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"$$\n",
"\\def\\CC{\\bf C}\n",
"\\def\\QQ{\\bf Q}\n",
"\\def\\RR{\\bf R}\n",
"\\def\\ZZ{\\bf Z}\n",
"\\def\\NN{\\bf N}\n",
"$$\n",
"# Project Euler one-liners\n",
"\n",
"Authors \n",
"- Thierry Monteil\n",
"- Contributors of projecteuler.net\n",
"\n",
"License \n",
"CC BY-NC-SA 2.0\n",
"\n",
"See \n",
"\n",
"> Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems. The problems range in difficulty and for many the experience is inductive chain learning. That is, by solving one problem it will expose you to a new concept that allows you to undertake a previously inaccessible problem. So the determined participant will slowly but surely work his/her way through every problem.\n",
"\n",
"For each of the first ten Project Euler problems listed below, find a one-line solution with Sage, do not reinvent the wheel !\n",
"\n",
"## 1: Multiples of 3 and 5\n",
"\n",
"### Question\n",
"\n",
"If we list all the natural numbers below $10$ that are multiples of $3$ or $5$, we get $3$, $5$, $6$ and $9$. The sum of these multiples is $23$.\n",
"\n",
"Find the sum of all the multiples of $3$ or $5$ below $1000$.\n",
"\n",
"### Answer"
],
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"#edit here, your solution should fit in this single-line cell."
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"source": [
"## 2: Even Fibonacci numbers\n",
"\n",
"### Question\n",
"\n",
"Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with $1$ and $2$, the first $10$ terms will be:\n",
"\n",
"> $1, 2, 3, 5, 8, 13, 21, 34, 55, 89, \\dots$\n",
"\n",
"By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.\n",
"\n",
"### Answer"
],
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"metadata": {}
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"execution_count": null,
"cell_type": "code",
"source": [
"#edit here, your solution should fit in this single-line cell."
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"outputs": [],
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"source": [
"## 3: Largest prime factor\n",
"\n",
"### Question\n",
"\n",
"The prime factors of $13195$ are $5$, $7$, $13$ and $29$.\n",
"\n",
"What is the largest prime factor of the number $600851475143$ ?\n",
"\n",
"### Answer"
],
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"metadata": {}
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"execution_count": null,
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"#edit here, your solution should fit in this single-line cell."
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"source": [
"## 4: Largest palindrome product\n",
"\n",
"### Question\n",
"\n",
"A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is\n",
"\n",
"> $9009 = 91 \\times 99$.\n",
"\n",
"Find the largest palindrome made from the product of two 3-digit numbers.\n",
"\n",
"### Answer"
],
"cell_type": "markdown",
"metadata": {}
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{
"execution_count": null,
"cell_type": "code",
"source": [
"#edit here, your solution should fit in this single-line cell."
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"source": [
"## 5: Smallest multiple\n",
"\n",
"### Question\n",
"\n",
"$2520$ is the smallest number that can be divided by each of the numbers from $1$ to $10$ without any remainder.\n",
"\n",
"What is the smallest positive number that is evenly divisible by all of the numbers from $1$ to $20$?\n",
"\n",
"### Answer"
],
"cell_type": "markdown",
"metadata": {}
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{
"execution_count": null,
"cell_type": "code",
"source": [
"#edit here, your solution should fit in this single-line cell. "
],
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"source": [
"## 6: Sum square difference\n",
"\n",
"### Question\n",
"\n",
"The sum of the squares of the first ten natural numbers is\n",
"\n",
"> $1^2 + 2^2 + ... + 10^2 = 385$.\n",
"\n",
"The square of the sum of the first ten natural numbers is\n",
"\n",
"> $(1 + 2 + ... + 10)^2 = 552 = 3025$.\n",
"\n",
"Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is\n",
"\n",
"> $3025 \u2212 385 = 2640$.\n",
"\n",
"Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.\n",
"\n",
"### Answer"
],
"cell_type": "markdown",
"metadata": {}
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"execution_count": null,
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"#edit here, your solution should fit in this single-line cell."
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"source": [
"## 7: 10001st prime\n",
"\n",
"### Question\n",
"\n",
"By listing the first six prime numbers: $2$, $3$, $5$, $7$, $11$, and $13$, we can see that the $6$-th prime is $13$.\n",
"\n",
"What is the $10001$-st prime number?\n",
"\n",
"### Answer"
],
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"execution_count": null,
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"#edit here, your solution should fit in this single-line cell."
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"source": [
"## 8: Largest product in a series\n",
"\n",
"### Question\n",
"\n",
"The four adjacent digits in the 1000-digit number $n$ below that have the greatest product are\n",
"\n",
"> $9 \\times 9 \\times 8 \\times 9 = 5832$."
],
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"execution_count": null,
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"source": [
"n = 7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450"
],
"outputs": [],
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"source": [
"Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?\n",
"\n",
"### Answer"
],
"cell_type": "markdown",
"metadata": {}
},
{
"execution_count": null,
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"source": [
"#edit here, your solution should fit in this single-line cell."
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"outputs": [],
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{
"source": [
"## 9: Special Pythagorean triplet\n",
"\n",
"### Question\n",
"\n",
"A Pythagorean triplet is a set of three natural numbers, $a < b < c$, for which, $a^2 + b^2 = c^2$\n",
"\n",
"For example, $3^2 + 4^2 = 9 + 16 = 25 = 5^2$.\n",
"\n",
"There exists exactly one Pythagorean triplet for which $a + b + c = 1000$. Find the product $abc$.\n",
"\n",
"### Answer"
],
"cell_type": "markdown",
"metadata": {}
},
{
"execution_count": null,
"cell_type": "code",
"source": [
"#edit here, your solution should fit in this single-line cell."
],
"outputs": [],
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{
"source": [
"## 10: Summation of primes\n",
"\n",
"### Question\n",
"\n",
"The sum of the primes below $10$ is $2 + 3 + 5 + 7 = 17$.\n",
"\n",
"Find the sum of all the primes below two million.\n",
"\n",
"### Answer"
],
"cell_type": "markdown",
"metadata": {}
},
{
"execution_count": null,
"cell_type": "code",
"source": [
"#edit here, your solution should fit in this single-line cell."
],
"outputs": [],
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}
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"display_name": "sagemath",
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