ROPE TIMER

You have two pieces of rope. Each piece will burn from end to end in exactly one hour. How can you measure 45 minutes by burning the rope? The rate at which the rope burns is not consistent (when half the length of a piece of rope has burned you cannot assume 30 minutes has passed).

FRUIT BASKET

You have three baskets filled with fruit. One has apples, one has oranges, and one has a mixture of apples and oranges. You cannot see the fruit in the baskets. There are labels for each category, but each basket has the wrong label. You are allowed to choose one basket and have someone show you one piece of fruit from that basket. Just by seeing the one piece of fruit, how can you determine how each basket should be labeled?

MOUNTAIN CLIMBING

On Monday morning at 9:00 am you start at the base of a mountain and begin hiking. Your pace is not regular and you take breaks along the way. Monday evening at 9:00 pm you reach the peak. On Tuesday morning at 9:00 am, after camping overnight, you start at the peak of the mountain and begin your return trip. You follow the exact same path from the previous day, but your pace is faster and you take more breaks. Tuesday evening at 9:00 pm you reach the base. Can you determine if there is a point you were at somewhere on the path at the same time of day Monday and Tuesday. (You are not asked to name the point, just whether or not such a point must exist.)

BRIDGE CROSSING

Four people must cross a rickety foot bridge at night. Many planks are missing and the bridge can only support two people at a time. The travelers must use a flashlight to guide them and they only have one flashlight with them. They each travel at different speeds and when two people are on the bridge they stay together and go at the speed of the slower person. None of them are strong enough to carry one of the others. The flashlight must be taken back across the bridge -- it cannot be thrown back. John can cross the bridge in one minute. Paul can do it in two minutes. George takes five minutes. And Ringo needs ten minutes. They must all get across in exactly 17 minutes. How can they do this? (Assume no time is spent between the time one trip across the bridge ends and the next trip starts.)

MARBLES

You have two large jars, 50 red marbles, and 50 blue marbles. One of the jars will be chosen at random. And then one of the marbles from that jar will be picked out at random. How do you distribute the marbles in order to maximize the chances that a red marble will be chosen? What will the odds be? All marbles must go in the jars.

GLOBE

How many points are there on Earth where, by traveling one mile south, one mile east, and one mile north, you will end up at the same point where you started?

BOXES Draw a line from Box A on the top to Box A on the bottom. Do the same for Boxes B and C. The lines that connect each pair may not touch each other, any of the other boxes, or the edge of the large box.

MILK & WATER

Bottle A contains a quart of milk. Bottle B contains a quart of water. You pour some milk from Bottle A into Bottle B and mix it well. Then you pour some of that mixture back into Bottle A so that each bottle contains a quart of liquid. What is the relationship between the amount of water in Bottle A and the amount of milk in Bottle B?

NUMBER SERIES

What line of numbers comes next in the following series?

1
11
21
1211
111221
312211

CARDS You have four cards that have a letter on one side and a number on the other side. Identify which card or cards must be turned over to test the rule, "if there is a vowel on one side, then there is an even number on the other side."

LIGHT SWITCHES

There are three switches outside a room. One of the switches controls the light inside the room. The door to the room is closed and you can't determine whether or not the light is on without opening the door. How can you figure out which switch controls the light without flipping the switches once the door has been opened? (There are no people or cameras in the room.)

QUARTERS

You play this game with one other person. Starting with an empty rectangular table and an unlimited supply of quarters, each person takes a turn placing a quarter anywhere on the table as long as it doesn't touch a quarter that's already been placed. The first player who is unable to place a quarter loses. You go first. What strategy do you employ to ensure you win?

TOOTHPICKS Arrange six identical toothpicks so they form eight equilateral triangles (each side of the triangle is the same length as the other sides of the same triangle).

TOOTHPICKS 2 Arrange six identical toothpicks so they form exactly four equilateral triangles (each side of the triangle is the same length as the other sides of the same triangle).

STATES

Ok, this isn't a logic puzzle like the others, but I like it a lot. Take the names of two U.S. states. Rearrange the letters to form the names of two other U.S. States. What are the states? (From Will Shortz's Sunday Puzzle, submitted to him by David Edelheit.)

WATER BOTTLES

You have a three-quart bottle, a five-quart bottle, and an unlimited supply of water. How can you measure exactly four quarts of water?

DAVE AND ERIC

Dave has a younger brother named Eric. They have a combined age of 42. Dave is twice as old as Eric was when Dave was as old as Eric is now. How old are Dave and Eric?