Math - Brain Teasers
On this page you'll find a selection of fun questions and activities that give
you practice thinking outside the box. Try them one at a time in any order to
exercise your brain! Some questions have more than one right answer; some
questions have several ways to get a solution.
you practice thinking outside the box. Try them one at a time in any order to
exercise your brain! Some questions have more than one right answer; some
questions have several ways to get a solution.
Tired Frog
A frog at the bottom of a forty-foot well, every day jumps up
three feet and at night falls back two.
How many days will it take him to get out of the well?
Pencil Squares
Fifteen pencils are laid out in five equal squares.
Your task is to take away just three pencils and leave only three equal squares.
Want to see more problems like the Pencil Squares problem? Check out this whole page of problems with match sticks
The Gardener
A homeowner asks their gardener to measure off a piece of lawn eight yards long. All he has with him is a rope, but he knows that the wooden shed on the property measures 5 yards by 7 yards.
How can he accomplish this task?
(Hint: This will take at least three steps.)
How can he accomplish this task?
(Hint: This will take at least three steps.)
Apple Cider
How can you measure exactly one liter of cider out of a barrel, if all you have available is a 3-liter pitcher and a 5-liter pitcher?
(See the Natural Library of Virtual Manipulatives website to see other questions like this one. This site allows you to move a diagram to help you solve the questions.)
Upending the Cups
Make yourself a row of seven cups, all turned upside down. Your challenge is to
turn them the right way up, but always turning over three at a time.
How can you turn them all the right way up, in just three rounds?
turn them the right way up, but always turning over three at a time.
How can you turn them all the right way up, in just three rounds?
Jack Cuts Down the Beanstalk
Jack is cutting down a beanstalk. The stalk is eight feet tall. He wants to cut it into four-foot lengths, but for each cut he makes, the fast-growing stalk will grow back two feet.
At this rate of cut-and-grow, how many lengths of four feet can Jack cut?
At this rate of cut-and-grow, how many lengths of four feet can Jack cut?
Party Favor Bag
As a party favor, your child is given a bag of candy. The bag consists of many M&Ms, Good & Plenty, Skittles, and Candy Corns. Half your child's pieces of candy are M&Ms. Half of the remaining pieces of candy is Good & Plenty. A fourth of the remaining pieces after the M&Ms and Good & Plenty are Skittles. The remaining pieces of candy are are Candy Corns.
If there are 12 Candy Corns in the bag, how many M&Ms are in the bag?
If there are 12 Candy Corns in the bag, how many M&Ms are in the bag?
Train Tunnel
How long does it take a mile-long train going 20 miles per hour to get completely through a two-mile long tunnel?
Pencil Box Problem
In the morning, Mrs. Rivera put some pencils for her students in a pencil box. After a while, she found that ½ of the pencils were gone. A little later, she found that 1/3 of the pencils that were left from when she checked before were gone. Still later, she found that ¼ of the pencils that were left the last time she had checked were gone. At that point, there were 15 pencils in the pencil box. No pencils were ever added to the pencil box.
How many pencils did Mrs. Rivera put in the pencil box in the morning?
How many pencils did Mrs. Rivera put in the pencil box in the morning?
Connect the Dots
Given a 3 by 3 array, connect all the dots with four straight lines. You may not retrace over any of your lines.
You may download a sheet of blank arrays by clicking "download file" below if you would like.
You may download a sheet of blank arrays by clicking "download file" below if you would like.
arrays_of_nine.docx | |
File Size: | 15 kb |
File Type: | docx |
Fishing Pole
A man buys a fishing pole. He tries to get on the bus to go home, however, the fishing pole is 5 feet long and the bus driver won't allow anything over 4 feet on the bus. So, the man goes into the hardware store and buys something and gets on the bus. The fishing pole is still whole. It was not broken or damaged in any way.
What did the man buy at the hardware store that allowed him to bring the fishing pole on the bus?
What did the man buy at the hardware store that allowed him to bring the fishing pole on the bus?
Room Numbers
Romain got a job painting numbers on all the rooms on the first floor of a large hotel. He painted all of the numbers from 100 to 199.
How many times did Romain paint the number 1?
How many times did Romain paint the number 1?
Game of Squares
This game moves through levels of difficulty. There are no directions. What do you think you do to play?
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How many levels can you get through?
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Hints
General Hints - Draw a picture to represent the problem. Be careful of short-cuts you are taking. Read carefully and do no make assumptions. Are your shortcuts and assumptions leading you to jump to an answer? Picture yourself in the situation. For hands-on problems, try them!
Tired Frog - The answer is not 40 days. Try again!
Connect the Dots - Think "outside the box".
Fishing Pole - Try using the Pythagorean Theorem.
Tired Frog - The answer is not 40 days. Try again!
Connect the Dots - Think "outside the box".
Fishing Pole - Try using the Pythagorean Theorem.
For additional math problems that are listed by levels, visit The University of Mississipi's math contest site.
If you'd like, you can print a file of advanced brain teasers designed for a long flight.
If you'd like, you can print a file of advanced brain teasers designed for a long flight.