add old solutions

21 files changed, 471 insertions, 0 deletions

diff --git a/1.lua b/1.lua
new file mode 100644
index 0000000..fe66121
--- /dev/null
+++ b/1.lua
@@ -0,0 +1,6 @@
+#!/usr/bin/lua
+local t = 0
+for i = 1, 999 do
+    if i % 3 == 0 or i % 5 == 0 then t = t + i end
+end
+print(t)
diff --git a/1.pl b/1.pl
new file mode 100755
index 0000000..85a8faa
--- /dev/null
+++ b/1.pl
@@ -0,0 +1,5 @@
+#!/usr/bin/perl
+use warnings;
+
+$t+=(!($_%5&& $_%3)?$_:0)for(1..999);
+print "$t\n";
diff --git a/10.lua b/10.lua
new file mode 100644
index 0000000..cca16c1
--- /dev/null
+++ b/10.lua
@@ -0,0 +1,21 @@
+function isprime(n)
+    if n < 2 then return false end
+    if n == 2 then return true end
+    if math.fmod(n, 2) == 0 then return false end
+    for i = 3, math.ceil(math.sqrt(n)), 2 do
+        if math.fmod(n, i) == 0 then return false end
+    end
+    return true
+end
+
+local i = 3
+local sum = 2
+while true do
+    if i >= 1000000 then break end
+    if isprime(i) then
+        if sum + i < sum then print("overflow") end
+        sum = sum + i
+    end
+    i = i + 2
+end
+print(sum)
diff --git a/12.lua b/12.lua
new file mode 100644
index 0000000..7ef1c0d
--- /dev/null
+++ b/12.lua
@@ -0,0 +1,31 @@
+-- only valid when n > 1
+function num_factors(n)
+    local ret = 2
+    local test = 2
+    local limit = math.sqrt(n)
+    while test < limit do
+        if n % test == 0 then
+            ret = ret + 2
+        end
+        test = test + 1
+    end
+    if limit == math.floor(limit) then ret = ret + 1 end
+    return ret
+end
+
+generate_triangle = coroutine.wrap(function()
+    local num = 0
+    local add = 1
+    while true do
+        num = num + add
+        add = add + 1
+        coroutine.yield(num)
+    end
+end)
+
+while true do
+    local n = generate_triangle()
+    local nn = num_factors(n)
+    print(n .. ": " .. nn)
+    if nn > 500 then break end
+end
diff --git a/13.lua b/13.lua
new file mode 100644
index 0000000..bcef1dd
--- /dev/null
+++ b/13.lua
@@ -0,0 +1,116 @@
+local nums = {
+    "37107287533902102798797998220837590246510135740250",
+    "46376937677490009712648124896970078050417018260538",
+    "74324986199524741059474233309513058123726617309629",
+    "91942213363574161572522430563301811072406154908250",
+    "23067588207539346171171980310421047513778063246676",
+    "89261670696623633820136378418383684178734361726757",
+    "28112879812849979408065481931592621691275889832738",
+    "44274228917432520321923589422876796487670272189318",
+    "47451445736001306439091167216856844588711603153276",
+    "70386486105843025439939619828917593665686757934951",
+    "62176457141856560629502157223196586755079324193331",
+    "64906352462741904929101432445813822663347944758178",
+    "92575867718337217661963751590579239728245598838407",
+    "58203565325359399008402633568948830189458628227828",
+    "80181199384826282014278194139940567587151170094390",
+    "35398664372827112653829987240784473053190104293586",
+    "86515506006295864861532075273371959191420517255829",
+    "71693888707715466499115593487603532921714970056938",
+    "54370070576826684624621495650076471787294438377604",
+    "53282654108756828443191190634694037855217779295145",
+    "36123272525000296071075082563815656710885258350721",
+    "45876576172410976447339110607218265236877223636045",
+    "17423706905851860660448207621209813287860733969412",
+    "81142660418086830619328460811191061556940512689692",
+    "51934325451728388641918047049293215058642563049483",
+    "62467221648435076201727918039944693004732956340691",
+    "15732444386908125794514089057706229429197107928209",
+    "55037687525678773091862540744969844508330393682126",
+    "18336384825330154686196124348767681297534375946515",
+    "80386287592878490201521685554828717201219257766954",
+    "78182833757993103614740356856449095527097864797581",
+    "16726320100436897842553539920931837441497806860984",
+    "48403098129077791799088218795327364475675590848030",
+    "87086987551392711854517078544161852424320693150332",
+    "59959406895756536782107074926966537676326235447210",
+    "69793950679652694742597709739166693763042633987085",
+    "41052684708299085211399427365734116182760315001271",
+    "65378607361501080857009149939512557028198746004375",
+    "35829035317434717326932123578154982629742552737307",
+    "94953759765105305946966067683156574377167401875275",
+    "88902802571733229619176668713819931811048770190271",
+    "25267680276078003013678680992525463401061632866526",
+    "36270218540497705585629946580636237993140746255962",
+    "24074486908231174977792365466257246923322810917141",
+    "91430288197103288597806669760892938638285025333403",
+    "34413065578016127815921815005561868836468420090470",
+    "23053081172816430487623791969842487255036638784583",
+    "11487696932154902810424020138335124462181441773470",
+    "63783299490636259666498587618221225225512486764533",
+    "67720186971698544312419572409913959008952310058822",
+    "95548255300263520781532296796249481641953868218774",
+    "76085327132285723110424803456124867697064507995236",
+    "37774242535411291684276865538926205024910326572967",
+    "23701913275725675285653248258265463092207058596522",
+    "29798860272258331913126375147341994889534765745501",
+    "18495701454879288984856827726077713721403798879715",
+    "38298203783031473527721580348144513491373226651381",
+    "34829543829199918180278916522431027392251122869539",
+    "40957953066405232632538044100059654939159879593635",
+    "29746152185502371307642255121183693803580388584903",
+    "41698116222072977186158236678424689157993532961922",
+    "62467957194401269043877107275048102390895523597457",
+    "23189706772547915061505504953922979530901129967519",
+    "86188088225875314529584099251203829009407770775672",
+    "11306739708304724483816533873502340845647058077308",
+    "82959174767140363198008187129011875491310547126581",
+    "97623331044818386269515456334926366572897563400500",
+    "42846280183517070527831839425882145521227251250327",
+    "55121603546981200581762165212827652751691296897789",
+    "32238195734329339946437501907836945765883352399886",
+    "75506164965184775180738168837861091527357929701337",
+    "62177842752192623401942399639168044983993173312731",
+    "32924185707147349566916674687634660915035914677504",
+    "99518671430235219628894890102423325116913619626622",
+    "73267460800591547471830798392868535206946944540724",
+    "76841822524674417161514036427982273348055556214818",
+    "97142617910342598647204516893989422179826088076852",
+    "87783646182799346313767754307809363333018982642090",
+    "10848802521674670883215120185883543223812876952786",
+    "71329612474782464538636993009049310363619763878039",
+    "62184073572399794223406235393808339651327408011116",
+    "66627891981488087797941876876144230030984490851411",
+    "60661826293682836764744779239180335110989069790714",
+    "85786944089552990653640447425576083659976645795096",
+    "66024396409905389607120198219976047599490197230297",
+    "64913982680032973156037120041377903785566085089252",
+    "16730939319872750275468906903707539413042652315011",
+    "94809377245048795150954100921645863754710598436791",
+    "78639167021187492431995700641917969777599028300699",
+    "15368713711936614952811305876380278410754449733078",
+    "40789923115535562561142322423255033685442488917353",
+    "44889911501440648020369068063960672322193204149535",
+    "41503128880339536053299340368006977710650566631954",
+    "81234880673210146739058568557934581403627822703280",
+    "82616570773948327592232845941706525094512325230608",
+    "22918802058777319719839450180888072429661980811197",
+    "77158542502016545090413245809786882778948721859617",
+    "72107838435069186155435662884062257473692284509516",
+    "20849603980134001723930671666823555245252804609722",
+    "53503534226472524250874054075591789781264330331690",
+}
+
+local sum1 = 0
+for _, v in ipairs(nums) do
+    v = v:sub(1, 8)
+    sum1 = sum1 + tonumber(v)
+end
+local sum2 = 0
+for _, v in ipairs(nums) do
+    v = v:sub(9, 16)
+    sum2 = sum2 + tonumber(v)
+end
+sum2 = tostring(sum2)
+sum2 = sum2:sub(1, sum2:len() - 8)
+print(sum1 + tonumber(sum2))
diff --git a/14.lua b/14.lua
new file mode 100644
index 0000000..96498ec
--- /dev/null
+++ b/14.lua
@@ -0,0 +1,20 @@
+function collatz(n)
+    local sum = 1
+    while true do
+        if n == 1 then break end
+        if n % 2 == 0 then n = n / 2
+        else n = n * 3 + 1 end
+        sum = sum + 1
+    end
+    return sum
+end
+
+local max = 0
+local maxnum = 0
+for i = 1, 999999 do
+    local sum = collatz(i)
+    print(i .. ": " .. sum)
+    if sum > max then max = sum; maxnum = i end
+end
+print("--------")
+print(maxnum .. ": " .. max)
diff --git a/145.lua b/145.lua
new file mode 100644
index 0000000..1713881
--- /dev/null
+++ b/145.lua
@@ -0,0 +1,12 @@
+-- this will take ~6h to run... need efficiency!
+function reversible(n)
+    local revn = n:reverse()
+    local str = tostring(n + revn)
+    return not str:match("[02468]")
+end
+
+local sum = 0
+for i = 1, 999999999 do
+    if i % 10 ~= 0 and reversible(tostring(i)) then sum = sum + 1 end
+end
+print(sum)
diff --git a/15.lua b/15.lua
new file mode 100644
index 0000000..8450302
--- /dev/null
+++ b/15.lua
@@ -0,0 +1,13 @@
+function combinations(n, r)
+    local numerator = 1
+    local denominator = 1
+    for i = n, n - r + 1, -1 do
+        numerator = numerator * i
+    end
+    for i = r, 1, -1 do
+        denominator = denominator * i
+    end
+    return numerator / denominator
+end
+
+print(combinations(40, 20))
diff --git a/17.lua b/17.lua
new file mode 100644
index 0000000..d745419
--- /dev/null
+++ b/17.lua
@@ -0,0 +1,38 @@
+function num_to_words(n)
+    local digits = {"one",     "two",       "three",    "four",     "five",
+                    "six",     "seven",     "eight",    "nine"}
+    local teens =  {"eleven",  "twelve",    "thirteen", "fourteen", "fifteen",
+                    "sixteen", "seventeen", "eighteen", "nineteen"}
+    local tens =   {"ten",     "twenty",    "thirty",   "forty",    "fifty",
+                    "sixty",   "seventy",   "eighty",   "ninety"}
+    local ret = ""
+    if n == 1000 then return digits[1] .. "thousand" end
+    if n >= 100 then
+        local hundred = math.floor(n / 100)
+        ret = ret .. digits[hundred] .. "hundred"
+        n = n - hundred * 100
+        if n > 0 then ret = ret .. "and" end
+    end
+    if n >= 10 then
+        if n == 10 then return ret .. tens[1] end
+        if n < 20 then
+            return ret .. teens[n - 10]
+        else
+            local ten = math.floor(n / 10)
+            ret = ret .. tens[ten]
+            n = n - ten * 10
+        end
+    end
+    if n >= 1 then
+        ret = ret .. digits[n]
+    end
+    return ret
+end
+
+local sum = 0
+for i = 1, 1000 do
+    local text = num_to_words(i)
+    print(i .. ": " .. text .. " (" .. text:len() .. ")")
+    sum = sum + text:len()
+end
+print(sum)
diff --git a/189.lua b/189.lua
new file mode 100644
index 0000000..a4ae546
--- /dev/null
+++ b/189.lua
@@ -0,0 +1,27 @@
+local triangle_graph = {
+}
+
+--[[
+http://en.wikipedia.org/wiki/Graph_coloring#Computing_the_chromatic_polynomial
+]]
+function chromatic_polynomial(g, t)
+    local edge_start
+    for v1, edges in ipairs(g) do
+        for v2index, v2 in ipairs(edges) do
+            if v1 == v2 then return 0 end
+            if not edge_start then edge_start = v1 end
+        end
+    end
+
+    if edge_start == nil then return t^#g end
+
+    local edge_end = table.remove(g[edge_start])
+    local edge_removed = chromatic_polynomial(g, t)
+    table.insert(g[edge_start], edge_end)
+
+    -- need to contract the edge here
+    local edge_contracted = chromatic_polynomial(g, t)
+    -- and then fix it back up
+
+    return edge_removed - edge_contracted
+end
diff --git a/2.lua b/2.lua
new file mode 100644
index 0000000..d70cdc3
--- /dev/null
+++ b/2.lua
@@ -0,0 +1,30 @@
+local function memoize(fn)
+    local t = {}
+    return function(x)
+        local y = t[x]
+        if y == nil then y = fn(x); t[x] = y end
+        return y
+    end
+end
+
+fib = memoize(function(n)
+    if n < 3 then return 1 end
+    return fib(n - 1) + fib(n - 2)
+end)
+
+local root5 = math.sqrt(5)
+local phi = (1 + root5)/2
+local function fib2(n)
+    return math.floor((phi^n-(1-phi)^n)/root5+0.5)
+end
+
+local sum = 0
+local i = 0
+while true do
+    i = i + 1
+    local n = fib(i)
+    if n > 1000000 then break end
+    if n % 2 == 0 then sum = sum + n end
+end
+
+print(sum)
diff --git a/2.pl b/2.pl
new file mode 100755
index 0000000..6b59aed
--- /dev/null
+++ b/2.pl
@@ -0,0 +1,18 @@
+#!/usr/bin/perl
+use strict;
+use warnings;
+
+my $root5 = sqrt 5;
+my $phi = (1 + $root5)/2;
+
+sub fib { int (($phi**$_[0]-(1-$phi)**$_[0])/$root5 + 0.5) }
+
+my $i = 0;
+my $sum = 0;
+while (1) {
+    $i++;
+    my $n = fib $i;
+    last if $n > 1000000;
+    $sum += $n if $n % 2 == 0;
+}
+print "$sum\n";
diff --git a/21.lua b/21.lua
new file mode 100644
index 0000000..d4a5334
--- /dev/null
+++ b/21.lua
@@ -0,0 +1,24 @@
+function d(n)
+    if n < 2 then return 0 end
+    local ret = 1
+    local test = 2
+    local limit = math.sqrt(n)
+    while test < limit do
+        if n % test == 0 then
+            ret = ret + test + n / test
+        end
+        test = test + 1
+    end
+    if limit == math.floor(limit) then ret = ret + limit end
+    return ret
+end
+
+local sum = 0
+for i = 1, 9999 do
+    local di = d(i)
+    if d(di) == i and i ~= di then
+        print(i .. ": " .. di)
+        sum = sum + i
+    end
+end
+print(sum)
diff --git a/3.lua b/3.lua
new file mode 100644
index 0000000..eff06a3
--- /dev/null
+++ b/3.lua
@@ -0,0 +1,8 @@
+local num = 317584931803
+local test = 3
+while true do
+    if num % test == 0 then num = num / test
+    else test = test + 2 end
+    if test > math.sqrt(num) then break end
+end
+print(num)
diff --git a/3.pl b/3.pl
new file mode 100755
index 0000000..7fbf7ad
--- /dev/null
+++ b/3.pl
@@ -0,0 +1,16 @@
+#!/usr/bin/perl
+use strict;
+use warnings;
+
+my $num = 317584931803;
+my $test = 3;
+while (1) {
+    if ($num % $test) {
+        $test += 2;
+    }
+    else {
+        $num /= $test;
+    }
+    last if $test > sqrt $num;
+}
+print "$num\n";
diff --git a/3.sh b/3.sh
new file mode 100755
index 0000000..3129d47
--- /dev/null
+++ b/3.sh
@@ -0,0 +1 @@
+factor 317584931803 | sed 's/.* \([[:digit:]]*\)/\1/'
diff --git a/4.lua b/4.lua
new file mode 100644
index 0000000..daec4bc
--- /dev/null
+++ b/4.lua
@@ -0,0 +1,16 @@
+local function is_palindrome(n)
+    local first_half = string.sub(n, 1, string.len(n) / 2)
+    local second_half = string.sub(n, -string.len(n) / 2)
+    return first_half == string.reverse(second_half)
+end
+
+local prods = {}
+for i = 100,999 do
+    for j = 100,i do
+        table.insert(prods, i * j)
+    end
+end
+table.sort(prods, function(a, b) return a > b end)
+for _, v in ipairs(prods) do
+    if is_palindrome(v) then print(v) break end
+end
diff --git a/5.lua b/5.lua
new file mode 100644
index 0000000..b407475
--- /dev/null
+++ b/5.lua
@@ -0,0 +1,21 @@
+local max_factors = {}
+for _, prime in ipairs({2, 3, 5, 7, 11, 13, 17, 19}) do
+    for i = prime, 20, prime do
+        local num_fact = 0
+        local tmp = i
+        while i % prime == 0 do
+            num_fact = num_fact + 1
+            i = i / prime
+        end
+        if num_fact > (max_factors[prime] or 0) then
+            max_factors[prime] = num_fact
+        end
+    end
+end
+
+local total = 1
+for prime, power in pairs(max_factors) do
+    total = total * prime^power
+end
+
+print(total)
diff --git a/6.lua b/6.lua
new file mode 100644
index 0000000..3c39a4b
--- /dev/null
+++ b/6.lua
@@ -0,0 +1,13 @@
+local function sum_of_squares(n)
+    local total = 0
+    for i = 1, n do
+        total = total + i^2
+    end
+    return total
+end
+
+local function square_of_sum(n)
+    return n^2*(n+1)^2/4
+end
+
+print(square_of_sum(100) - sum_of_squares(100))
diff --git a/7.lua b/7.lua
new file mode 100644
index 0000000..d5af641
--- /dev/null
+++ b/7.lua
@@ -0,0 +1,19 @@
+function isprime(n)
+    if n < 2 then return false end
+    if n == 2 then return true end
+    if math.fmod(n, 2) == 0 then return false end
+    for i = 3, math.ceil(math.sqrt(n)), 2 do
+        if math.fmod(n, i) == 0 then return false end
+    end
+    return true
+end
+
+local i = 2
+local primes = 0
+while true do
+    if isprime(i) then
+        primes = primes + 1
+        if primes == 10001 then print(i); break end
+    end
+    i = i + 1
+end
diff --git a/8.lua b/8.lua
new file mode 100644
index 0000000..486ffca
--- /dev/null
+++ b/8.lua
@@ -0,0 +1,16 @@
+local number = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450"
+
+local max = 0
+local index = 1
+while true do
+    local str = number:sub(index, index + 4)
+    if str:len() < 5 then break end
+    local prod = str:sub(1, 1) *
+                 str:sub(2, 2) *
+                 str:sub(3, 3) *
+                 str:sub(4, 4) *
+                 str:sub(5, 5)
+    if prod > max then max = prod end
+    index = index + 1
+end
+print(max)