Archimedes

school of mathematics and programming

BRAIN GYMNASTICS

Grades from 2 to 8

The Brain Gymnastics program is a mental workout designed to prepare young minds for the twenty first century life-style. The class stretches the students’ reasoning beyond day-to-day thinking by challenging them with exciting and puzzling problems.


Students get an opportunity to develop their investigative, creative, and critical thinking skills by exploring mathematical topics and brainteasers in an inspiring and competitive team setting.


Brain Gymnastics targets the student’s problem solving skills and emphasizes understanding concepts rather than memorizing rules. After experiencing the Brain Gymnastics program, mathematics will become something to enjoy discovering and playing with.  


For a detailed schedule of the Brain Gymnastics classes broken down by grades, please click HERE.

Archimedes Box Brainteaser

Brainteaser is a form of a puzzle that requires thinking out of the box, creativity and posting-questions skill.
One of the earliest known brainteaser enthusiasts was the Greek mathematician Archimedes.
His puzzle Ostomachion (shown in the figure on the left), also known as Loculus Archimedius (Archimedes' box in Latin) is similar to Tangram but much more difficult. The aim of the game is to make a square in as many ways possible, using all the pieces.

Brain Gymnastics sample problems

The following is an example of the problems that students will experience in the Brain Gymnastics classes using the Archimedes square puzzle.


  • How many pieces are in Archimedes square puzzle? (grade 2-3)
  • If you want to color one piece of the puzzle every day starting from Monday on what day of the week will you finish coloring the puzzle. (grade 2-4)
  • How many more triangle pieces than quadrilateral pieces are in Archimedes Box puzzle? (grade 2-5)
  • Color the puzzle in such way that all the same kinds of polygons are the same color and the different kinds of polygons are different colors. How many colors are needed? (grade 4-6)
  • Color the puzzle in such way that the same area pieces are the same color and the pieces with the different areas are different colors. How many colors are needed? (grade 6-8)
  • Express the area of each piece of the Archimedes Box as a fraction of the square. (grade 6-8)
  • What is the greatest fraction such that the area of any piece in Archimedes' square is an integer multiple of that fraction? (grade 6-8)

(HINT: use the square with a grid on the right)

 

Send us your solutions of at least two sample problems (your grade level)  with an explanation and get one math game class free and an ice-cream gift card. (for new students only)