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Product Overview:


Below are a list of products that can be purchased for a student, school or a contact.

'Current Year' refers to the Caribou Cup year from 1 July to 30 June.

Purchasable For Students

The book in form of a downloadable pdf file (currently only available in English) introduces the reader to calcrostic puzzles. Different solving techniques are explained and demonstrated with examples. Apart from logical thinking when creating case distinctions one can use algebra for formulating and solving simple equations, can use inequalities, the pigeonhole principle, divisibility rules up to more challenging algebra when trying to solve rational calcrostic puzzles. A collection of calcrostics for the different types provides practice material for a wide range of difficulty levels suitable for students from grade 3/4 to 11/12. Contents: 1. What is a Calcrostic? 1.1. Did you know? 2. How to Solve Calcrostics? 2.1. Clues, clues, clues, 2.2. An Example Solution 2.3. More Solutions, 2.4. Puzzles involving Rational Numbers, 2.4.1. Qualitative Description, 2.4.2. Partial Fraction Decomposition of Rational Numbers, 2.4.3. Conclusions and Examples, 3. Integer 3 × 3 Problems, 4. Integer 3 × 3 Problems with Diagonals, 5. Rational 3 × 3 Problems, 5.1. A 3 × 3 Problem with Solution, 5.2. More 3 × 3 Problems, 6. Rational 5 × 5 Problems, 6.1. A 5 × 5 Problem with Solution, 6.2. More 5 × 5 Problems, 7. Rational 7 × 7 Problems, 7.1. A few 7 × 7 Problems with Solution, 7.2. More 7 × 7 Puzzles.

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 11/12 contests held this current school year
  • The bonus of accessing these questions online under Previous Tests after the contest is held
  • As another bonus, access to interactive games if not already available
This purchase is ideal for students who want to try out current year contest questions and see the detailed solutions without participating in the contests themselves. Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 3/4 contests held this current school year
  • The bonus of accessing these questions online under Previous Tests after the contest is held
  • As another bonus, access to interactive games if not already available
This purchase is ideal for students who want to try out current year contest questions and see the detailed solutions without participating in the contests themselves. Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 5/6 contests held this current school year
  • The bonus of accessing these questions online under Previous Tests after the contest is held
  • As another bonus, access to interactive games if not already available
This purchase is ideal for students who want to try out current year contest questions and see the detailed solutions without participating in the contests themselves. Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 7/8 contests held this current school year
  • The bonus of accessing these questions online under Previous Tests after the contest is held
  • As another bonus, access to interactive games if not already available
This purchase is ideal for students who want to try out current year contest questions and see the detailed solutions without participating in the contests themselves. Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 9/10 contests held this current school year
  • The bonus of accessing these questions online under Previous Tests after the contest is held
  • As another bonus, access to interactive games if not already available
This purchase is ideal for students who want to try out current year contest questions and see the detailed solutions without participating in the contests themselves. Available in English, French, and Persian

Contest participation for the current school year (July-June) for one grade 11/12 student.

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 11/12 contests of the 2015/16 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 11/12 contests of the 2016/17 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 11/12 contests of the 2017/18 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

Contest participation for the current school year (July-June) for one grade 3/4 student.

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 3/4 contests of the 2015/16 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 3/4 contests of the 2016/17 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 3/4 contests of the 2017/18 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

Contest participation for the current school year (July-June) for one grade 5/6 student.

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 5/6 contests of the 2015/16 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 5/6 contests of the 2016/17 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 5/6 contests of the 2017/18 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

Contest participation for the current school year (July-June) for one grade 7/8 student.

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 7/8 contests of the 2015/16 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 7/8 contests of the 2016/17 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 7/8 contests of the 2017/18 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

Contest participation for the current school year (July-June) for one grade 9/10 student.

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 9/10 contests of the 2015/16 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 9/10 contests of the 2016/17 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 9/10 contests of the 2017/18 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This grants all inclusive access for one grade 11/12 student, for the current school year (July-June). All Inclusive Access Includes:

  • Contest Access
  • Written Solutions Practice Tests for the Current Year and all Grade Levels
  • Written Solutions Practice Tests for all previous Years back to 2009 and all Grade Levels
  • The Calcrostic Book
  • The Mini-Courses:
    • Chomp iChomp
    • Geometree
    • Proof By Induction
    • Mazes

This grants all inclusive access for one grade 3/4 student, for the current school year (July-June). All Inclusive Access Includes:

  • Contest Access
  • Written Solutions Practice Tests for the Current Year and all Grade Levels
  • Written Solutions Practice Tests for all previous Years back to 2009 and all Grade Levels
  • The Calcrostic Book
  • The Mini-Courses:
    • Chomp iChomp
    • Geometree
    • Proof By Induction
    • Mazes

This grants all inclusive access for one grade 5/6 student, for the current school year (July-June). All Inclusive Access Includes:

  • Contest Access
  • Written Solutions Practice Tests for the Current Year and all Grade Levels
  • Written Solutions Practice Tests for all previous Years back to 2009 and all Grade Levels
  • The Calcrostic Book
  • The Mini-Courses:
    • Chomp iChomp
    • Geometree
    • Proof By Induction
    • Mazes

This grants all inclusive access for one grade 7/8 student, for the current school year (July-June). All Inclusive Access Includes:

  • Contest Access
  • Written Solutions Practice Tests for the Current Year and all Grade Levels
  • Written Solutions Practice Tests for all previous Years back to 2009 and all Grade Levels
  • The Calcrostic Book
  • The Mini-Courses:
    • Chomp iChomp
    • Geometree
    • Proof By Induction
    • Mazes

This grants all inclusive access for one grade 9/10 student, for the current school year (July-June). All Inclusive Access Includes:

  • Contest Access
  • Written Solutions Practice Tests for the Current Year and all Grade Levels
  • Written Solutions Practice Tests for all previous Years back to 2009 and all Grade Levels
  • The Calcrostic Book
  • The Mini-Courses:
    • Chomp iChomp
    • Geometree
    • Proof By Induction
    • Mazes

This grants all inclusive access for an individual, for the current school year (July-June). All Inclusive Access Includes:

  • Written Solutions Practice Tests for the Current Year and all Grade Levels
  • Written Solutions Practice Tests for all previous Years back to 2009 and all Grade Levels
  • The Calcrostic Book
  • The Mini-Courses:
    • Chomp iChomp
    • Geometree
    • Proof By Induction
    • Mazes

The purchase grants access to the Chomp and iChomp 'Some Food For Thought', for an individual for the current school year (July-June). This material is available in English and French. It contains parts that are suitable for all grades including elementary school students (e.g. hints how to improve playing strength), for middle school students (introduction of binary numbers, their arithmetic including the XOR operator and conversion to decimal numbers) and for high school students (short theorems including their proofs by induction and Sprague Grundy theory that is applicable to all impartial combinatorial games, not only Chomp and iChomp). A number of results are new including exact algorithms for specific classes of positions and a hypothesis about similarities between losing positions in Chomp and primary numbers. No prerequisites are needed for any part. All details are derived from first principles. Over 60 questions and their answers guide the reader in the study.

The purchase grants an individual access to GeomeTree for the current school year (July-June). 56 interactive geometry worksheets are grouped in 9 categories and cover not only curriculum material and interactive constructions but also formula discovery and proofs, with content suitable for elementry, middle and high school. Worksheets are organized in a tree of dependencies to guide through a structured and consistent experience of learning and discovery. No prerequisites are required. All worksheets have an introduction, a guided interactive construction, a summary and a quiz page. The interested student can find additional challenges beyond school curriculum, for example, the geometry of playing Billards, the construction of 72°-36°-18°-9° Angles, of a pentagon and a 17 gon.

This purchase buys for the period of the current school year (July-June) for an individual, access to a tutorial (in English, French and Persian) on mazes which are completely general, except fulfilling two simple conditions:

  • any two points can be linked, and
  • there is no closed path
This class of mazes has remarkable properties despite its generality. After explaining notations the reader is lead to discover up to 6 magic points in all these mazes and how to use them for finding the solution. 30 questions are discussed and illustrated with examples. This tutorial is not a prerequisite for being able to solve interactive maze questions in contests but it helps to understand global structures in such mazes.

Grants an individual access to the interactive proofs by induction site for the current school year (July-June). This site is currently only available in English. It gives a detailed description of the proofing technique by induction with a simple example discussed step by step. It then allows practicing the method by performing 46 different proofs by induction for summation rules, product rules, and theorems about divisibility and Fibonacci sequences. All proofs can be followed step by step in an example mode and then performed interactively by the user. This is a unique online learning tool. The user has complete freedom of how to formulate the proof. Each step is checked by an automatic proof verification system. At the end, the user can print a copy of their own proof or have it emailed.

This grants all inclusive access for each student in an entire school, for the current school year (July-June). All Inclusive Access Includes:

  • Current Caribou Cup Contest Participation in one age group
  • Current Caribou Cup Written Solutions Practice Tests
  • Written Solutions Practice Tests for all previous Years back to 2009 and all Grade Levels
  • The Calcrostic Book
  • The Mini-Courses/Tutorials:
    • GeomeTree
    • Chomp iChomp
    • Proof By Induction
    • Mazes

This purchase buys for the period of the current school year (July-June) for an entire school

  • Access to written solutions for the contests of the 2015/16 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an entire school

  • Access to written solutions for the contests of the 2016/17 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available

This purchase buys for the period of the current school year (July-June) for an entire school

  • Access to written solutions for the contests of the 2017/18 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

The book in form of a downloadable pdf file (currently only available in English) introduces the reader to calcrostic puzzles. Different solving techniques are explained and demonstrated with examples. Apart from logical thinking when creating case distinctions one can use algebra for formulating and solving simple equations, can use inequalities, the pigeonhole principle, divisibility rules up to more challenging algebra when trying to solve rational calcrostic puzzles. A collection of calcrostics for the different types provides practice material for a wide range of difficulty levels suitable for students from grade 3/4 to 11/12. Contents: 1. What is a Calcrostic? 1.1. Did you know? 2. How to Solve Calcrostics? 2.1. Clues, clues, clues, 2.2. An Example Solution 2.3. More Solutions, 2.4. Puzzles involving Rational Numbers, 2.4.1. Qualitative Description, 2.4.2. Partial Fraction Decomposition of Rational Numbers, 2.4.3. Conclusions and Examples, 3. Integer 3 × 3 Problems, 4. Integer 3 × 3 Problems with Diagonals, 5. Rational 3 × 3 Problems, 5.1. A 3 × 3 Problem with Solution, 5.2. More 3 × 3 Problems, 6. Rational 5 × 5 Problems, 6.1. A 5 × 5 Problem with Solution, 6.2. More 5 × 5 Problems, 7. Rational 7 × 7 Problems, 7.1. A few 7 × 7 Problems with Solution, 7.2. More 7 × 7 Puzzles.

The purchase grants access to the Chomp and iChomp 'Some Food For Thought', for an entire school for the current school year (July-June). This material is available in English and French. It contains parts that are suitable for all grades including elementary school students (e.g. hints how to improve playing strength), for middle school students (introduction of binary numbers, their arithmetic including the XOR operator and conversion to decimal numbers) and for high school students (short theorems including their proofs by induction and Sprague Grundy theory that is applicable to all impartial combinatorial games, not only Chomp and iChomp). A number of results are new including exact algorithms for specific classes of positions and a hypothesis about similarities between losing positions in Chomp and primary numbers. No prerequisites are needed for any part. All details are derived from first principles. Over 60 questions and their answers guide the reader in the study.

Contest access for all students and grades in a single school, for the current school year (July-June).

This purchase buys for the period of the current school year (July-June) for an entire school

  • access to written solutions for the contests held this current school year
  • The bonus of accessing these questions online under Previous Tests after the contest is held
  • As another bonus, access to interactive games if not already available
This purchase is ideal for students who want to try out current year contest questions and see the detailed solutions without participating in the contests themselves. Available in English, French, and Persian

The purchase grants school wide access to GeomeTree for the current school year (July-June). 56 interactive geometry worksheets are grouped in 9 categories and cover not only curriculum material and interactive constructions but also formula discovery and proofs, with content suitable for elementry, middle and high school. Worksheets are organized in a tree of dependencies to guide through a structured and consistent experience of learning and discovery. No prerequisites are required. All worksheets have an introduction, a guided interactive construction, a summary and a quiz page. The interested student can find additional challenges beyond school curriculum, for example, the geometry of playing Billards, the construction of 72°-36°-18°-9° Angles, of a pentagon and a 17 gon.

This purchase buys for the period of the current school year (July-June) for an entire school, access to a tutorial on mazes which are completely random, except fulfilling two simple conditions:

  • any two points can be linked, and
  • there is no closed path
This class of mazes has remarkable properties despite its generality. After explaining notations the reader is lead to discover up to 6 magic points in all these mazes and how to use them for finding the solution. 30 questions are discussed and illustrated with examples. This tutorial is not a prerequisite for being able to solve interactive maze questions in contests but it helps to understand global structures in such mazes.

Grants all students of a school access to the interactive proofs by induction site for the current school year (July-June). This site is currently only available in English. It gives a detailed description of the proofing technique by induction with a simple example discussed step by step. It then allows practicing the method by performing 46 different proofs by induction for summation rules, product rules, and theorems about divisibility and Fibonacci sequences. All proofs can be followed step by step in an example mode and then performed interactively by the user. This is a unique online learning tool. The user has complete freedom of how to formulate the proof. Each step is checked by an automatic proof verification system. At the end, the user can print a copy of their own proof or have it emailed.

The book in form of a downloadable pdf file (currently only available in English) introduces the reader to calcrostic puzzles. Different solving techniques are explained and demonstrated with examples. Apart from logical thinking when creating case distinctions one can use algebra for formulating and solving simple equations, can use inequalities, the pigeonhole principle, divisibility rules up to more challenging algebra when trying to solve rational calcrostic puzzles. A collection of calcrostics for the different types provides practice material for a wide range of difficulty levels suitable for students from grade 3/4 to 11/12. Contents: 1. What is a Calcrostic? 1.1. Did you know? 2. How to Solve Calcrostics? 2.1. Clues, clues, clues, 2.2. An Example Solution 2.3. More Solutions, 2.4. Puzzles involving Rational Numbers, 2.4.1. Qualitative Description, 2.4.2. Partial Fraction Decomposition of Rational Numbers, 2.4.3. Conclusions and Examples, 3. Integer 3 × 3 Problems, 4. Integer 3 × 3 Problems with Diagonals, 5. Rational 3 × 3 Problems, 5.1. A 3 × 3 Problem with Solution, 5.2. More 3 × 3 Problems, 6. Rational 5 × 5 Problems, 6.1. A 5 × 5 Problem with Solution, 6.2. More 5 × 5 Problems, 7. Rational 7 × 7 Problems, 7.1. A few 7 × 7 Problems with Solution, 7.2. More 7 × 7 Puzzles.

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 11/12 contests held this current school year
  • The bonus of accessing these questions online under Previous Tests after the contest is held
  • As another bonus, access to interactive games if not already available
This purchase is ideal for students who want to try out current year contest questions and see the detailed solutions without participating in the contests themselves. Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 3/4 contests held this current school year
  • The bonus of accessing these questions online under Previous Tests after the contest is held
  • As another bonus, access to interactive games if not already available
This purchase is ideal for students who want to try out current year contest questions and see the detailed solutions without participating in the contests themselves. Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 5/6 contests held this current school year
  • The bonus of accessing these questions online under Previous Tests after the contest is held
  • As another bonus, access to interactive games if not already available
This purchase is ideal for students who want to try out current year contest questions and see the detailed solutions without participating in the contests themselves. Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 7/8 contests held this current school year
  • The bonus of accessing these questions online under Previous Tests after the contest is held
  • As another bonus, access to interactive games if not already available
This purchase is ideal for students who want to try out current year contest questions and see the detailed solutions without participating in the contests themselves. Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 9/10 contests held this current school year
  • The bonus of accessing these questions online under Previous Tests after the contest is held
  • As another bonus, access to interactive games if not already available
This purchase is ideal for students who want to try out current year contest questions and see the detailed solutions without participating in the contests themselves. Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 11/12 contests of the 2015/16 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 11/12 contests of the 2016/17 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 11/12 contests of the 2017/18 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 3/4 contests of the 2015/16 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 3/4 contests of the 2016/17 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 3/4 contests of the 2017/18 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 5/6 contests of the 2015/16 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 5/6 contests of the 2016/17 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 5/6 contests of the 2017/18 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 7/8 contests of the 2015/16 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 7/8 contests of the 2016/17 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 7/8 contests of the 2017/18 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 9/10 contests of the 2015/16 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 9/10 contests of the 2016/17 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This purchase buys for the period of the current school year (July-June) for an individual

  • Access to written solutions for the grade 9/10 contests of the 2017/18 school year with the possibility to try these questions out online under Previous Tests
  • As a bonus, access to interactive games if not already available
Available in English, French, and Persian

This grants all inclusive access for an individual, for the current school year (July-June). All Inclusive Access Includes:

  • Written Solutions Practice Tests for the Current Year and all Grade Levels
  • Written Solutions Practice Tests for all previous Years back to 2009 and all Grade Levels
  • The Calcrostic Book
  • The Mini-Courses:
    • Chomp iChomp
    • Geometree
    • Proof By Induction
    • Mazes

The purchase grants access to the Chomp and iChomp 'Some Food For Thought', for an individual for the current school year (July-June). This material is available in English and French. It contains parts that are suitable for all grades including elementary school students (e.g. hints how to improve playing strength), for middle school students (introduction of binary numbers, their arithmetic including the XOR operator and conversion to decimal numbers) and for high school students (short theorems including their proofs by induction and Sprague Grundy theory that is applicable to all impartial combinatorial games, not only Chomp and iChomp). A number of results are new including exact algorithms for specific classes of positions and a hypothesis about similarities between losing positions in Chomp and primary numbers. No prerequisites are needed for any part. All details are derived from first principles. Over 60 questions and their answers guide the reader in the study.

The purchase grants an individual access to GeomeTree for the current school year (July-June). 56 interactive geometry worksheets are grouped in 9 categories and cover not only curriculum material and interactive constructions but also formula discovery and proofs, with content suitable for elementry, middle and high school. Worksheets are organized in a tree of dependencies to guide through a structured and consistent experience of learning and discovery. No prerequisites are required. All worksheets have an introduction, a guided interactive construction, a summary and a quiz page. The interested student can find additional challenges beyond school curriculum, for example, the geometry of playing Billards, the construction of 72°-36°-18°-9° Angles, of a pentagon and a 17 gon.

This purchase buys for the period of the current school year (July-June) for an individual, access to a tutorial (in English, French and Persian) on mazes which are completely general, except fulfilling two simple conditions:

  • any two points can be linked, and
  • there is no closed path
This class of mazes has remarkable properties despite its generality. After explaining notations the reader is lead to discover up to 6 magic points in all these mazes and how to use them for finding the solution. 30 questions are discussed and illustrated with examples. This tutorial is not a prerequisite for being able to solve interactive maze questions in contests but it helps to understand global structures in such mazes.

Grants an individual access to the interactive proofs by induction site for the current school year (July-June). This site is currently only available in English. It gives a detailed description of the proofing technique by induction with a simple example discussed step by step. It then allows practicing the method by performing 46 different proofs by induction for summation rules, product rules, and theorems about divisibility and Fibonacci sequences. All proofs can be followed step by step in an example mode and then performed interactively by the user. This is a unique online learning tool. The user has complete freedom of how to formulate the proof. Each step is checked by an automatic proof verification system. At the end, the user can print a copy of their own proof or have it emailed.

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Purchasable For Entire School

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Purchasable For Contact

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