Acertain four-cylinder combination lock has 55 numbers on it. to open it, you turn to a number on the first cylinder, then to a second number on the second cylinder, and then to a third number on the third cylinder and so on until a four-number lock combination has been effected. repetitions are allowed, and any of the 55 numbers can be used at each step to form the combination. (a) how many different lock combinations are there? (b) what is the probability of guessing a lock combination on the first try?

What is the value of x in the equation 6(x + 1) – 5x = 8 + 2(x – 1)?

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

If you had $1,900,000, how many days would it take you to spend all if you spent $1 a second. (there are 86,400 seconds in a day)