Repository_kt: The Knight’s Tour

Repository for the Knight’s Tour: App_KT1

App_KT: Solve the Knight's Tour Problem -- human solution

App_KT: Solve the Knight’s Tour Problem — human solution (Download below)

From Human Solutions to Program Solutions.

Computational Thinking, Creativity and Pedagogy in Programming: The Knight’s Tour

Finding human solutions to a problem, sometimes provides a basis for, or serves as a pointer to, devising and implementing algorithms for program solutions, which can in turn lead to solution strategies for program solutions to more complex problems

Human Solutions

The recent CAS Tenderfoot program proposed ‘the simple knight’s tour’ for secondary teachers and their pupils as a productive, fertile exercise in the computational thinking necessary to look at human solutions. In this first article we run with the idea, using guided discovery and enquiry-based learning as a basis for discussion, in which teachers and pupils can attempt to find a variety of human solutions to this and related problems. We show how a simple model of computational thinking, including creativity, heuristics, symmetry, induction, and deduction, underpins this approach while using problem representations on click/touch screens of interactive game boards, diagrams, and some ideas from graph theory.

Programming Solutions

In the discussions in the follow up article, we will look further into the human solutions we have developed with a view to transform them where possible into program solutions for the knight’s tour and for more general problems. This will involve introducing data structure representations for: lists, stacks, arrays, trees and graphs, and programming with non-trivial recursion. No previous knowledge of these concepts is assumed.

The Problem Stated

A knight is placed on the board (Figure 1(a)) at position 1, and we are asked to find if there is a sequence of chess ‘knight’ moves, which will take the knight around the board: 1. So that it visits each of the other 11 numbered squares once only (the open path solution); 2. and returns to the starting position 1 in one more final move (the closed path solution).

App_KT is the first of a series of software apps designed to help with Computational Thinking to find a human solution to the simple knight’s tour problem.

Downloads

  1. A Course in Computational Thinking, Creativity and Pedagogy in Programming:The Knight’s Tour —Part 1: Human Solutions — A PDF version
  2. Part 2: Program Solutions and Answers for Part 1 — to be written
  3. App_KT1, an interactive app, to help you find a human solution to the simple Knight’s Tour problem — A Python 3 program

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  1. A Course in Computational Thinking, Creativity and Pedagogy in Programming 1:The Knight’s Tour —Part 1: Human Solutions — A PDF version
  2. Part 2: Program Solutions and Answers for Part 1 — to be written
  3. This is a Python 3 program: kt_app1, the source code, which is in development. Copy and run with IDLE.

    Knight’s Tour App 1 (4×4 board, 12 square)

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