Solution to "Is it a valid number coding test". See the first comment below for test cases.

valid-number.js

/**
 * The main function.
 * @param s
 * @returns {boolean}
 */
function isNumber(s) {

    s = s.trim();

    var chars = new Set(s);

    // Set a sequence point so we knoww
    var kSEQ = ';';
    if (chars.has(kSEQ)) return false;
    s += kSEQ;

    var tokens = new Set('0123456789+-.e'),
        len   = s.length,
        c     = '',
        e     = 'e',
        p     = '+',
        m     = '-',
        d     = '.',
        i     = 0,
        hasE  = false,
        hasS  = false,
        hasD  = false,
        hasN  = false;

    c = s.charAt(i);

    while (c !== kSEQ) {

        // This is not a valid token

        if (! tokens.has(c)) return false;

        // Is this a sign?
        else if (c === p || c === m) {

            // 1 ) If we have seen the sign before, the number is invalid.
            // 2 ) If we just saw a number, it is invalid.
            // 3 ) If we have seen `.` but not `e`, it is invalid.

            if (hasS) return false;
            if (hasN) return false;
            if (hasD && ! hasE) return false;

            // 1 ) Mark the sign.

            hasS = true;
        }

        // Is this a decimal?
        else if (c === d) {

            // 1 ) If we have seen the decimal already, the num is invalid.

            if (hasD) return false;

            // 1 ) Mark the `.`

            hasD = true;
        }

        // Is this an `e`?
        else if (c === e) {

            // 1 ) If we have seen `e` before, the num is invalid.
            // 2 ) If we have not seen a number, it is invalid.

            if (hasE) return false;
            if (! hasN) return false;

            // 1 ) We can reset the sign value after `e`
            // 2 ) Mark the `.` as seen (skips useless comparisons)
            // 3 ) Reset the number marker.
            // 4 ) Mark the `e`

            hasS = false;
            hasD = true;
            hasN = false;
            hasE = true;
        }

        // Otherwise, it must be a number, just keep reading.
        else {
            hasN = true;
        }

        c  = s.charAt(++i);
    }

    return hasN;
}

var tests = [ ".e1", ".2e81", "46.e3", " -.", "-1.", "1.-", "1-2", " ", "3.", ".", "e", "+", "-", ".1", "0", " 0.1 ", "abc", "1 a", "2e10", " -90e3   ", " 1e", "e3", " 6e-1", " 6-e1", " 99e2.5 ", "53.5e93", " --6 ", "-+3", "95a54e53", "0.0", "1.2", "3", "0.0", "1.2.3", ".2", "1.", "1e2", "3.5e4e", ".2e81", "1.2345E-02", "1--2", "1++2", "1+-2", "1-+2", "2.3+e2", "2.3e+2", "2e.3", "3.456e4", "0", "0.0", "0.e0", "0.e-0", "0.e+0", "1-2", "1+2", "2e0", "2e-0", "2e+0", "2e1.2", ".e-0", "1..2", "1-.2", "1--", "1++", "+1+", "+1-", "-1-", "-1+", "-.3e6", " -.7e+0435", "166e-02767", "166e-02", "166e-027" ];  

var expects = [ false, true, true, false, true, false, false, false, true, false, false, false, false, true, true, true, false, false, true, true, false, false, true, false, false, true, false, false, false, true, true, true, true, false, true, true, true, false, true, false, false, false, false, false, false, true, false, true, true, true, true, true, true, false, false, true, true, true, false, false, false, false, false, false, false, false, false, false, true, true, true, true, true ]; 

To use the test data, create a loop to call isNumber(test) on each item in the tests array and compare the result to the same item in the expects array.

tests.map(function(test, i) {
    console.log(isNumber(test), expects(i));
}