const problem5 = () => {
    // The possible symbols that can be inserted between digits
    const JOIN = 0; // insert nothing
    const ADD  = 1; // insert +
    const SUB  = 2; // insert -

    // One way of inserting the symbols is represented as a number
    // whose base three digits represent each symbol.
    // The first symbol to be inserted is the least significant
    // base-3 digit, etc.
    // eg.  s=00120121 base 3  is  1+2-3+45-6+789

    // Computes the value of the expression where the given
    // symbols are inserted between the digits 1-9.
    const evaluate = (s) => {
        // ex:
        //   s = ??021210 base 3
        //          sign___        ___symbol
        //                 \      /
        //   12 + 3 - 4 + 5 - 67 ? 8 ? 9
        //   \____________/   \|    \__digit
        //        sum          \__num
        let sum = 0;
        let sign = +1;
        let num = 1;
        for (let digit = 2; digit <= 9; digit++) {
            const symbol = s % 3;
            s = (s / 3)|0;
            if (symbol === JOIN) {
                num = 10*num + digit;
            } else {
                sum += sign*num;
                sign = (symbol === ADD ? +1 : -1);
                num = digit;
            }
        }
        sum += sign*num;
        return sum;
    }
    // Print the digits 1-9, with the given symbols inserted,
    // to a string.
    const show = (s) => {
        let res = "1";
        for (let digit = 2; digit <= 9; digit++) {
            const symbol = s % 3;
            s = (s / 3)|0;
            if (symbol === ADD)
                res += " + ";
            else if (symbol === SUB)
                res += " - ";
            res += digit;
        }
        return res;
    }

    for (let s = 0; s !== Math.pow(3,8); s++)
        if (evaluate(s) === 100)
            console.log(show(s) + " = 100");
}