Math Unplugged: Games & Puzzles

Math Unplugged: Games & Puzzles

Step into math where logic, puzzles, & strategy come alive! Knight's Tour, Peg Solitaire, infinite hotels—pure playful thinking.

Course Instructor

Prof. G. Arunkumar

Duration

8 Weeks

Course Fee

500

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About The Course

Math Unplugged: Puzzles and Games is an 8-week outreach course designed by Dr. G. Arunkumar from the Department of Mathematics, IIT Madras. This engaging program introduces school students to the playful and powerful side of mathematics through puzzles, games, and curious problems. From the Knight’s Tour to Peg Solitaire, from logic-based challenges to the infinite hotel paradox, the course brings mathematics to life without relying on formulas or textbooks. Through visual demonstrations, thought-provoking questions, and interactive storytelling, the course aims to spark curiosity, foster problem-solving skills, and uncover the deep connections between recreational mathematics and mathematical thinking.

Course Instructor

Prof. G. Arunkumar

Prof. G. Arunkumar
Assistant Professor, IIT Madras

Dr. G. Arunkumar is an Assistant Professor in the Department of Mathematics at IIT Madras. His research interests lie in Algebraic Combinatorics, Spectral Graph Theory, and the theory of Lie Algebras. He is actively involved in mathematical outreach and student enrichment programs, with a strong passion for making mathematics engaging and accessible to young learners. Through this course, he aims to help school students experience the joy of mathematical discovery beyond textbooks.

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Content Overview

Course Duration: 8 Weeks

Week 1: The Knight’s Tour and Mathematical Exploration

  • Meet the chess pieces and discover how they inspire puzzles
  • Non-attacking chess pieces and the classic knight’s tour challenge
  • Smart strategies: the Warnsdorff heuristic and the power of backtracking

Week 2: Knight Tours on Rectangular Chessboards

  • Do knight tours exist on bigger, rectangular boards?
  • Taking apart and understanding closed knight tours
  • Why chessboard coloring matters: tours on 4×n boards

Week 3: Tours of Leapers

  • Beyond the knight: tours of leapers such as the Camel and Giraffe
  • A general look at when such tours exist
  • Connection to graph theory: Hamiltonian circuits

Week 4: The Peg Solitaire Game

  • Can you solve Peg Solitaire on the English board?
  • The French version – and how group theory comes to the rescue!

Week 5: The World of Infinities, Part 1

  • A quick survey of really big numbers
  • Injections, surjections, bijections, and how we compare sizes of sets
  • The strange but famous Hilbert’s Hotel paradox

Week 6: The World of Infinities, Part 2 – Beyond Infinity

  • How do you “list” a set?
  • Not all infinities are the same size!
  • The big question: is there a “largest” infinity?

Week 7: Counting Areas of Shapes

  • What do we really mean by “dimension”?
  • A first step into areas under curves: the idea of integration
  • Pick’s Theorem: counting areas neatly on the lattice

Week 8: A Road to the Future – Open Problems and Directions

  • Frankl’s Union-Closed Sets Conjecture
  • Singmaster’s Conjecture: how many times can a number appear in Pascal’s triangle?
  • The Twin Primes Conjecture: are there infinitely many pairs of primes 2 apart?
  • Ramsey Theory: why it’s “better to fight the aliens”
  • Thinking ahead: exploring higher studies in mathematics

Live Sessions: Weekly live interactive sessions on Saturdays

Course Eligibity

Students from partnered schools in any stream of Class X, XI and XII

Assessment Layout

Assignments: The course includes the release of 4 bi-weekly online assignments (every alternate week). Students need to attempt at least 3 of these assignments and must achieve a minimum score of 40 marks in each to be eligible for the certificate.

Take-Home Project: An optional project consisting of questions that cover all the topics from the theory videos, accompanied by a small project report.

Final Exam: An optional online final exam designed to assess the knowledge gained throughout the course, which can only be attempted after completing and submitting the required assignments and the take-home project.

Certificate Acquisition

Participation Certificate - Check Sample Certificate

To receive this participation certificate, a student must pass 3 out of 4 assignments with an average score of at least 40 marks.

Completion Certificate - Check Sample Certificate

To receive this completion certificate, a student must fulfill the following criteria:

  1. A student must pass 3 out of 4 assignments with an average score of at least 40 marks.
  2. Submission of the take-home project is mandatory for the student.
  3. Once the above two conditions are satisfied, the student should attempt the final exam and must receive a minimum score of 40 marks.