Summle solver (https://summle.net/)

solve.js

const target = 486;
const nums = [3, 3, 6, 8, 9, 100];

const op = [['+', (a, b) => a + b], ['-', (a, b) => a - b], ['*', (a, b) => a * b], ['/', (a, b) => a / b]];

let numSolutions = 0;
let bestSolution;

function solve(nums, solution) {
    for (let i = 0; i < nums.length; i++) {
        for (let j = 0; j < nums.length; j++) {
            if (j != i) {
                for (let k = 0; k < op.length; k++) {
                    const res = op[k][1](nums[i], nums[j]);
                    if (Number.isInteger(res)) {
                        const newSolution = [...solution, `${nums[i]} ${op[k][0]} ${nums[j]} = ${res}`];
                        if (res == target) {
                            numSolutions++;
                            if (!bestSolution || newSolution.length < bestSolution.length) {
                                bestSolution = newSolution;
                                console.log(newSolution);
                            }
                        } else {
                            if (newSolution.length < 5) {
                                const newNums = nums.slice();
                                newNums.splice(i, 1);
                                newNums.splice(j - (i < j ? 1 : 0), 1);
                                newNums.push(res);
                                solve(newNums, newSolution);
                            }
                        }
                    }
                }
            }
        }
    }
}

solve(nums, []);
console.log(numSolutions);

Output:

❯ node solve.js
[ '3 + 3 = 6', '6 * 8 = 48', '6 + 48 = 54', '9 * 54 = 486' ]
[ '3 * 3 = 9', '6 * 9 = 54', '9 * 54 = 486' ]
6368

Interesting. Thanks for this solver. wouldn't the "best" be [ '3 * 3 = 9', '9 * 6 = 54', '9 * 54 = 486' ] though, right? only 3 "moves"

?

Program prints first solution it finds, then if it finds better solution, with less steps, it prints that also, etc. So, in output there is one solution with 4 steps, and one with 3 steps - similar to yours.