puzzle.js

#!/usr/bin/env node

/**
 * Solve the problem by guessing.
 * 
 * @param {number} n
 * @param {number} k
 * @param {number} min
 * @param {Int8Array} src 
 * @param {Int8Array} dst 
 * @param {() => void} fn 
 */
function solve(n, k, min, src, dst, fn) {
    if (src.length == 0) {
        fn();
        return;
    }

    // Each time we add k things, let's make sure that
    // everything that remains is greater than the min
    // of the previously selected items.
    if (src.length < n && (src.length % k) == 0) {
        if (Math.min(...src) < min) {
            return;
        }
        min = n;
    }

    let tmp = new Int8Array(src.length - 1);
    src.forEach((x) => {
        dst[0] = x;
        let j = 0;
        src.forEach((y) => {
            if (x != y) {
                tmp[j] = y;
                j++;
            }
        });
        solve(n, k, Math.min(min, x), tmp, dst.subarray(1), fn);
    });
}

/**
 * Create a string to show the solution.
 * 
 * @param {Int8Array} sol 
 */
function format(sol) {
    let ad = sol[1]*10 + sol[2],
        bd = sol[4]*10 + sol[5],
        cd = sol[7]*10 + sol[8];
    return `${sol[0]}/${ad} + ${sol[3]}/${bd} + ${sol[6]}/${cd} = 1`;
}

/**
 * Does this guess solve the problem?
 * 
 * @param {Int8Array} sol 
 * @returns {boolean}
 */
function isSolution(sol) {
    let ad = sol[1]*10 + sol[2],
        bd = sol[4]*10 + sol[5],
        cd = sol[7]*10 + sol[8],
        s = sol[0]/ad + sol[3]/bd + sol[6]/cd;
    return s > 0.9999 && s < 1.0001;
    
}

let n = 9,
    k = 3,
    src = new Int8Array(n).map((x, i) => {
        return i + 1;
    }),
    dst = new Int8Array(n);

solve(n, k, n, src, dst, () => {
    if (isSolution(dst)) {
        console.log(format(dst));
    }
});