non profit math problem

[PAHH]

Hello all:
This may be the only question I ever ask here, so pardon if I posted in wrong forum.

I work for Habitat for Humanity, a non-profit 501(c) (3) org. A local business donated an open floor safe without a combination. We could really use this safe in our office. The manufacturer no longer has the master combination and want over $500 to come out to fix. We can't afford that, but from looking at the keypad, there are 4 numbers that look dirty and well used. Those numbers are: 2587

Can anyone provide me a list of all the number combinations possible for those four numbers?

 

[mmm4444bot]

Goofed-up post deleted by author

 

[PAHH]

Mark:

Thank you for the education! I just found out from the safe manufacturer that it is a 6 number combination. So I guess that means 6x5x4x3x2x1=720 possible combinations?

Do you have the time or interest to post these combos all based on 4 numbers used= 2578 ?

If not, thanks again for your answer!

Volunteers ROCK!

 

[mmm4444bot]

I deleted my first reply, since it no longer applies.

By the way, since the order of the digits in these numberings is important, we actually call each numbering a "permutation", not a "combination".

In other words, in a geek's world, locks would be called permutation locks, not combination locks.

Well, now we need to find all of the 6-digit "permutations with repetition" of the numbers {2, 5, 7, 8}, where each number appears at least once in the permutation.

Off the top of my head, I'm drawing a blank, as to a formula to count this set of permutations.

If we remove the constraint that each of the four available numbers must appear somewhere in the permutation, then there are 4,096 permutations possible.

I mean, with repetition, there are now four choices available for each of the six digits.

4 × 4 × 4 × 4 × 4 × 4 = 4[sup:153gbgq0]6[/sup:153gbgq0] = 4096

But that includes permutations like 222888, 222228, 755555, and so forth. We need to eliminate the permutations that do not include at least one 2, 5, 7, and 8.

I need to think about this, and I probably won't until tomorrow because I'll probably end up programming the computer to list and count them versus figuring out a mathematical formula, and I won't have time for that today.

Denis, need a project ?

 

[mmm4444bot]

If my programming holds water, then here's the list of the 1,560 six-digit permutations with repetition of digits {2, 5, 7, 8} where each digit appears at least once.

222578
222587
222758
222785
222857
222875
225278
225287
225578
225587
225728
225758
225778
225782
225785
225787
225788
225827
225857
225872
225875
225877
225878
225887
227258
227285
227528
227558
227578
227582
227585
227587
227588
227758
227785
227825
227852
227855
227857
227858
227875
227885
228257
228275
228527
228557
228572
228575
228577
228578
228587
228725
228752
228755
228757
228758
228775
228785
228857
228875
252278
252287
252578
252587
252728
252758
252778
252782
252785
252787
252788
252827
252857
252872
252875
252877
252878
252887
255278
255287
255578
255587
255728
255758
255778
255782
255785
255787
255788
255827
255857
255872
255875
255877
255878
255887
257228
257258
257278
257282
257285
257287
257288
257528
257558
257578
257582
257585
257587
257588
257728
257758
257778
257782
257785
257787
257788
257822
257825
257827
257828
257852
257855
257857
257858
257872
257875
257877
257878
257882
257885
257887
257888
258227
258257
258272
258275
258277
258278
258287
258527
258557
258572
258575
258577
258578
258587
258722
258725
258727
258728
258752
258755
258757
258758
258772
258775
258777
258778
258782
258785
258787
258788
258827
258857
258872
258875
258877
258878
258887
272258
272285
272528
272558
272578
272582
272585
272587
272588
272758
272785
272825
272852
272855
272857
272858
272875
272885
275228
275258
275278
275282
275285
275287
275288
275528
275558
275578
275582
275585
275587
275588
275728
275758
275778
275782
275785
275787
275788
275822
275825
275827
275828
275852
275855
275857
275858
275872
275875
275877
275878
275882
275885
275887
275888
277258
277285
277528
277558
277578
277582
277585
277587
277588
277758
277785
277825
277852
277855
277857
277858
277875
277885
278225
278252
278255
278257
278258
278275
278285
278522
278525
278527
278528
278552
278555
278557
278558
278572
278575
278577
278578
278582
278585
278587
278588
278725
278752
278755
278757
278758
278775
278785
278825
278852
278855
278857
278858
278875
278885
282257
282275
282527
282557
282572
282575
282577
282578
282587
282725
282752
282755
282757
282758
282775
282785
282857
282875
285227
285257
285272
285275
285277
285278
285287
285527
285557
285572
285575
285577
285578
285587
285722
285725
285727
285728
285752
285755
285757
285758
285772
285775
285777
285778
285782
285785
285787
285788
285827
285857
285872
285875
285877
285878
285887
287225
287252
287255
287257
287258
287275
287285
287522
287525
287527
287528
287552
287555
287557
287558
287572
287575
287577
287578
287582
287585
287587
287588
287725
287752
287755
287757
287758
287775
287785
287825
287852
287855
287857
287858
287875
287885
288257
288275
288527
288557
288572
288575
288577
288578
288587
288725
288752
288755
288757
288758
288775
288785
288857
288875
522278
522287
522578
522587
522728
522758
522778
522782
522785
522787
522788
522827
522857
522872
522875
522877
522878
522887
525278
525287
525578
525587
525728
525758
525778
525782
525785
525787
525788
525827
525857
525872
525875
525877
525878
525887
527228
527258
527278
527282
527285
527287
527288
527528
527558
527578
527582
527585
527587
527588
527728
527758
527778
527782
527785
527787
527788
527822
527825
527827
527828
527852
527855
527857
527858
527872
527875
527877
527878
527882
527885
527887
527888
528227
528257
528272
528275
528277
528278
528287
528527
528557
528572
528575
528577
528578
528587
528722
528725
528727
528728
528752
528755
528757
528758
528772
528775
528777
528778
528782
528785
528787
528788
528827
528857
528872
528875
528877
528878
528887
552278
552287
552578
552587
552728
552758
552778
552782
552785
552787
552788
552827
552857
552872
552875
552877
552878
552887
555278
555287
555728
555782
555827
555872
557228
557258
557278
557282
557285
557287
557288
557528
557582
557728
557782
557822
557825
557827
557828
557852
557872
557882
558227
558257
558272
558275
558277
558278
558287
558527
558572
558722
558725
558727
558728
558752
558772
558782
558827
558872
572228
572258
572278
572282
572285
572287
572288
572528
572558
572578
572582
572585
572587
572588
572728
572758
572778
572782
572785
572787
572788
572822
572825
572827
572828
572852
572855
572857
572858
572872
572875
572877
572878
572882
572885
572887
572888
575228
575258
575278
575282
575285
575287
575288
575528
575582
575728
575782
575822
575825
575827
575828
575852
575872
575882
577228
577258
577278
577282
577285
577287
577288
577528
577582
577728
577782
577822
577825
577827
577828
577852
577872
577882
578222
578225
578227
578228
578252
578255
578257
578258
578272
578275
578277
578278
578282
578285
578287
578288
578522
578525
578527
578528
578552
578572
578582
578722
578725
578727
578728
578752
578772
578782
578822
578825
578827
578828
578852
578872
578882
582227
582257
582272
582275
582277
582278
582287
582527
582557
582572
582575
582577
582578
582587
582722
582725
582727
582728
582752
582755
582757
582758
582772
582775
582777
582778
582782
582785
582787
582788
582827
582857
582872
582875
582877
582878
582887
585227
585257
585272
585275
585277
585278
585287
585527
585572
585722
585725
585727
585728
585752
585772
585782
585827
585872
587222
587225
587227
587228
587252
587255
587257
587258
587272
587275
587277
587278
587282
587285
587287
587288
587522
587525
587527
587528
587552
587572
587582
587722
587725
587727
587728
587752
587772
587782
587822
587825
587827
587828
587852
587872
587882
588227
588257
588272
588275
588277
588278
588287
588527
588572
588722
588725
588727
588728
588752
588772
588782
588827
588872
722258
722285
722528
722558
722578
722582
722585
722587
722588
722758
722785
722825
722852
722855
722857
722858
722875
722885
725228
725258
725278
725282
725285
725287
725288
725528
725558
725578
725582
725585
725587
725588
725728
725758
725778
725782
725785
725787
725788
725822
725825
725827
725828
725852
725855
725857
725858
725872
725875
725877
725878
725882
725885
725887
725888
727258
727285
727528
727558
727578
727582
727585
727587
727588
727758
727785
727825
727852
727855
727857
727858
727875
727885
728225
728252
728255
728257
728258
728275
728285
728522
728525
728527
728528
728552
728555
728557
728558
728572
728575
728577
728578
728582
728585
728587
728588
728725
728752
728755
728757
728758
728775
728785
728825
728852
728855
728857
728858
728875
728885
752228
752258
752278
752282
752285
752287
752288
752528
752558
752578
752582
752585
752587
752588
752728
752758
752778
752782
752785
752787
752788
752822
752825
752827
752828
752852
752855
752857
752858
752872
752875
752877
752878
752882
752885
752887
752888
755228
755258
755278
755282
755285
755287
755288
755528
755582
755728
755782
755822
755825
755827
755828
755852
755872
755882
757228
757258
757278
757282
757285
757287
757288
757528
757582
757728
757782
757822
757825
757827
757828
757852
757872
757882
758222
758225
758227
758228
758252
758255
758257
758258
758272
758275
758277
758278
758282
758285
758287
758288
758522
758525
758527
758528
758552
758572
758582
758722
758725
758727
758728
758752
758772
758782
758822
758825
758827
758828
758852
758872
758882
772258
772285
772528
772558
772578
772582
772585
772587
772588
772758
772785
772825
772852
772855
772857
772858
772875
772885
775228
775258
775278
775282
775285
775287
775288
775528
775582
775728
775782
775822
775825
775827
775828
775852
775872
775882
777258
777285
777528
777582
777825
777852
778225
778252
778255
778257
778258
778275
778285
778522
778525
778527
778528
778552
778572
778582
778725
778752
778825
778852
782225
782252
782255
782257
782258
782275
782285
782522
782525
782527
782528
782552
782555
782557
782558
782572
782575
782577
782578
782582
782585
782587
782588
782725
782752
782755
782757
782758
782775
782785
782825
782852
782855
782857
782858
782875
782885
785222
785225
785227
785228
785252
785255
785257
785258
785272
785275
785277
785278
785282
785285
785287
785288
785522
785525
785527
785528
785552
785572
785582
785722
785725
785727
785728
785752
785772
785782
785822
785825
785827
785828
785852
785872
785882
787225
787252
787255
787257
787258
787275
787285
787522
787525
787527
787528
787552
787572
787582
787725
787752
787825
787852
788225
788252
788255
788257
788258
788275
788285
788522
788525
788527
788528
788552
788572
788582
788725
788752
788825
788852
822257
822275
822527
822557
822572
822575
822577
822578
822587
822725
822752
822755
822757
822758
822775
822785
822857
822875
825227
825257
825272
825275
825277
825278
825287
825527
825557
825572
825575
825577
825578
825587
825722
825725
825727
825728
825752
825755
825757
825758
825772
825775
825777
825778
825782
825785
825787
825788
825827
825857
825872
825875
825877
825878
825887
827225
827252
827255
827257
827258
827275
827285
827522
827525
827527
827528
827552
827555
827557
827558
827572
827575
827577
827578
827582
827585
827587
827588
827725
827752
827755
827757
827758
827775
827785
827825
827852
827855
827857
827858
827875
827885
828257
828275
828527
828557
828572
828575
828577
828578
828587
828725
828752
828755
828757
828758
828775
828785
828857
828875
852227
852257
852272
852275
852277
852278
852287
852527
852557
852572
852575
852577
852578
852587
852722
852725
852727
852728
852752
852755
852757
852758
852772
852775
852777
852778
852782
852785
852787
852788
852827
852857
852872
852875
852877
852878
852887
855227
855257
855272
855275
855277
855278
855287
855527
855572
855722
855725
855727
855728
855752
855772
855782
855827
855872
857222
857225
857227
857228
857252
857255
857257
857258
857272
857275
857277
857278
857282
857285
857287
857288
857522
857525
857527
857528
857552
857572
857582
857722
857725
857727
857728
857752
857772
857782
857822
857825
857827
857828
857852
857872
857882
858227
858257
858272
858275
858277
858278
858287
858527
858572
858722
858725
858727
858728
858752
858772
858782
858827
858872
872225
872252
872255
872257
872258
872275
872285
872522
872525
872527
872528
872552
872555
872557
872558
872572
872575
872577
872578
872582
872585
872587
872588
872725
872752
872755
872757
872758
872775
872785
872825
872852
872855
872857
872858
872875
872885
875222
875225
875227
875228
875252
875255
875257
875258
875272
875275
875277
875278
875282
875285
875287
875288
875522
875525
875527
875528
875552
875572
875582
875722
875725
875727
875728
875752
875772
875782
875822
875825
875827
875828
875852
875872
875882
877225
877252
877255
877257
877258
877275
877285
877522
877525
877527
877528
877552
877572
877582
877725
877752
877825
877852
878225
878252
878255
878257
878258
878275
878285
878522
878525
878527
878528
878552
878572
878582
878725
878752
878825
878852
882257
882275
882527
882557
882572
882575
882577
882578
882587
882725
882752
882755
882757
882758
882775
882785
882857
882875
885227
885257
885272
885275
885277
885278
885287
885527
885572
885722
885725
885727
885728
885752
885772
885782
885827
885872
887225
887252
887255
887257
887258
887275
887285
887522
887525
887527
887528
887552
887572
887582
887725
887752
887825
887852
888257
888275
888527
888572
888725
888752

 

[PAHH]

EPIC!!!

I am humbled by your commitment here! It will take some time, as this safe (actually door to the safe, as it is already open) hibernates when wrong info is keyed in, but I will return when success is achieved!

THANK YOU!!!,

 

[mmm4444bot]

I hope that your office has a lot of volunteers.

If you're serious about using trial-and-error to discover the permutation, I strongly suggest that you first take a second look at those buttons.

I mean, a very close examination. Are you sure that no other buttons show any wear at all ?

Electronic locks are usually programmable; some can retain multiple permutations, all of which work to open the safe. Permutations can be turned off and on, as needs arise to give various persons access.

Consider a scenario where two permutations were used at lot: 221777 and 554888.

Over time, the 2, 5, 7, and 8 buttons would show a lot of wear; the 1 and 4 buttons would not show much wear.

I mean, I don't want to rain on your parade. Perhaps, you'll discover a permutation that works. It's just the thought that your approach may be flawed and you'll end up investing a lot of effort for nothing that makes me feel bad.

I wish you good fortune, either way.

Cheers ~ Mark