Project Euler/6 - Revision history

Admin: Replacing charlesreid1.com:3000 with git.charlesreid1.com

2019-10-09T03:49:00Z

Replacing charlesreid1.com:3000 with git.charlesreid1.com

← Older revision		Revision as of 03:49, 9 October 2019
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	The problem: https://projecteuler.net/problem=6		The problem: https://projecteuler.net/problem=6

	The solution: https://charlesreid1.com~~:3000~~/cs/euler/src/master/006/Problem006.java		The solution: https://git.charlesreid1.com/cs/euler/src/master/006/Problem006.java

	==Project Euler Problem 6==		==Project Euler Problem 6==
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	Project Euler Link: https://projecteuler.net/problem=6		Project Euler Link: https://projecteuler.net/problem=6

	Link to solution, git.charlesreid1.com: https://charlesreid1.com~~:3000~~/cs/euler/src/master/Problem006.java		Link to solution, git.charlesreid1.com: https://git.charlesreid1.com/cs/euler/src/master/Problem006.java

	Principle: this utilizes two summations that are useful to know off the top of your head. If you do, it makes this an O(1) problem. If not, it makes it an O(N) problem.		Principle: this utilizes two summations that are useful to know off the top of your head. If you do, it makes this an O(1) problem. If not, it makes it an O(N) problem.

Admin: /* Flags */

2017-07-08T08:46:51Z

Flags

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	}		}
	</pre>		</pre>

			==The generalization==

			This exercise links in with the pythagorean theorem, the binomial theorem, and the misconception that many students in algebra have about the rules for distributing exponents.



	==Flags==		==Flags==

Admin at 08:43, 8 July 2017

2017-07-08T08:43:15Z

← Older revision		Revision as of 08:43, 8 July 2017
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			The problem: https://projecteuler.net/problem=6

			The solution: https://charlesreid1.com:3000/cs/euler/src/master/006/Problem006.java

	==Project Euler Problem 6==		==Project Euler Problem 6==

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	===Code Implementations===		==Code Implementations==

	The implementations of the above formulas in Java:		The implementations of the above formulas in Java:

Admin: Admin moved page Project Euler/SoS to Project Euler/6

2017-07-05T04:12:49Z

Admin moved page Project Euler/SoS to Project Euler/6

← Older revision	Revision as of 04:12, 5 July 2017
(No difference)

Admin: /* Project Euler Problem 6 */

2017-06-15T21:11:22Z

Project Euler Problem 6

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 \sum_{i=1}^{n} i^2 = \dfrac{n(n+1)(2n+1)}{6}
 </math>
 ===Code Implementations===

Admin: /* Project Euler Problem 6 */

2017-06-15T21:03:08Z

Project Euler Problem 6

← Older revision		Revision as of 21:03, 15 June 2017
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	==Project Euler Problem 6==		==Project Euler Problem 6==

	The sum of the squares of the first 10 integers is x.		The sum of the squares of the first 10 integers is 385.

	The square of the sum of the first 10 integers is y.		The square of the sum of the first 10 integers is 3025.

	Their difference is y-x.		Their difference is 3025 - 385 = 2640.

	Find this for the first 100 integers.		Find this for the first 100 integers.

Admin: /* Project Euler Problem 6 */

2017-06-15T21:02:23Z

Project Euler Problem 6

← Older revision		Revision as of 21:02, 15 June 2017
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	</math>		</math>

			===Code Implementations===

			The implementations of the above formulas in Java:

			<pre>
			/** Formula for the sum of the square of integers up to N. */
			public static int sum_of_squares(int n) {
			int result = (n(n+1)(2*n+1))/6;
			return result;
			}

			/** Formula for the sum of the integers up to N, squared. */
			public static int square_of_sum(int n) {
			int result = (n*(n+1))/2;
			result *= result;
			return result;
			}
			</pre>

	==Flags==		==Flags==

Admin at 21:01, 15 June 2017

2017-06-15T21:01:47Z

← Older revision		Revision as of 21:01, 15 June 2017
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	\sum_{i=1}^{n} i^2 = \dfrac{n(n+1)(2n+1)}{6}		\sum_{i=1}^{n} i^2 = \dfrac{n(n+1)(2n+1)}{6}
	</math>		</math>



			==Flags==


			{{ProjectEulerFlag}}
			[[Category:Math]]
			[[Category:Squares]]
			[[Category:Combinatorics]]

Admin: Created page with "==Project Euler Problem 6== The sum of the squares of the first 10 integers is x. The square of the sum of the first 10 integers is y. Their difference is y-x. Find this f..."

2017-06-15T21:01:11Z

Created page with "==Project Euler Problem 6== The sum of the squares of the first 10 integers is x. The square of the sum of the first 10 integers is y. Their difference is y-x. Find this f..."

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==Project Euler Problem 6==

The sum of the squares of the first 10 integers is x.

The square of the sum of the first 10 integers is y.

Their difference is y-x.

Find this for the first 100 integers.

Project Euler Link: https://projecteuler.net/problem=6

Link to solution, git.charlesreid1.com: https://charlesreid1.com:3000/cs/euler/src/master/Problem006.java

Principle: this utilizes two summations that are useful to know off the top of your head. If you do, it makes this an O(1) problem. If not, it makes it an O(N) problem.

The two summations are:

<math>
\sum_{i=1}^{n} i = \dfrac{n(n+1)}{2}
</math>

and

<math>
\sum_{i=1}^{n} i^2 = \dfrac{n(n+1)(2n+1)}{6}
</math>