What are the next two numbers in this series? This is a purely arithmetic series.

30, 33, 42, 50, 55, 80, 88, 152, 162, 174, ?, ?

There are 4 women who want to cross a bridge. They all begin on the same side. You have 17 minutes to get all of them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time.

You have 4 jars of pills. Each pill is a certain weight, except for contaminated pills contained in one jar, where each pill is weight + 1. How could you tell which jar had the contaminated pills in just one measurement?

You have two jars, 50 red marbles and 50 blue marbles. A jar will be picked at random, and then a marble will be picked from the jar. Placing all of the marbles in the jars, how can you maximize the chances of a red marble being picked? What are the exact odds of getting a red marble using your scheme?

The San Francisco Chronicle has a word game where all the letters are scrambled up and you have to figure out what the word is. Imagine that a scrambled word is 5 characters long:

1. How many possible solutions are there?
2. What if we know which 5 letters are being used?
3. Develop an algorithm to solve the word.

A rope burns non-uniformly for exactly one hour. How do you measure 45 minutes, given two such ropes?

One train leaves Los Angeles at 15mph heading for New York. Another train leaves from New York at 20mph heading for Los Angeles on the same track. If a bird, flying at 25mph, leaves from Los Angeles at the same time as the train and flies back and forth between the two trains until they collide, how far will the bird have traveled?

You are in the dark, and on the floor there are six shoes of three colors, and a heap of twenty-four socks, black and brown. How many socks and shoes must you take into the light to be certain that you have a matching pair of socks and a matching pair of shoes?

Ten gnomes are about to be executed. Although they don’t like the idea, they are each selfless and want to do anything (even by sacrificing themselves) in order to help their fellow gnomes. They are told what will happen to them: They will each be lined up single file, so that they are each facing the gnome in front of them. Each of them will be given a red or a white hat on their head, and from the back of the line (the gnome who can see everyone else) they will ask him to state his hat color, ‘red’ or ‘white.’ If he can state it correctly (he cannot see his own hat, only those in front of him), he is allowed to live. Knowing what is going to happen to them, they are allowed to devise a strategy beforehand. How many people can they guarantee to save, and what strategy will ensure this? (There are NOT five reds and five whites necessarily!)

A milkman has two empty jugs: a three gallon jug and a five gallon jug. How can he measure exactly one gallon without wasting any milk?