Logic Puzzles

Each prisoner may open 50 of 100 boxes to find their own number. Random guessing succeeds with probability (1/2)^100; the optimal strategy does astronomically better.

Two ropes each burn for 60 minutes, but unevenly. Measure exactly 45 minutes: how few times must you put flame to a rope end?

Albert knows the month, Bernard knows the day, and three cryptic statements pin down the date. When is Cheryl's birthday?

100 prisoners in a line, each guessing their own hat color. How many can be guaranteed to survive with the right strategy?

100 prisoners, one light switch, and a fatal declaration to time perfectly. How does the designated counter know when everyone has visited?

A visitor tells 100 blue-eyed perfect logicians something they all already "know." On which night does everything change?

Four people crossing at speeds 1, 2, 5, and 10 minutes share one flashlight, two at a time. What is the fastest total crossing?

A camel must move 3000 bananas across 1000 km, carrying 1000 at a time and eating 1 per km. How many bananas can arrive?

Three children's ages multiply to 36 and sum to the house number next door, yet that isn't enough. One more clue settles it.

An unmarked 3-gallon jug, an unmarked 5-gallon jug, unlimited water. How few steps to exactly 4 gallons?

A fly zigzags at 75 mph between two trains closing at 100 mph from 100 miles apart. How far does it fly?

One road leads to safety, one to doom, and the guard is either a truth-teller or a liar. How many yes/no questions do you need?

Person k toggles every kth locker, for k = 1 to 100. After all the passes, how many lockers are open?

Three jars (apples, oranges, mixed) and every label is wrong. How few fruit draws guarantee correct relabeling?

S knows the sum, P knows the product, and four cryptic statements identify two secret numbers. Freudenthal's "Impossible Puzzle."

Twelve identical-looking balls, one counterfeit of unknown weight, and a balance scale. How few weighings always suffice?

Three switches downstairs, one incandescent bulb upstairs. How many inspection trips do you need to match switch to bulb?

25 horses, a 5-horse track, no timer. How many races to guarantee finding the fastest three?

With only two identical eggs and 100 floors, how many drops guarantee you find the critical floor?

A farmer, a one-item boat, and three mutually hungry passengers. What is the minimum number of river crossings?