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Classic Brain Teasers and Riddles

(Click on the question to see the answer.)

46. There are only 5 sisters in a room and nobody else. Ann is reading, Rose is cooking, Lorraine is playing chess, Mary is playing the piano. What is the fifth sister doing?


Most likely playing chess with Lorraine.

How many pieces of pizza can you create with 4 complete straight line cuts of a circular pizza and without stacking slices either?



How could you cut the following shape into 4 exactly congruent pieces?


Four people arrive at a river with a narrow bridge that can only hold two people at a time. It's nighttime and they have one torch that has to be used when crossing the bridge. Person A can cross the
bridge in 1 minute, B in 2 minutes, C in 5 minutes, and D in 8 minutes. When two people cross the bridge together, they must move at the slower person's pace. Can they all get across the bridge in 15 minutes or less?


  1. Person A and B go across first (2 minutes)
    [CD] ===AB>=== [ _ ]
  2. Person A comes back (1 minute)
    [CD] ===<A==== [ B ]
  3. Person C and D go across next (8 minutes)
    [ A ] ===CD>===[ B ]
  4. Person B comes back (2 minutes)
    [ A ] ===<B==== [CD]
  5. Person A and B go across together (2 minutes)
    [ _ ] ===AB>===[CD]
  • Total of 15 minutes

You have two lengths of fuse cord rope, and you know that each of them will take exactly one minute to burn in total if you start burning them from either end. However, the rope varies in thickness and some parts may burn at different speeds, so half of a minute length may take more or less than half a minute to burn. How can you use the ropes to measure when exactly 45 seconds has elapsed, with no timepieces and without cutting the rope?


Start by setting the first rope on fire at both ends and the second rope at just one end. Since the first rope was burning from both ends it will finish burning in exactly 30 seconds. When the first rope finishes burning, the second rope should be 30 seconds into its burn, so light the other end of the second rope on fire. It should take the second rope 15 more seconds to burn since it has 30 seconds of burn time but burning from both ends. When the second rope finishes, exactly 45 seconds will have passed.

51. What occurs once in a year, twice in a week, but not once in a day?


The letter "e"

  • year
  • week

52. Did you realize that 3.14 could spell PIE?



A jeweler is asked to join four small 3-link chains (shown at the right) into a large circular 12-link chain. In order to join two closed links, one of the links needs to be cut, placed onto the other link, and then closed. What is the minimum number of cuts she would need to make?

ANSWER: 3 cuts

54. Two campers are trying to settle an argument over how much drinking water is inside a large barrel. One camper thinks the barrel is more than half full while the other says it's less than half full. How can they settle the argument without using any measuring tools?

ANSWER: They could open the top and tilt the barrel until the water comes up to the edge of the opening. If the barrel is exactly half full you will be able to see the corner of botttom. If the barrel is less than half full you will be able to see part of the bottom of the barrel. If the barrel is more than half full you will only be able to see the edge.

You have a bucket containing one gallon of water and a bucket containing one gallon of grape juice. You fill a one-cup measuring cup with grape juice and pour it into the water bucket. You then fill the measuring cup with one cup of the water-juice mixture and pour it back into the grape juice bucket. At that point, is there more water in the grape juice, or more grape juice in the water?

ANSWER: The proportion of the juice in water is equal to the proportion of water in the juice.

If we simplify this problem with an example that's similar, it might be easier to understand. Consider if we had 90 units of water and 90 units of juice. Then we mixed 10 units of juice in the water.

The container would now be holding 100 units of liquid and the other container would have 80 units of juice. The new mixture would be 90/100 =90% water.

Now if we took 10 units of the mixture (which would be 9 units of water & 1 unit of juice) to pour back in the 80 units of juice.

The juice container would now hold 81 units of juice and 9 units of water whereas the water container mixture previously held 10 units of juice and 90 units of water but we removed 1 unit of juice and 9 units of water there by changing the water proportion to (90-9) = 81 units of water and (10 - 1) units of juice.

A farmer has a fox, a chicken and a sack of grain. He must cross a river with only one of them at a time. If he leaves the fox with the chicken the fox will eat the chicken; if he leaves the chicken with the grain the chicken will eat it. How can you get all three across safely?


  1. Farmer and Chicken go across.
    [Fx, Gr] ====(Fr, Ck>=== [ _ ]
  2. Farmer comes back alone and leave the Chicken
    [Fx, Gr] ====<Fr_ )==== [ Ck ]
  3. Farmer and the Fox go across
    [ Gr ] =====(Fr, Fx>====[ Ck ]
  4. Farmer leaves the Fox and brings back the Chicken
    [ Gr ] ====<Fr,Ck)==== [Fx]
  5. Farmer takes the Grain across and leaves the Chicken
    [ Ck ] ====(Fr, Gr>====[Fx]
  6. Farmer comes back alone and leaves the Grain with the Fox.
    [ Ck ] ====< Fr_ ) ==== [Fx, Gr]
  7. Farmer takes the Chicken back across
    [ _ ] ====(Fr, Ck>====[Fx, Gr]

The picture below shows a map of an office building. Josh wondered one day if he could find a path such that he walked through all of the doors in the office exactly once. Is it possible to create a path for Josh to walk through every door without walking through any door more than once?



ANSWER: There are several correct paths but all of them either start or end in rooms 'A' and 'D'

Leonhard Euler was able to determine a method for determinig if similar types of paths were traversable by studying the famous Konigsberg bridge problem. He was able to prove it is impossible to find a singular path in which a person could walk over each of the following bridges exactly once (..or can you find a path?)

See Unit 7-3 on Euler Circuits and Paths for more information.

How much earth is there in a hole in the ground which is 25 ft. long, 6 ft. wide, and 2 ft. deep?

ANSWER: None. It's a hole.

How can you move just one pencil and completely reverse the grouping of pencils from 1,2,3,4 to 4,3,2,1?


Can you find a way to place 6 X's on the Tic-Tac-Toe board such that you still don't have 3 in a row any where on the board?



  Contact Information: Matt Winking

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