#!/usr/bin/env lua
-- Problem 13: Find the first ten digits of the sum of one-hundred 50-digit
-- numbers.
--
-- Work out the first ten digits of the sum of the following one-hundred
-- 50-digit numbers.
local numbers = {
    '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 number_count = 100;
local target_length = 10;

-- We have X numbers with up to Y digits each.
-- Any given column of digits can sum to no more than 9X, which has log10(9X)
-- digits and can thus afford that many places.
-- So let's add up the leftmost 10 + log10(9X) digits.
local prefix_length = target_length + math.log10(number_count * 9);

local truncated_numbers = {};
for i, number in ipairs(numbers) do
    -- Cheerfully assuming there are no short numbers (which there aren't)
    truncated_numbers[i] = string.sub(number, 1, prefix_length);
end

-- There are too many digits to add manually, so we're going to do it a digit
-- at a time
local sum = {0};
while string.len(truncated_numbers[1]) ~= 0 do
    for i, number in ipairs(truncated_numbers) do
        local digit = string.sub(number, -1);
        sum[1] = sum[1] + tonumber(digit);
        truncated_numbers[i] = string.sub(number, 1, -2);
    end
    
    -- Remove the carry and shift it onto the front of the digit list
    local carry = math.floor(sum[1] / 10);
    sum[1] = sum[1] % 10;
    table.insert(sum, 1, carry);
end

-- Join, truncate, print
local answer = string.sub(table.concat(sum), 1, 10);
print(answer);
