I am NOT programmer.

five_problems.js

// Q.1
// for loop
function sumForLoop(arr) {
    var ret = 0;
    for (let i = 0; i < arr.length; ++i) {
        ret += arr[i];
    }
    return ret;
}
// while loop
function sumWhileLoop(arr) {
    var ret = 0, i = 0;
    while (i < arr.length) {
        ret += arr[i];
        ++i;
    }
    return ret;
}
// recursive loop
function sumRecursiveLoop(arr, i) {
    i = i === void(0) ? 0 : ++i;
    var ret = arr[i];
    if (arr.length) return ret;
    return ret + sumRecursiveLoop(arr, i);
}

// Q.2
function concatList(arr1, arr2) {
    var arr = [];
    var length = Math.max(arr1.length, arr2.length);
    for(let i = 0; i < length; ++i) {
        if (i < arr1.length) arr.push(arr1[i]);
        if (i < arr2.length) arr.push(arr2[i]);
    }
    return arr;
}

// Q.3
function fibonacci(arr) {
    if (arr === void(0)) arr = [0, 1];
    if (arr.length === 100) return arr;
    arr.push(arr[arr.length - 2] + arr[arr.length - 1]);
    return fibonacci(arr);
}

// Q.4
function sortMax(arr) {
    arr = arr.slice();
    arr.sort(function(a, b) {
        return Math.pow(b, Math.floor(Math.log(a) / Math.LN10) + 1) - Math.pow(a, Math.floor(Math.log(b) / Math.LN10) + 1);
    });
    return parseInt(arr.join(""));
}

// Q.5
function sumHundred() {
    var arr = [1, 2, 3, 4, 5, 6, 7, 8, 9];
    var times = Math.pow(3, arr.length - 1);
    
    for(let i = 0; i < times; ++i) {
        let number = 0,
            status = ("0".repeat(arr.length) + i.toString(3)).slice(1 - arr.length).split("");
        
        for(let j = 0, prev = 0; j < arr.length; j++) {
            let sign = status[j - 1] === "2" ? -1 : 1,
                prevSign = prev < 0 ? -1 : 1,
                pre = prev === 0 ?  arr[j] * sign : (Math.abs(prev) + arr[j]) * prevSign;
            
            if (status[j] === "0") {
                prev = pre * 10;
                continue;
            }
            number += pre;
            prev = 0;
        }
        
        if (number === 100) {
            let ans = "";
            
            arr.forEach((value, index) => {
                ans += value;
                if (index < status.length) ans += ["", " + ", " - "][parseInt(status[index])];
            });
            console.log(ans);
        }
    }
}

Answer to Five programming problems every Software Engineer should be able to solve in less than 1 hour