Brainteaser Rep to anyone who even attemps an answer (within reason)

I'm trying to make a quiz to help revise for a module at uni and have come across this in the revision notes, anybody fancy a guess?.

An Internet banking system allows customers to select their own 6-digit
security number. Two digits are selected at random by the bank for the
client to enter as an authentication mechanism each time the customer
logs in. Assuming an eavesdropper is able to read the digits entered by
the customer what is the least possible number of logins the
eavesdropper would have to see in order to learn the security number?

99 Comments

just a guess but 110?

I would say 3 but I assume its a trick question or something

Banned

this is part of an examination paper

bolton.ac.uk/Qua…pdf

Original Poster

There are 4 choices.

A 1 login
B 3 logins
C 15 logins
D 30 logins

I'm leaning towards once myself, maybe a trick question?. Either that or a badly written question:)

Banned

once.

Original Poster

casparwhite;7524705

this is part of an examination … this is part of an examination paperhttp://bolton.ac.uk/Quality/QAEContents/ExaminationPapers/Documents/200809Sem2/K-P/LCT2504.pdf



yup I'm sitting it on tuesday i'm making a multiple choice quiz on my iphone to help me remember. the first quarter of the exam is multiple choice & I have answered virtually all the rest just this one thats throwing me.

Original Poster

sassie;7524713

once.



Thats what I think it just seems to obvious though thats what was throwing me.:thinking:

Strange question.. Seems like a trick to me.

Gonna go with one.

How can you get a 6digit security number from seeing someone enter 2 numbers?

Banned

danmc;7524717

Thats what I think it just seems to obvious though thats what was … Thats what I think it just seems to obvious though thats what was throwing me.:thinking:



ide deffo go with one, i think its one of those that throw a load of bits in to make it appear more than it is

one..

one, but think the same as you to easy so must be a trick

Original Poster

bigfoot100;7524722

How can you get a 6digit security number from seeing someone enter 2 … How can you get a 6digit security number from seeing someone enter 2 numbers?



sassie;7524723

ide deffo go with one, i think its one of those that throw a load of bits … ide deffo go with one, i think its one of those that throw a load of bits in to make it appear more than it is



Trickyjabs;7524729

one..



Cheers all think I'm defo going for one If they where using a everypossible 2 combination of 0-9 surely it would be 99.

Cheers again all have some rep i'm off to bed.

Banned

well it aint any of the other ones

Its obviously 3 - the security number is 6 digits long and the customer types 2 of them in at random each time to login. As long as the random bit selects all 6 different numbers in 3 attempts then the thief gets the entire security number.

Banned

danmc;7524741

Cheers all think I'm defo going for one If they where using a … Cheers all think I'm defo going for one If they where using a everypossible 2 combination of 0-9 surely it would be 99.Cheers again all have some rep i'm off to bed.



no because ther is only 6 digits - lol

if it was about the two numbers and they are random it would be 36

3 i think!!!

2 digits of a 6 digit code each time..
if cust is given 2 digits each log in then it would be 3 min, assuming he gets 2 different each time!!!!

maybe...

It's late and I can't wrap my head around the question. When the customer goes to log in, does it mean they have to enter two digits into a string, like so:

4 2 2 [ ? ] [ ? ] 1

Or does it mean that only two digits appear on the screen like so:

4 [ ? ] 2 [ ? ] [ ? ] [? ]

and they have to enter the rest?

Or am I missing the point entirely?

We_Are_138;7524777

It's late and I can't wrap my head around the question. When the customer … It's late and I can't wrap my head around the question. When the customer goes to log in, does it mean they have to enter two digits into a string, like so:4 2 2 [ ? ] [ ? ] 1Or does it mean that only two digits appear on the screen like so:4 [ ? ] 2 [ ? ] [ ? ] [? ]and they have to enter the rest?Or am I missing the point entirely?



Basically I think it says please enter for example digit 3 and 5 of your security number

I can't see how it can possibly be one, it has to be 3

Banned

bigfoot100;7524789

Basically I think it says please enter for example digit 3 and 5 of your … Basically I think it says please enter for example digit 3 and 5 of your security number



then if completely random it would take 36 goes to cover all possibilities

Assuming the eavesdropper does not see the attempted/failed login guesses the answer would be 3

bigfoot100;7524789

Basically I think it says please enter for example digit 3 and 5 of your … Basically I think it says please enter for example digit 3 and 5 of your security number



God, I'm an idiot. Thanks for that.

I get asked this quite often when I use my card online.

If that's the case, then I would agree and say it would be 3 times. If the only information on the screen are the two presumably disguised numbers, I think the minimum would be 3 and then would require a lot of luck, too.

sassie;7524798

then if completely random it would take 36 goes to cover all possibilities



Yer but it asks for the least possible which is 3

Banned

bigfoot100;7524808

Yer but it asks for the least possible which is 3



the least possible, but numbers are still random, i dont think it has anything to do with the two numbers

Assuming an eavesdropper is able to read the digits entered by the customer
I'm with Sassie

sassie;7524798

then if completely random it would take 36 goes to cover all possibilities



No, not at all. Let's say for example the code was: 1 2 3 4 5 6 - when you get to the screen which requires your code, you will be asked for two numbers. In this case, let's say they asked for the 3rd and 5th number, which in this simple example would be 3 and 5. The next time they may ask for the 1st and 6th one, which will obviously be 1 and 6. Then on the third time they may ask you for the 2nd and 4th, which will be 2 and 4.

If this happened in the above sequence, they would know that your entire 6 digit code is: 1 2 3 4 5 6 after 3 viewings.

However... I guess it could only need one time, as let's say on the first occasion it asked for digits 3 and 5, it might ask for the same digits the next time. So if you were extremely jammy, you could do it in one, however you wouldn't get the entire code, just 2 digits.

sassie;7524811

the least possible, but numbers are still random, i dont think it has … the least possible, but numbers are still random, i dont think it has anything to do with the two numbers



Yer so if they asked for the number of logins that would guarantee the security number then I agree. However they are asking for the least possible number it has nothing to do with the randomness. The least possible logins occurs when each consecutive login has two different numbers from the security numbers which after 3 attempts would give the answer.

We_Are_138;7524818

on the first occasion it asked for digits 3 and 5, it might ask for the … on the first occasion it asked for digits 3 and 5, it might ask for the same digits the next time. So if you were extremely jammy, you could do it in one, however you wouldn't get the entire code, just 2 digits.



Which isnt the question.. it asks you how many times to know the sequrity number, implying the whole 6 digits.

so yes it is 3.

Banned

We_Are_138;7524818

No, not at all. Let's say for example the code was: 1 2 3 4 5 6 - when … No, not at all. Let's say for example the code was: 1 2 3 4 5 6 - when you get to the screen which requires your code, you will be asked for two numbers. In this case, let's say they asked for the 3rd and 5th number, which in this simple example would be 3 and 5. The next time they may ask for the 1st and 6th one, which will obviously be 1 and 6. Then on the third time they may ask you for the 2nd and 4th, which will be 2 and 4.If this happened in the above sequence, they would know that your entire 6 digit code is: 1 2 3 4 5 6 after 3 viewings.However... I guess it could only need one time, as let's say on the first occasion it asked for digits 3 and 5, it might ask for the same digits the next time. So if you were extremely jammy, you could do it in one, however you wouldn't get the entire code, just 2 digits.



pmsl, an evesdropper they said, not someone sat on her shoulder looking at what digits they where asking for

Banned

Jetpac;7524827

Which isnt the question.. it asks you how many times to know the sequrity … Which isnt the question.. it asks you how many times to know the sequrity number, implying the whole 6 digits.so yes it is 3.



random means random, not 1 of each number

sassie;7524828

pmsl, an evesdropper they said, not someone sat on her shoulder looking … pmsl, an evesdropper they said, not someone sat on her shoulder looking at what digits they where asking for



What are you talking about? It's asking hypothetically how many times they would have to see someone enter the code.

Banned

im off to bed, good luck and im sticking with 1, night all xxx

sassie;7524828

pmsl, an evesdropper they said, not someone sat on her shoulder looking … pmsl, an evesdropper they said, not someone sat on her shoulder looking at what digits they where asking for



Are you saying they can't see what number the bank ask for? Surely then you could never be sure, because if there was a repeat digit involved you wouldn't know if it was a new digit or where it was in the sequence.

Jetpac;7524827

Which isnt the question.. it asks you how many times to know the sequrity … Which isnt the question.. it asks you how many times to know the sequrity number, implying the whole 6 digits.so yes it is 3.



Sorry, didn't see this post.

As it asks for the entire code, then I agree, it's 3. I was just saying that you could possibly gain access by seeing them enter 2 digits once, even though it's unrelated to the question. ;-)

sassie;7524757

no because ther is only 6 digits - lolif it was about the two numbers and … no because ther is only 6 digits - lolif it was about the two numbers and they are random it would be 36


Wrong because there are no guarantees that all the numbers will come up in a random sequence it could ask for the same number over and over again. Highly improbable but still possible.

Three!!

I say the minimum is 3 (and the maximum is infinite). It's just 6 divided by 2.

sassie;7524828

pmsl, an evesdropper they said, not someone sat on her shoulder looking … pmsl, an evesdropper they said, not someone sat on her shoulder looking at what digits they where asking for



Assuming an eavesdropper is able to [SIZE="5"]read [/SIZE]the digits … Assuming an eavesdropper is able to [SIZE="5"]read [/SIZE]the digits entered bythe customer what is the least possible number of logins theeavesdropper would have to [SIZE="5"]see[/SIZE]



3

Without a doubt 3, it HAS to be.

6 digit security, 2 digits asked for on each attempt, therefore 3 attempts is the MINIMUM number of times that would be required to see the entire code.
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