026.js

// A unit fraction contains 1 in the numerator. The decimal
// representation of the unit fractions with denominators 2 to 10 are
// given:

//     1/2 = 0.5
//     1/3 = 0.(3)
//     1/4 = 0.25
//     1/5 = 0.2
//     1/6 = 0.1(6)
//     1/7 = 0.(142857)
//     1/8 = 0.125
//     1/9 = 0.(1)
//     1/10 = 0.1

// Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It
// can be seen that 1/7 has a 6-digit recurring cycle.

// Find the value of d < 1000 for which 1/d contains the longest
// recurring cycle in its decimal fraction part.

function recurringLength(n) {
    var remainders = [], value = 1, i = 0;
    while (!remainders[value] && value !== 0) {
        remainders[value] = i;
        value *= 10;
        value %= n;
        i++;
    }
    return i - (remainders[value] || 0);
}

function maxReccuringLength(d) {
    var max = 0;
    for (var i = 1; i <=d; i++) {
        if (max >= i) continue;
        if (recurringLength(i) > max) {
            max = i;
        }
    }
    return max;
}

console.log( maxReccuringLength(1000) );