pe by Julia

pe3

@time for i = 1:10
    factor(600851475143)|>keys|>maximum|>println
end

pe4

function pe4()
    for s = 1998:-1:200, i = 999:-1:s-999
        pro = string(i * (s-i))
        pro == reverse(pro) && return pro
    end
end
@time println(pe4())

pe12

function countFactor(n::Int)
    count = 1
    for i in values(factor(n))
        count *= i + 1
    end
    count
end
function pe12(lim::Int)
    i = 8
    while countFactor(div(i*(i+1), 2)) < lim
        i += 1
    end
    div(i*(i+1), 2)
end
@time for i = 1:5
    pe12(500)|>println
end

pe14

d = Dict{Int, Int}()
d[1] = 1
function PE14(n::Int)
    haskey(d, n) && return d[n]
    iseven(n) ? (d[n] = PE14(div(n, 2)) + 1) : (d[n] = PE14(3n+1) + 1)
end
function main()
    crt = idx = 0
    for i = 1:1000000
        t = PE14(i)
        t > crt && (crt = t; idx = i)
    end
    idx
end
@time main()|>println

pe15

d = Dict{(Int, Int), Int}()
function rec(m::Int, n::Int)
    (m == 0 || n == 0) && return 1
    haskey(d, (m, n)) && return d[m, n]
    return d[m, n] = rec(m-1, n) + rec(m, n-1)
end
@time rec(20, 20)

pe23

function PE23(lim::Int)
    factorsum = ones(Int, lim)
    for f = 2:lim
        factorsum[2f:f:end] += f
    end
    p = trues(lim)
    abundant = find(factorsum .> [1:lim])
    for i in abundant, j in abundant
        (i + j > lim) && continue
        p[i+j] = false
    end
    sum(find(p))
end
@time PE23(28123)

pe24

a = [0:9]
perm = zeros(Int, 10)
used = trues(10)
global cnt = 0
function PE24(pos::Int)
    if pos == 11
        global cnt += 1
        cnt == 1000000 && println(perm)
    else
        for i = 1:10
            if used[i]
                perm[pos] = a[i]
                used[i] = false
                pe24(pos + 1)
                cnt == 1000000 && return 0
                used[i] = true
            end
        end
    end
end
@time PE24(1)

pe27

function pe27(lim::Int)
    crt = 40; p = 0
    for b in primes(lim), a = -b:1000
        i = 1
        while isprime(i*i + a*i + b)
            i += 1
        end
        i > crt && (crt = i; p = a*b)
    end
    println(p)
end
@time pe27(1000)

pe30

function PE30(n::Int)
    total = 0
    for i =2:n*9^n
        s = 0; num = i
        while num != 0
            s += (num % 10)^ n
            num = div(num, 10)
        end
        s == i && (total += s)
    end
    println(total)
end
@time PE30(5)

pe31

coins = [1, 2, 5, 10, 20, 50, 100, 200]
function PE31(lim::Int, i::Int)
    total = 0
    lim == 0 && return 1
    i == 1 && return 1
    for _ = 0:div(lim, coins[i])
        total += pe31(lim, i-1)
        lim -= coins[i]
    end
    total
end
@time PE31(200, 8)

pe32

function PE32()
    demo = Set{Char}("123456789")
    res = Set{Int}()
    for a = 1:99, b = 12:9999
        c = a * b
        a < 10 && b < 1000 && continue
        b < 100 && c < 10000 && continue
        b > 100 && c > 10000 && continue
        strc = string(c)
        ('0' in strc) && continue
        d = Set{Char}()
        union!(d, string(a)); union!(d, string(b)); union!(d, strc)
        d == demo && union!(res, c)
    end
    sum(res)
end
@time PE32()

pe34

function PE34(lim::Int)
    total = 0
    for i =10:lim
        s = 0
        num = i
        while num != 0
            s += factorial(num % 10)
            num = div(num, 10)
        end
        s == i && (total += s)
    end
    println(total)
end
@time PE34(2540160)

pe60

i4, i5, i6, i7, i8 = sqrt(s), (1+sqrt(1+24s))/6, (1+sqrt(1+8s))/4, (3+sqrt(9+40s))/10, (1+sqrt(1+3s))/3

pe62

function PE62()
    count = Dict{Array{Char, 1}, Int}()
    num = Dict{Array{Char, 1}, Array{Int, 1}}()
    i = 1
    t = sort(collect(string(i^3)))
    while get(count, t, 0) != 4
        idx = get(count, t, 0) + 1
        count[t] = idx
        num[t] = get(num, t, Array(Int, 4))
        num[t][idx] = i^3
        i += 1
        t = sort(collect(string(i^3)))
    end
    println(num[t])
end
@time PE61()