Investing in the Mind: Math and Logic Problems


Math and logic have been with us, to some degree, since the beginning of civilization. The evolution has been an interesting one and has led us to some of the most challenging puzzles, problems, and riddles of our time.

In the early days, we relied on raw reasoning to solve our problems. With the development of complex language and culture, it wasn’t long before specialists cropped up and with them the language of numbers that came to formalize much of our logic – mathematics. In this way, they were always tied together; you can’t have math without logic, and without math, reasoning would be all the more difficult.

Later in the 19th century we came to know modern math logic when it diverged from pure logic, so it became a section of mathematics in its own right. It quickly trickled down into school curriculum and engineering. Since then math logic problems have been teasing the brains of people everywhere, from elementary students to mathematicians and even puzzle experts.

We have compiled a list of challenging math, logic, and math logic problems for anyone to try out, from students to puzzle experts. They are sure to give your brain a workout. Have fun and good luck.


Beginner Level (kids) – Math and Logic Problems

Math and logic are best when introduced at a young age to help the developing mind grasp concepts and explore the difference between logic and fallacies early on. Utilize any of these links to get your students started on the right path early in their education.

  • NRICH has twenty-two fun games and problems available online to be solved by young learners. These are simple problems with basic images that can be viewed online or printed out for classroom use.
  • Arlington Public Schools offers links to a multitude of mathematical challenges for students in the brain games section. The majority of their links go to other sites such as PBS Kids and the British Broadcasting Corporation.
  • The Mathematics Education Collaborative has created a list of various traditional board and card games that can be played offline and that encourage logical thinking. Why not take learning offline while keeping it fun?
  • The U.S. Energy Information Administration offers a printable document on wind logic puzzles as a teachers’ resource for younger students. Let students learn about the environment, energy, and logic all at the same time!
  • The National Institute of Environmental and Health Sciences has REBUS puzzle boxes to be solved. According to them, a REBUS is a “picture representation of a name, work, or phrase.” Use these visual puzzles to help expand minds.


Intermediate Level (teens and young adults) – Math and Logic Problems

Here are some more challenging math and logic problems for the next level of students. It is important to practice logical thinking at every stage of learning.

  • The University of California Los Angeles has a handout that includes several puzzles that can be done in the classroom or at home without the use of a computer.
  • org has an interactive 3D logic game that can be played in your browser without needing to install or download anything.
  • The AIMS Center for Math and Science Education offers six interesting and entertaining logic puzzles aimed at working the mind.
  • Stetson University has a wide choice of simple visual logic puzzles that seem much more like a game than work.
  • The University of Utah offers a series of word puzzles that only require logical thinking. No particular math skills are required!


Advanced Level (teens and young adults) – Math and Logic Problems

Still up for a challenge? Here are four more options for the brave.

  • Cut the Knot has an extensive interactive mathematics miscellany and puzzles section covering several areas of mathematics and logic. They cover algebra, arithmetic, geometry, and much more.
  • Wabash College posts a new problem every couple of weeks in case you ever run out of challenges. Access to previous problems is also available if you want to catch up.
  • The University of California, Davis has a print out with some challenging logical puzzles for you to solve. Why not give them a try?
  • The City of New York Board of Education offers an example of logic puzzles as they are currently required to meet education standards. If you are interested in current school requirements, this might be a good place to stop by.


Experts Only – Math and Logic Problems

Are you ready for the expert level? Several universities, as well as the National Security Agency offer complex logic problems at some of the most difficult levels. Are you still looking for more after this? Why not consider creating a few logic problems of your own to challenge others? Sometimes the true challenge is in making the perfect puzzle.

  • Eastern Kentucky University has a few challenges that most people have failed. Are you up for a real challenge?
  • University of Southern California’s West Semitic Research Project has a Papyrus puzzle, and a promise that you will receive a letter acknowledging that you are a “Master Papyrologist” if you send a self-addressed stamped envelope along with the solved puzzle. Could you be one of the few to attain this title?
  • Stanford University has a copy of “Einstein’s Puzzle,” an interesting riddle of unknown origins, although it is often attributed to Einstein himself. It is rumored that 98% of people who attempt it do not manage to successfully complete the puzzle.
  • Missouri State University’s problem corner offers challenges for both high school students and experts. Once you get to their page, just pick the link to the section that most interests you.
  • Purdue University has an archive of problems from previous semesters if you are interested in trying out problems that prior students have been given.
  • The U.S. National Security Agency has a puzzle periodical for employees and anyone else up for the challenge. They say that expressing difficult cryptographic problems is just part of the advanced engineering problems they are deeply involved with at work, so why not have a publication dedicated to it?