108 lines
4.0 KiB
Plaintext
108 lines
4.0 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "8744af43",
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"metadata": {},
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"source": [
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"# Largest Product in a Series\n",
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"> The four adjacent digits in the 1000-digit number that have the greatest product are $9 \\times 9 \\times 8 \\times 9 = 5832$.\n",
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"> ```\n",
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"73167176531330624919225119674426574742355349194934\n",
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"96983520312774506326239578318016984801869478851843\n",
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"85861560789112949495459501737958331952853208805511\n",
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"12540698747158523863050715693290963295227443043557\n",
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"66896648950445244523161731856403098711121722383113\n",
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"62229893423380308135336276614282806444486645238749\n",
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"30358907296290491560440772390713810515859307960866\n",
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"70172427121883998797908792274921901699720888093776\n",
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"65727333001053367881220235421809751254540594752243\n",
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"52584907711670556013604839586446706324415722155397\n",
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"53697817977846174064955149290862569321978468622482\n",
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"83972241375657056057490261407972968652414535100474\n",
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"82166370484403199890008895243450658541227588666881\n",
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"16427171479924442928230863465674813919123162824586\n",
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"17866458359124566529476545682848912883142607690042\n",
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"24219022671055626321111109370544217506941658960408\n",
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"07198403850962455444362981230987879927244284909188\n",
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"84580156166097919133875499200524063689912560717606\n",
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"05886116467109405077541002256983155200055935729725\n",
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"71636269561882670428252483600823257530420752963450\n",
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"> ```\n",
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"> Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?\n",
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"\n",
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"First, let's load the number as a tuple."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "699aa447",
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"metadata": {},
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"outputs": [],
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"source": [
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"num = tuple(int(d) for d in \"7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "8b53af56",
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"metadata": {},
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"source": [
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"Now we'll just do a sliding window over the number to find the thirteen adjacent digits with the greatest product."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "6b760673",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(5, 5, 7, 6, 6, 8, 9, 6, 6, 4, 8, 9, 5)"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"subnums = (num[i:i+13] for i in range(0, len(num)-13))\n",
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"max(subnums, key=prod)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "4148d160",
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"metadata": {},
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"source": [
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"Their product is 23514624000."
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "SageMath 9.5",
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"language": "sage",
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"name": "sagemath"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.2"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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