Professor's Lab

[Casey]

Dr. Ray protects his computer system from those pesky university freshmen by incorporating a secret code that only he knows how to work out.

Two numbers appear on his screen, and he can't log in until he types in a third number, related to the first two.

However, certain freshman spies kept an eye on him as he entered the secret code several times. For instance, when 1 and 2 appeared on the screen, he typed in 9 to log in. When 3 and 4 appeared, he typed in 20. When 5 and 6 appeared, he typed in 12.

Finally, when it was safe to do so, a freshman spy broke in and started up the computer. The numbers 17 and 12 appeared on the screen.

What number should the Freshman spy type in to gain access to Dr. Ray's computer?

[K.J.Healey]

Anyone have any ideas? Seems too obscure to me.

[Gokul43201]

With the information given, there are an infinite number of possible solutions.

Consider, for instance the code : z = Ax + Bx^2 + Cy where A,B, C constitute the key; x,y are the provided pair and z is the correct password for that pair.

Plugging in the numbers provided, we have :
9 = A + 2B + C
20 = 3A + 4B + 9C
12 = 5A + 6B + 25C.

Gives A = 149/8, B = -29/8, C = -19/8.

But the code could easily be z = Ax^n + Bx^m + Cy^k, or any of several other possibilities, and still produce the 3 given results.

The problem with this kind of code, though is that is hard to quickly generate a password mentally if you have to wrestle with fractions llike 149/8. The other drawback...this particular example doesn't always give integer passwords.

[Casey]

Gokul43201 - thank you for one of the possible solutions. I am however looking for a specific answer to "What number should the Freshman spy type in to gain access to Dr. Ray's computer?" When the numbers 17 and 12 appeared on the screen.









-------------------------------------------------------------

The plans was simple, like my brother-in-law Phil. But
unlike Phil, this plan just might work.

[K.J.Healey]

Gokul43201 - thank you for one of the possible solutions. I am however looking for a specific answer to "What number should the Freshman spy type in to gain access to Dr. Ray's computer?" When the numbers 17 and 12 appeared on the screen.


The right one?
EDIT : Or none. Entering this code only lets you then login. So they would also have to know the Dr's User/pass or have their own.

[cdhotfire]

this one is a duzy.

[Casey]

The right one?
EDIT : Or none. Entering this code only lets you then login. So they would also have to know the Dr's User/pass or have their own.


LOL. There is a correct answer.

EDIT: Upon powering up the computer there are two ramdom numbers given, you must enter the third number in order to log on to the university's system, I'll state for the record they have the professors username and password as well, but this info is not needed to figure out the teaser . The third number is related to the first two. The examples 1 - 2 enter 9 also 3 - 4 enter 20 and 5 - 6 enter 12 are purely data for finding the solution.

cul,

Casey

[cdhotfire]

im saying they type in 54.

[Casey]

im saying they type in 54.


CDHOTFIRE, What makes you say they type in 54. Is this a guess or can you back it up?


Casey

[cdhotfire]

do not caps my name plz, and no its not a guess. I represented each number with a letter kind of like goku did, then I found all the letters. After that I just plugged them into 17 and 12 and found that it should be 54. It was 54. sometin, but i rounded it off.

[Casey]

cdhotfire, 54 is not correct.

[cdhotfire]

k, u could have just said that, didnt have to get mad. :smile:

[Casey]

cdhotfire, I aplogize if I came across as mad, angry or yelling. I was not. I had my key lock on as I was typing your name before and didn't think about the caps. My bad. This is all in fun. Good try, no hard feelings, I didn't mean to offend you either. k.

cul,

Casey

[cdhotfire]

:biggrin: its all tight.

[cdhotfire]

this is one of the hardest brain thingers ive seen. :tongue2:

[recon]

We should get everyone on PF to start posting random numbers on this page. Sooner or later, one of us will hit upon the right answer. :rofl:

I pick the number 29. Is this right? :smile:

BTW, I went through a very long process of number playing to arrive at this number. It wasn't random. :cool:

[check]

I got it. Took me about 3 minutes:
number of letters in first number x number of letters in second number
1 , 2 = 9
one (3) x two (3) = 9
3 , 4 = 20
three (5) x four (4) = 20
5 , 6 = 12
five (4) x six (3) = 12
17 , 12 = ??
seventeen (9) x twelve (6) = 54

So I'm ALSO saying 54.

[humanino]

Yep ! We confirm 23 after a wavelet analysis of the fractal dimension at the surface of the cookies sent in several stores, especially saturday. Of course, we took great care in excluding the green and chinese fries. It took us an entire team of 59 computing squirrels, and also the Fast Femto Tripdog madness, but we could not find any pizza left. Maybe if the microwave was set on freezing mode, we would also have found 17.

[Gokul43201]

There you go...check's logged in :smile:

[recon]

I got it. Took me about 3 minutes:
number of letters in first number x number of letters in second number
1 , 2 = 9
one (3) x two (3) = 9
3 , 4 = 20
three (5) x four (4) = 20
5 , 6 = 12
five (4) x six (3) = 12
17 , 12 = ??
seventeen (9) x twelve (6) = 54

So I'm ALSO saying 54.

I would vote for this as the correct answer. The easiest solution is always the best...for me. :biggrin: :biggrin:

[cdhotfire]

yay, atleast people agree with my awnser :smile: , good to c im not alone.

[TenaliRaman]

Casey earlier declares 54 as incorrect but check's answer does fit the bill correctly and its no outside the box solution .... So if occam is right, i will assume check's answer to be right.

But there is tho just one problem that 9 is not unique to 1 and 2 neither is 54 unique to 17 and 12 and it may be interpreted differently for different numbers once we get over to 100's.

Now if casey modifies his original problem saying that the third number is unique to the combination of first and second number then check's answer will get invalidated.

-- AI

[cdhotfire]

Casey come back and tell me the awnser, :cry: . I need to know. Unless someone else can get it.

[Gokul43201]

Someone has got it : check check's post (#17)

[cdhotfire]

Yes yes I also said it was 54, in a later post, and Casey said it was not 54. So :cry: .

[check]

Maybe Casey lied because he thought you just guessed.

[cdhotfire]

hmmm, maybe so. 54 seems like the most resenable awnser so that must be it. :tongue:

[Gokul43201]

Yes yes I also said it was 54, in a later post, and Casey said it was not 54. So :cry: .

I'm sure Casey meant to say that you have not solved it.

Clearly, your method was not the correct one, and you were very lucky to get the correct answer with the wrong method.

[cdhotfire]

Indeed I was but still I got the right awnser, so he should not have lied. :redface:

[cronxeh]

if 54 is the answer and that is the problem - this is pathetic.

so far here is what i cooked up.. and i gotta hit the snooze button now.. and plus im stuck anyway


x1 x2 y
1 2 9 odd
3 4 20 even
5 6 12 even
17 12 ? ???

So I was thinking first number is always odd.. and second one is always even, but their resultant is not always the same.

I tried some linear dependence:

9 = 1A + 2B
20= 3A + 4B
12= 5A + 6B

A=-15/2 B=33/4
y = Ax1 + Bx2

Works good for 1st and 3rd problems.. I tried to see the relationship between the two linear sets.. and.. well nothing. Doesnt work for 2nd equation (3 4 20).

But yea. if its 54.. blah at you

[check]

cronxeh,

54 being the correct answer (by the method I discribed) does not make this a pathetic problem. Brain teasers (at least the good ones) require you to think outside of the box and generally have a solution that, when you discover or hear about it, you think "that was so simple, why didn't I think about that?" or "why didn't I think of that sooner?"
If the 'teaser' just requires you to derive some gigantic, boring formula, then it's really just another one of your everyday word problems.

[cronxeh]

well arent im glad that this isnt one of those pathetic problems :)

[cdhotfire]

lol, why arent you? :shy:

[cdhotfire]

Wheres Casey when you need him? :grumpy:

[cronxeh]

seriously man i need to know the answer :cry:

[cdhotfire]

Me too. I think im gonna commit suicide if i dont know in, 1 2 3, bang bang. :tongue2:

[grotto]

The answer is most definitely 9*6. There is simply no other less complex solution. 54 is correct.

[cdhotfire]

thanks for the insperation :biggrin: