Fun Brain Teasers 

These brain teasers can lighten the mood and provide a nice diversion for kids (and adults too).  When I speak to elementary school students about important skills to learn to work at Microsoft or any job for that matter, I stress the importance of hard work and good problem solving ability.  Here are some of my favorite brain teasers because they are fun for most any age (elementary and up).

Please share your favorite kid-friendly brain teasers.  Answers further below.

QUESTIONS

  1. You need to transport a 3 items: a Wolf, a Sheep and a Hay Bale across a river on a boat that can only hold 1 item at a time.  If left together the Wolf would eat the Sheep, and the Sheep would eat  the Hay Bale.  How do you avoid something eating something else while transporting each item?
  2. How do you get 4 members of your favorite rock band to a concert that starts in 17 minutes.  They have to cross an old bridge that can only hold 2 of them at a time.  Each member walks at a different speed:  1, 2, 5 and 10 minutes to cross the bridge.  By the way, it is night, and they only have 1 flashlight.  So each pair has to cross together sharing the flashlight and walking at the speed of the slowest person.    What combination of 2 walking over and 1 coming back to return the flashlight (no tossing it back) will get the entire band to the concert in 17 minutes?
  3. Connect 3 rows of 3 dots using a straight line (do not lift your pencil) that only changes direction 3 times.
    9 Dot Problem
  4. A farmer has an L shaped field (2 units square with a 1 unit square cut out of one corner for the farm house - like squares A, B or C).
    4 Square Problem
    He wants to give an equal size and shape portion of the field to each of his children when he dies (every child must get 1 unbroken plot of land).  As each child is born he computes the size and shape required.  How would the farmer do this if he had:
    1. 1 child (simple)
    2. 2 children (simple)
    3. 3 children (simple)
    4. 4 children (hard)
  5. You have a balance beam scale and 7 balls.  1 ball is slightly heavier but requires the scale to know for sure.  What’s the fewest number of measurements required to determine which ball is heavier than the others?
  6. Calculate 24 for each set of 4 numbers.  You can use each number only once as listed but they can be in any order and these operators can be used:  + - x / ()
    1.  1     2     3     4  =  24 (easy)
    2. 10    10     4     4  =  24 (medium)
    3.  7     3     3     7  =  24 (hard)

ANSWERS:

  1. This is a simple permutation and combinations problem, but helps to build confidence for the next similar, but more challenging problem.
    1. Take the Sheep over first.  You don’t have to worry about the Wolf eating the Hay Bale while you are gone.
    2. Come back and take the Wolf over second.  When you drop off the Wolf take the Sheep back with you (this is the trick).
    3. Leave the Sheep back where you started and take the Hay Bale over third.
    4. Finally go back and take the Sheep over again.
  2. Supposedly Microsoft gives interviewees around 20 minutes to complete this problem. I’ve seen adults pull their hair out and never figure out the answer or write a program to determine all possible permutations and combinations until they get the answer.  I’ve also seen a 5th grader work the answer out in her head in 2 minutes.
    1. The 1 and 2 minute members walk over together with the flashlight and the 1 minute member carries the flashlight back (2 minutes over + 1 minute back = 3 minutes).
    2. The 5 and 10 minute members walk over and the 2 minute member you left over the bridge carries the flashlight back (10 minutes over + 2 minutes back = 12 minutes, 3 + 12 = 15 minutes have passed so far).
    3. The 1 and 2 minute members walk over a second time to complete the trek (2 minutes over, 15 + 2 = 17 minutes total).

      NOTE: You can send either 1 or 2 back during the first trip and the result is the same.  The trick is to get the fastest members over first to be ready to run the flashlight back.  You then minimize the effect of the slowest members by having them cross together.
  3. This problem literally involves “thinking outside the box,” which is a good hint to help someone solve it.
    9 Dot Solution
  4. This is a common factorial problem in geometric form. A good hint to give if someone is stuck is to ask, “What if the farmer had 6 or even 12 children?”
    Click here for PowerPoint slides with the answers
  5. 2 measurements (or 1 if you get lucky).  This is a practical example of a binary search algorithm.

    Weigh 3 balls on the left side and 3 balls on the right side of the scale. If they balance then the heaviest ball is the 7th that wasn’t weighed.  You got lucky and found the heaviest ball in 1 measurement!

    If they don’t balance, put 1 ball from the heavier set of 3 on each side of the scale. If they balance then the heaviest ball is the 3rd that wasn’t weighed.  Otherwise the heaviest is the one that tips the scale.  You found the heaviest ball in 2 measurements.
  6. The 3rd one is really tricky until you think to use your elementary school fractions knowledge.
    1. 1 x 2 x 3 x 4  =  24 (easy)
    2. ((10 x 10) - 4) / 4  =  24 (medium)
    3. 7 x (3 + (3 / 7))  =  24 (hard)