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problem 8 content update
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goformarty committed Feb 28, 2018
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<!DOCTYPE html>
<html lang="en">

<head>
<meta charset="UTF-8">
<title>Euler Project Solutions</title>
<link rel="stylesheet" href="style.css">
</head>

<body>
<div class="site-wrapper">
<div class="title">
Expand All @@ -13,103 +15,170 @@ <h5>Solutions by Marty Stepien</h5>
</div>
<div class="description">
<h5>What is Problem Euler?</h5>
<p>Project Euler is a website with a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. The motivation for starting Project Euler, and its continuation, is to provide a platform for the inquiring mind to delve into unfamiliar areas and learn new concepts in a fun and recreational context.</p>
<p>You can visit and join here: <a href="https://projecteuler.net/">https://projecteuler.net</a></p>
<p>Project Euler is a website with a series of challenging mathematical/computer programming problems that will require more
than just mathematical insights to solve. The motivation for starting Project Euler, and its continuation, is to provide
a platform for the inquiring mind to delve into unfamiliar areas and learn new concepts in a fun and recreational context.</p>
<p>You can visit and join here:
<a href="https://projecteuler.net/">https://projecteuler.net</a>
</p>
</div>
<!-- Problem 1 -->
<div class="problemContainer">
<h2>Problem 1</h2>
<h4>Multiples of 3 and 5</h4>
<br />
<p>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.<br /><br />Find the sum of all the multiples of 3 or 5 below given number.</p>
<p>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.
<br />
<br />Find the sum of all the multiples of 3 or 5 below given number.</p>
<br />
<input id="input1" type="number" min="1" max="10000" placeholder="Enter your number" />
<button id="btn1">Calculate</button>
<br /><br />
<h5 class="answer">Answer: <span id="answer1"></span></h5>
<br />
<br />
<h5 class="answer">Answer:
<span id="answer1"></span>
</h5>
</div>

<!-- Problem 2 -->
<div class="problemContainer">
<h2>Problem 2</h2>
<h4>Even Fibonacci numbers</h4>
<br />
<p>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: <br />1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...<br /><br />By considering the terms in the Fibonacci sequence whose values do not exceed given number, find the sum of the even-valued terms.</p>
<p>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:
<br />1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
<br />
<br />By considering the terms in the Fibonacci sequence whose values do not exceed given number, find the sum of the even-valued
terms.</p>
<br />
<input id="input2" type="number" min="1" max="5000000" placeholder="Enter your number" />
<button id="btn2">Calculate</button>
<br /><br />
<h5 class="answer">Answer: <span id="answer2"></span></h5>
<br />
<br />
<h5 class="answer">Answer:
<span id="answer2"></span>
</h5>
</div>

<!-- Problem 3 -->
<div class="problemContainer">
<h2>Problem 3</h2>
<h4>Largest prime factor</h4>
<br />
<p>The prime factors of 13195 are 5, 7, 13 and 29.<br /><br />What is the largest prime factor of the given number?</p>
<p>The prime factors of 13195 are 5, 7, 13 and 29.
<br />
<br />What is the largest prime factor of the given number?</p>
<br />
<input id="input3" type="number" min="1" max="5000000" placeholder="Enter your number" />
<button id="btn3">Calculate</button>
<br /><br />
<h5 class="answer">Answer: <span id="answer3"></span></h5>
<br />
<br />
<h5 class="answer">Answer:
<span id="answer3"></span>
</h5>
</div>

<!-- Problem 4 -->
<div class="problemContainer">
<h2>Problem 4</h2>
<h4>Largest palindrome product</h4>
<br />
<p>A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.<br /><br />Find the largest palindrome made from the product of two same digit long numbers - specify the number of digits.</p>
<p>A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is
9009 = 91 × 99.
<br />
<br />Find the largest palindrome made from the product of two same digit long numbers - specify the number of digits.</p>
<br />
<input id="input4" type="number" min="1" max="10" placeholder="Enter your number" />
<button id="btn4">Calculate</button>
<br /><br />
<h5 class="answer">Answer: <span id="answer4"></span></h5>
<br />
<br />
<h5 class="answer">Answer:
<span id="answer4"></span>
</h5>
</div>

<!-- Problem 5 -->
<div class="problemContainer">
<h2>Problem 5</h2>
<h4>Smallest multiple</h4>
<br />
<p>2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.<br /><br />What is the smallest positive number that is evenly divisible by all of the numbers from 1 to the given number?</p>
<p>2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
<br />
<br />What is the smallest positive number that is evenly divisible by all of the numbers from 1 to the given number?</p>
<br />
<input id="input5" type="number" min="1" max="100" placeholder="Enter your number" />
<button id="btn5">Calculate</button>
<br /><br />
<h5 class="answer">Answer: <span id="answer5"></span></h5>
<br />
<br />
<h5 class="answer">Answer:
<span id="answer5"></span>
</h5>
</div>

<!-- Problem 6 -->
<div class="problemContainer">
<h2>Problem 6</h2>
<h4>Sum square difference</h4>
<br />
<p>The sum of the squares of the first ten natural numbers is 385. The square of the sum of the first ten natural numbers is 3025. <br /><br /> Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 − 385 = 2640. <br /> <br /> Find the difference between the sum of the squares of the specified first natural numbers and the square of the sum.</p>
<p>The sum of the squares of the first ten natural numbers is 385. The square of the sum of the first ten natural numbers
is 3025.
<br />
<br /> Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025
− 385 = 2640.
<br />
<br /> Find the difference between the sum of the squares of the specified first natural numbers and the square of the sum.</p>
<br />
<input id="input6" type="number" min="1" max="200" placeholder="Enter your number" />
<button id="btn6">Calculate</button>
<br /><br />
<h5 class="answer">Answer: <span id="answer6"></span></h5>
<br />
<br />
<h5 class="answer">Answer:
<span id="answer6"></span>
</h5>
</div>

<!-- Problem 7 -->
<div class="problemContainer">
<h2>Problem 7</h2>
<h4>10001st prime</h4>
<br />
<p>By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the nth prime number?</p>
<p>By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the Nth prime
number?</p>
<br />
<input id="input7" type="number" min="1" max="15000" placeholder="Enter your number" />
<button id="btn7">Calculate</button>
<br />
<br />
<h5 class="answer">Answer:
<span id="answer7"></span>
</h5>
</div>

<!-- Problem 8 -->
<div class="problemContainer">
<h2>Problem 8</h2>
<h4>Largest product in a series</h4>
<br />
<p>The four adjacent digits in the below 1000-digit number that have
the greatest product are 9 × 9 × 8 × 9 = 5832</p>
<p style="font-family: monospace; overflow-wrap: break-word;">7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450</p>
<p>What is the value of the largest product of N adjacent digits in the 1000-digit number? </p>
<br />
<input id="input7" type="number" min="1" max="15000" placeholder="Enter your number" />
<button id="btn7">Calculate</button>
<br /><br />
<h5 class="answer">Answer: <span id="answer7"></span></h5>
<br />
<br />
<h5 class="answer">Answer:
<span id="answer7"></span>
</h5>
</div>
</div>



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