 digit numbers arrived at
together with their mother palindromes are :

75257 9135748206
799997 2067193845
8055508 4913860257
42944924 2361970854

It is interesting to note that 6300036 leads to pandigital 1467908532, which matches identically
with each stage of iteration of 630036 to 146798532. I came across another curio as well :

630036   146798532
6300036 1467908532

9530359   123894675
95300359 1238904675

Following closely resembling palindromes lead to closely matching pandigitals :

592070295 2960351478
952070259 4760351298

This task began at my son’s residence in Florida US and was completed at Bangalore India.
I was thrilled at the discovery of each of these pandigitals.

I am grateful to you for your encouragement and guidance in this venture.
B.S.Rangaswamy "



In total there are 117 palindromes that yield pandigital numbers
The smallest one is 75257 and the largest one is 4376006734 ¬

1. Typical generation of pandigitals (10 digits) from palindromes through Fibonacci iteration
1
75257
75258
150515
225773
376288
602061
978349
1580410
2558759
4139169
6697928
10837097
17535025
28372122
45907147
74279269
120186416
194465685
314652101
509117786
823769887
1332887673
2156657560
3489545233
5646202793
9135748026
1
799997
799998
1599995
2399993
3999988
6399981
10399969
16799950
27199919
43999869
71199788
115199657
186399445
301599102
487998547
789597649
1277596196
2067193845
1
6431346
6431347
12862693
19294040
32156733
51450773
83607506
135058279
218665785
353724064
572389849
926113913
1498503762
1
408676804
408676805
817353609
1226030414
2043384023
3269414437
5312798460
1
561262165
561262166
1122524331
1683786497
2806310828
4490097325
7296408153
1
760474067
760474068
1520948135
2281422203
3802370338
6083792541
1
93811839
93811840
187623679
281435519
469059198
750494717
1219553915
1970048632
3189602547
1
1206776021
1206776022
2413552043
3620328065
6033880108
9654208173
1
3067447603
3067447604
6134895207
1
4068228604
4068228605
8136457209
117
in total

2. Above are 117 palindromes in ascending order, leading to pandigitals (10 digits)
75257
799997
2877782
4364634
4689864
5068605
6300036
6431346
6881886
8055508
15844851
42944924
54777745
93811839
95300359
146353641
177858771
185121581
185222581
187333781
207313702
238242832
245363542
295747592
310717013
314878413
324151423
348616843
350878053
354010453
358070853
370464073
370797073
390474093
394070493
395313593
395727593
407525704
408676804
460363064
473303374
475686574
506939605
527121725
527454725
530878035
536454635
547252745
561262165
590272095
592070295
629171926
642676246
655191556
695525596
740838047
760474067
782484287
841303148
914272419
950272059
952070259
1089229801
1097337901
1098228901
1206776021
1289009821
1295335921
1298008921
1395225931
1397007931
2068448602
2069339602
2158448512
2159339512
2359119532
2365445632
2369009632
2456336542
2458118542
2465335642
2468008642
3067447603
3069229603
3076446703
3079119703
3157447513
3159229513
3175445713
3179009713
3256446523
3259119523
3265445623
3269009623
3456226543
3457117543
3465225643
3467007643
3475115743
3476006743
4067337604
4068228604
4076336704
4078118704
4086226804
4087117804
4158228514
4175335714
4178008714
4185225814
4187007814
4258118524
4268008624
4286006824
4365225634
4367007634
4376006734

3. Queen and King combinations of
palindromes vs. pandigitals
 PalindromeNinedigital PalindromePandigital 
 QUEEN KING 
  630036
9530359
128909821
129808921
139707931
236909632
246808642
317909713
326909623
346707643
347606743
417808714
418707814
426808624
428606824
436707634
437606734
146798532
123894675
257819643
259617843
279415863
473819265
493617285
635819427
653819247
693415287
695213487
835617429
837415629
853617249
857213649
873415269
875213469
  6300036
95300359
1289009821
1298008921
1397007931
2369009632
2468008642
3179009713
3269009623
3467007643
3476006743
4178008714
4187007814
4268008624
4286006824
4367007634
4376006734
1467908532
1238904675
2578019643
2596017843
2794015863
4738019265
4936017285
6358019427
6538019247
6934015287
6952013487
8356017429
8374015629
8536017249
8572013649
8734015269
8752013469
 

4. Scintillating Grid
one pair each of digits 0, 3, 4, 6 & 7
 PalindromePandigital 
  0346707643
0347606743
0436707634
0437606734
3067447603
3076446703
3467007643
3476006743
4067337604
4076336704
4367007634
4376006734
0693415287
0695213487
0873415269
0875213469
6134895207
6152893407
6934015287
6952013487
8134675209
8152673409
8734015269
8752013469
 















Contributions

B.S. Rangaswamy (email) - go to topic 1

B.S. Rangaswamy (email) - go to topic 2









[up TOP OF PAGE]


(All rights reserved) - Last modified : July 10, 2014.
Patrick De Geest - Belgium flag - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com