Problem #20

Problem link
Solution:

package main

import (
    "big"
    "strconv"
)

func main() {
    mul := big.NewInt(1)
    for i := 2; i <= 100; i++ {
        mul.Mul(mul, big.NewInt(int64(i)))
    }
    result, digit := 0, 0
    for i := range mul.String() {
        digit, _ = strconv.Atoi(string(mul.String()[i]))
        result += digit
    }
    println(result)
}

Result: 648
Time: 0m0.023s

Problem #25

Problem link
Solution:

package main

import (
    "big"
)

func main() {
    a, b, c, counter := big.NewInt(int64(1)), big.NewInt(int64(2)), big.NewInt(int64(0)), 2
    for len(a.String()) < 1000 {
        c.Neg(a) //c is a temp variable
        a.Add(a, b)
        b.Neg(c)
        counter++
    }
    println(counter)
}

Result: 4782
Time: 0m2.108s

Problem #26

Problem link
Solution:

package main

import (
    "big"
)

//using Fermat's little theorem we need to find the largest prime less than 1000
//see details: http://en.wikipedia.org/wiki/Repeating_decimal#Fractions_with_prime_denominators

func main() {
    //find primes
    arr := make([]bool, 1000)
    arr[0], arr[1] = true, true
    prime := 3
    var k int
    for {
        for k = prime * 2; k < len(arr); k += prime {
            arr[k] = true
        }
        for k = prime + 2; k < len(arr) && arr[k]; k += 2 {
        }
        if k < len(arr) {
            prime = k
        } else {
            break
        }
    }

    //iterate over primes in reverse direction
    b := big.NewInt(0)
    var i int
    for k = prime; k > 0; k -= 2 {
        if !arr[k] && k%2 != 0 {
        inner:
            for i = 1; i < k; i++ {
                if b.Mod(b.Sub(b.Exp(big.NewInt(10), big.NewInt(int64(i)), nil), big.NewInt(1)), big.NewInt(int64(k))).Int64() == 0 {
                    break inner
                }
            }
            if k-i == 1 {
                println(k)
                return
            }
        }
    }
}

Result: 983
Time: 0m0.041s

Problem #29

Problem link
Solution:

package main

import (
    "big"
)

func main() {
    strMap := make(map[string]int)
    for a := 2; a < 101; a++ {
        for b := 2; b < 101; b++ {
            bigA := big.NewInt(int64(a))
            bigB := big.NewInt(int64(b))
            bigA.Exp(bigA, bigB, nil)
            strMap[bigA.String()] = 0
        }
    }
    println(len(strMap))
}

Result: 9183
Time: 0m0.300s

Problem #48

Problem link
Solution:

package main

import (
    "big"
)

func main() {
    result := big.NewInt(0)
    power := big.NewInt(0)
    var number *big.Int
    for i := 1; i < 1001; i++ {
        number = big.NewInt(int64(i))
        power.Exp(number, number, nil)
        result.Add(result, power)
    }
    str := result.String()
    println(str[len(str)-10 : len(str)])
}

Result: 9110846700
Time: 0m0.090s