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CP-SAT - Magic Square

Problem: fill a square grid with distinct numbers so every row, column, and diagonal has the same sum.

Show code

import { CpModel, CpSat, sum } from 'or-tools-wasm/cp-sat';

const size = 5;
const numCells = size * size;
const model = new CpModel();
const cells = Array.from({ length: numCells }, (_, index) =>
  model.newIntVar(1, numCells, `cell_${index}`));
model.addAllDifferent(cells);
const target = (size * (numCells + 1)) / 2;
const addSum = (indices: number[]) =>
  model.addEquality(sum(indices.map((index) => cells[index])), target);

for (let row = 0; row < size; row += 1) {
  addSum(Array.from({ length: size }, (_, column) => row * size + column));
}
for (let column = 0; column < size; column += 1) {
  addSum(Array.from({ length: size }, (_, row) => row * size + column));
}
addSum(Array.from({ length: size }, (_, index) => index * size + index));
addSum(Array.from({ length: size }, (_, index) => index * size + size - index - 1));

const result = await CpSat.solve(model, {
  executor: 'worker',
  numWorkers: 4,
  logSearchProgress: true,
});
if (result.hasSolution) console.log(cells.map((cell) => result.value(cell)));

This page exercises the cp_sat_api WASM module by building and solving a magic square model directly in the browser.

Model

Each grid cell is an integer decision variable.
All numbers in the square must be distinct.
Every row, column, and diagonal must have the same magic sum.
CP-SAT searches for a grid assignment satisfying all arithmetic constraints.

Size Workers Executor

Latest solution:

Run the solver to view a magic square.

Status / Response: