# Professor's Lab

1. Sep 17, 2004

### 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?

2. Sep 17, 2004

### K.J.Healey

Anyone have any ideas? Seems too obscure to me.

3. Sep 17, 2004

### Gokul43201

Staff Emeritus
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.

Last edited: Sep 17, 2004
4. Sep 17, 2004

### 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.

5. Sep 17, 2004

### K.J.Healey

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.

6. Sep 17, 2004

### cdhotfire

this one is a duzy.

7. Sep 17, 2004

### Casey

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

Last edited: Sep 17, 2004
8. Sep 17, 2004

### cdhotfire

im saying they type in 54.

9. Sep 17, 2004

### Casey

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

Casey

10. Sep 17, 2004

### 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.

11. Sep 17, 2004

### Casey

cdhotfire, 54 is not correct.

12. Sep 17, 2004

### cdhotfire

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

13. Sep 17, 2004

### 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

14. Sep 17, 2004

### cdhotfire

its all tight.

15. Sep 17, 2004

### cdhotfire

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

16. Sep 18, 2004

### 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?

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

17. Sep 18, 2004

### 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.

18. Sep 18, 2004

### 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.

19. Sep 18, 2004

### Gokul43201

Staff Emeritus
There you go...check's logged in

20. Sep 18, 2004

### recon

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