Q1: Shoulder to shoulder the kings servents comb the 50-meter-long field by takingtwo steps forward and one step back. How many steps do they take forward and back if every step is 50cm long?

A1: Firstly, There are 5000cm in 50m. Thus, the servents must take 5000cm/50cm=100 steps to cover the field completety. Moreover, to move one unit forward (1 step) the servents must take 3 steps. Therefore, I came up with the following solution: 3*100-2=300-2=298 steps altogether. I subtracted 2, because we don't want to include the extra step forward and back once the servents have reached the 100th step.

Q2: On the starship enterprisethere are 8 cabinets to store belongings. All of them have a different lock. captain Picard gave all 8 keys to Mr. Data. The keys have no marks on them. In the worst case scenario, how many tries does Mr. Data need in order to find the right key to every lock?

A1: Well, to match the first key with one of the lockers the worst case is he has to try all 8 unitl he finds a match. After that, he must try the remaing 7 lockers until he finds a match, and so on. Thus, the worst case scenario is Mr. Data must try to match the keys with lockers 8! times.

Q3: Adam asked his parents what their favorite positive integers are. He told the sum of these (not necessarily differen) 2 numbers to his younger sister Bea and the product of the 2 numbers to his older sister Cecilia. When the sisters were together, Bea noted that she can't figure out what the numbers are. Hearing this, Cecilia also said that she is unable to figure out the numbers. At this point, Bea changed her mind and said "Now, I know what the numbers are". What are the numbers?

A3: This is the one I am really stuck on. I am not how to approach the problem.