What is the secret code for Dr. Kai's computer system?

  • Thread starter Thread starter Derivative86
  • Start date Start date
Derivative86
Messages
26
Reaction score
0
Dr. Kai protects his computer system from those pesky Cortex spys 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 Cortex 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 Cortex spy broke in and started up the computer. The numbers 17 and 12 appeared on the screen.

What number should the Cortex spy type into gain access to Dr. Kai's computer?
 
Last edited:
Mathematics news on Phys.org
I could solve it for you, but instead I'm going to give you a hint.

Write down the numbers in English, then analyze them. (e.g. 3 = three, 4 = four, etc.)
 
Ok I did i don't see a pattern

One Two Nine
Three Four Twenty
Five Six Twelve
Seventeen Twelve ?
 
Count the number of letters then think what operation could generate the required answer
 
Ah I see thanks! So the answer is 9 * 6 = 54
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
Back
Top