A group of individuals are living on an island when a visitor arrives with an unusual order: all blue-eyed people must leave the island immediately. Every evening at 8:00 p.m., a flight will depart. Everyone can see everyone else's eye colour, but no one knows their own (nor is anyone allowed to tell them). Furthermore, they have no idea how many people have blue eyes, but they do know that at least one person has. How long will it take for the blue-eyed individuals to leave?

A government agency comes to the conclusion that it must use encryption in order to safeguard the communication that takes place between itself and its overseas counterparts. It is determined to design a proprietary cryptographic algorithm for this reason during a meeting with its counterparts, and this will be done in order to: Is there a justification for this choice. What risks are being taken?

Solve question given in image

We analyzed a program which was supposedly used for cracking some cryptographic algorithms. During the investigations we determined that the program input size can be varied in a wide range and for N-bit input the program result is also always N bit long. Additionally we found that the program working time depends significantly on input length N, especially when N is greater than 10-15. Our test also revealed, that the program working time depends only on input length, not the input itself. During our tests, we fixed the following working times (with an accuracy of one hundredth of a second): N=2-16.38 seconds N = 5-16.38 seconds N = 10-16.44 seconds N=15-18.39 seconds N=20-1 minute 4.22 seconds We also planned to test the program for N=25 and N = 30, but for both cases the program didn't finish within half an hour and was forced to terminate it. Finally, we decided for N= 30 to not terminate the program, but to wait a little bit longer. The result was 18 hours 16 minutes 14.62…