PIN puzzle #2 (easier than the last, all welcome)

[Jon Corby]

I have an automated phone system which requires me to enter a 4-digit PIN using the phone keys. The system unlocks when the last 4 digits entered (in the correct sequence) are your PIN, that is to say that any previous invalid key presses are ignored. For example, if your pin is 1123, entering 1123, 11123, 41123 will all result in success.

Say you have amnesia and forget your PIN. What is the minimum number of keypresses required to be guaranteed entry to the system?

[Eoin Monaghan]

What if you had amnesia and forgot why you there in the first place?

[Jon Corby]

What if you had amnesia and forgot why you there in the first place?

Good point. You'd have also forgotten the phone number to call in the first instance before you got as far as the PIN part. I need to rethink.

[Jon O'Neill]

I have an automated phone system

you ... forget your PIN.

Why do I have a pin to your system?

My suggestion for the wording is..

"You are trying to break into Jeff Stelling's automated phone system..."

[Matt Morrison]

I can only guess that this seeming ridiculously fucking hard to me when you've called it easy shows how dumb I am. No idea.

[Jon Corby]

I have an automated phone system

you ... forget your PIN.

Why do I have a pin to your system?

My suggestion for the wording is..

"You are trying to break into Jeff Stelling's automated phone system..."

Another good point. Perhaps my amnesia has made me forget my identity, such that I now think I'm you? This is getting confusing.

[Howard Somerset]

Having tried a few simpler examples, with shorter pins, and fewer numbers to choose from, I'm going to take a wild guess at 10003, but yet to be convinced that this is correct. It certainly can't be less.

(edited to remove spoiler)

[Howard Somerset]

Getting slightly more convinced of 10003 now, as I've found more possibilities that fit the pattern.

[Howard Somerset]

Pretty well satisfied now that 10003 is correct. But don't ask me to produce a string that long.

[Jon Corby]

You certainly couldn't get any lower than that Howard. But can you actually build such a string of digits? (I can )

[Howard Somerset]

But can you actually build such a string of digits? (I can )

I'm sure I could, given enough time and patience. I've managed an equivalent string for a number of easier targets with no difficulty at all.

[Howard Somerset]

You certainly couldn't get any lower than that Howard. But can you actually build such a string of digits? (I can )

I can, now, having spent a few minutes pondering over it before getting up. I won't demonstrate the full string, but will for a cut-down one which involves a three digit pin, with just the numbers 1, 2, 3, 4 from which to chose.

In the general case, with an A digit pin, and B different digits to choose from, the minimum string is B^A + (A-1) characters long. This even works for the trivial cases when either A or B are one.

One way of choosing a suitable string is to start with A-1 of the highest digit possible, and then for all subsequent selections make sure that the digit chosen gives the lowest pin number which has not already been selected.

So, for the problem given, the string will start 9990000100020003 ...

For the three-digit pin, with only 1,2,3,4 to choose from, my algorithm generates the following 66 character string:
441112113114122123124132133134142143144222322423323424324433343444
and, unless I've made a careless typing error, this contains all possible 3 digit pins, each occurring just once.

[Dinos Sfyris]

wat howard did

[Jon Corby]

Beautifully done Howard. Here's the full string btw:

Code: Select all

99900001000200030004000500060007000800090011001200130014001500160017001800190021002200230024002500260027002800290031003200330034003500360037003800390041004200430044004500460047004800490051005200530054005500560057005800590061006200630064006500660067006800690071007200730074007500760077007800790081008200830084008500860087008800890091009200930094009500960097009800990101020103010401050106010701080109011101120113011401150116011701180119012101220123012401250126012701280129013101320133013401350136013701380139014101420143014401450146014701480149015101520153015401550156015701580159016101620163016401650166016701680169017101720173017401750176017701780179018101820183018401850186018701880189019101920193019401950196019701980199020203020402050206020702080209021102120213021402150216021702180219022102220223022402250226022702280229023102320233023402350236023702380239024102420243024402450246024702480249025102520253025402550256025702580259026102620263026402650266026702680269027102720273027402750276027702780279028102820283028402850286028702880289029102920293029402950296029702980299030304030503060307030803090311031203130314031503160317031803190321032203230324032503260327032803290331033203330334033503360337033803390341034203430344034503460347034803490351035203530354035503560357035803590361036203630364036503660367036803690371037203730374037503760377037803790381038203830384038503860387038803890391039203930394039503960397039803990404050406040704080409041104120413041404150416041704180419042104220423042404250426042704280429043104320433043404350436043704380439044104420443044404450446044704480449045104520453045404550456045704580459046104620463046404650466046704680469047104720473047404750476047704780479048104820483048404850486048704880489049104920493049404950496049704980499050506050705080509051105120513051405150516051705180519052105220523052405250526052705280529053105320533053405350536053705380539054105420543054405450546054705480549055105520553055405550556055705580559056105620563056405650566056705680569057105720573057405750576057705780579058105820583058405850586058705880589059105920593059405950596059705980599060607060806090611061206130614061506160617061806190621062206230624062506260627062806290631063206330634063506360637063806390641064206430644064506460647064806490651065206530654065506560657065806590661066206630664066506660667066806690671067206730674067506760677067806790681068206830684068506860687068806890691069206930694069506960697069806990707080709071107120713071407150716071707180719072107220723072407250726072707280729073107320733073407350736073707380739074107420743074407450746074707480749075107520753075407550756075707580759076107620763076407650766076707680769077107720773077407750776077707780779078107820783078407850786078707880789079107920793079407950796079707980799080809081108120813081408150816081708180819082108220823082408250826082708280829083108320833083408350836083708380839084108420843084408450846084708480849085108520853085408550856085708580859086108620863086408650866086708680869087108720873087408750876087708780879088108820883088408850886088708880889089108920893089408950896089708980899090911091209130914091509160917091809190921092209230924092509260927092809290931093209330934093509360937093809390941094209430944094509460947094809490951095209530954095509560957095809590961096209630964096509660967096809690971097209730974097509760977097809790981098209830984098509860987098809890991099209930994099509960997099809991111211131114111511161117111811191122112311241125112611271128112911321133113411351136113711381139114211431144114511461147114811491152115311541155115611571158115911621163116411651166116711681169117211731174117511761177117811791182118311841185118611871188118911921193119411951196119711981199121213121412151216121712181219122212231224122512261227122812291232123312341235123612371238123912421243124412451246124712481249125212531254125512561257125812591262126312641265126612671268126912721273127412751276127712781279128212831284128512861287128812891292129312941295129612971298129913131413151316131713181319132213231324132513261327132813291332133313341335133613371338133913421343134413451346134713481349135213531354135513561357135813591362136313641365136613671368136913721373137413751376137713781379138213831384138513861387138813891392139313941395139613971398139914141514161417141814191422142314241425142614271428142914321433143414351436143714381439144214431444144514461447144814491452145314541455145614571458145914621463146414651466146714681469147214731474147514761477147814791482148314841485148614871488148914921493149414951496149714981499151516151715181519152215231524152515261527152815291532153315341535153615371538153915421543154415451546154715481549155215531554155515561557155815591562156315641565156615671568156915721573157415751576157715781579158215831584158515861587158815891592159315941595159615971598159916161716181619162216231624162516261627162816291632163316341635163616371638163916421643164416451646164716481649165216531654165516561657165816591662166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[Dinos Sfyris]

You misspelt Dinos