Counting of Arms

logic-02.js

/*
 * The inhabitants of Mars have 1, 2 or 3 arms.
 * Once 5 Martians gathered and counted their arms: they had 10 arms in total.
 * How many one-armed, two-armed and three-armed Martians gathered?
 * Find all the options.
 */

// (15, 5) -> [ 0, 0, 1, 2, 0 ]
const intToTernary = (i, size) => [...i.toString(3).padStart(size, "0")].map(Number);

const checkSample = (ternary, total) => {
    const sum = ternary.reduce((acc, trit) => acc + trit + 1, 0);
    return sum === total;
}

getStats = (ternary) => {
    const counts = {};
    for (let i = 0; i < ternary.length; i++) {
        const count = ternary[i] + 1;
        counts[count] = counts[count] ? counts[count] + 1 : 1;
    }
    return counts;
};

const getPermutations = (size, total) => {
    const result = [];
    for (let i = 0; i < 3 ** size; i++) {
        const ternary = intToTernary(i, size);
        if (checkSample(ternary, total)) {
            const stats = getStats(ternary);
            result.push({ ternary, stats});
        }
    }
    return result;
};

const allOptions = getPermutations(5, 10).map((option) => JSON.stringify(option.stats));
const optionsSet = new Set(allOptions);
const uniqueOptions = [...optionsSet].map((sOption) => JSON.parse(sOption));
console.log(uniqueOptions);

// Unique options:
// [
//     { '1': 2, '2': 1, '3': 2 },
//     { '1': 1, '2': 3, '3': 1 },
//     { '2': 5 }
// ]