9.1.7 Checkerboard V2 Answers

This post provides clear, step-by-step answers and reasoning for the puzzle titled “9.1.7 Checkerboard v2.” It covers the puzzle setup, key observations, the complete solution(s), common pitfalls, and an optimization note.

Course Context: CodeHS Unit 9.1 typically covers "Strings" or "Methods" depending on the version, but in the AP CSA or Standard Java track, 9.1.7 is often a culminating exercise on using nested for loops and conditionals to create a visual pattern.

The Assignment: You are given a Checkerboard class that extends GraphicsProgram. Your task is to write a program that draws a standard 8x8 checkerboard pattern. The board should have: 9.1.7 checkerboard v2 answers

Why "v2"? The "v2" indicates this is the second version of the assignment, usually with stricter requirements regarding method structure, color constants, or resizing behavior.

A checkerboard follows a simple parity rule: This post provides clear, step-by-step answers and reasoning

Cell at row r, column c is black if (r + c) % 2 == 0, otherwise white (or vice versa).

That’s the essence. But a deep understanding goes beyond memorizing that formula — it’s about why that works: Why "v2"

This is a classic problem of permutations. For the first checker, there are (n^2) possible squares. Once a square is chosen, for the second checker, there are ((n-1)^2) possible squares (since a row and a column are now off-limits), and so on. However, a more straightforward way to think about it is:

However, a simpler and more systematic approach to solving this problem is to consider it as arranging (n) distinct objects into (n) distinct rows (or columns) such that no row (or column) gets more than one object. This directly translates to (n!) (n factorial) arrangements, as there are (n) choices for the first position, (n-1) for the second, and so on, down to 1 choice for the last position.

Given an (n \times n) checkerboard, how many ways can you place (n) checkers such that no two checkers are on the same row or column?