Five Fives - Revision history

Unknown user: /* Five Fives */

2025-04-09T17:29:43Z

Five Fives

← Older revision		Revision as of 17:29, 9 April 2025
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	(It is useful to build a table of different combinations of 5 to help out: [[Five Fives/Table of 5s]])		(It is useful to build a table of different combinations of 5 to help out: [[Five Fives/Table of 5s]])

	~~<math>~~
	~~1 = \left( \dfrac{ \ln{\left(\dfrac{5}{\sqrt{5}} \right) } }{ \ln{5} } \right) + \left( \dfrac{ \ln{\sqrt{5}} }{ \ln{5} } \right)~~
	~~</math>~~

	~~<math>~~
	~~1 = \dfrac{5 \times 5 \times 5 - 5}{5!}~~
	~~</math>~~

	<math>		<math>

2025-04-05T12:27:29Z

Five Fives

@@ Line 395: / Line 395: @@
 </math>
 <math>
@@ Line 402: / Line 411: @@
 </math>

2025-04-05T11:02:58Z

Five Fives

← Older revision		Revision as of 11:02, 5 April 2025
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	90 = \left( 5 + 5 \right) \left( 5 + 5 + \cos{\left( 5 \pi \right)} \right)		90 = \left( 5 + 5 \right) \left( 5 + 5 + \cos{\left( 5 \pi \right)} \right)
	</math>		</math>




	<math>		<math>

2025-04-05T11:02:28Z

Five Fives

← Older revision		Revision as of 11:02, 5 April 2025
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	</math>		</math>

			<math>
			83 = 5! - 5 - \left( \dfrac{ \ln{ 5 } }{ \ln{ \left( \sqrt{ 5 } \right) } } \right)
			</math>

			<math>
			84 = 5! - 5 \times 5 - \phi^{5} + \phi^{-5}
			</math>

			<math>
			84 = \dfrac{ \phi \left( \phi^{5+5} \right) - 55 }{ \phi } - 5
			</math>

			<math>
			85 = 5! - 5 \times 5 + 5 - 5!!
			</math>

			<math>
			86 = 5! - \dfrac{5!}{5} + 5 - 5!!
			</math>

			<math>
			87 = 55 + \left( \dfrac{ \ln{\left(5\right)} }{ \ln{\left(\sqrt{5}\right)} } \right)^{5}
			</math>

			<math>
			88 = \left( \phi^5 - \phi^{-5} \right) \left( \phi^5 - 5 \phi + 5 \right)
			</math>

			<math>
			89 = 5! - \dfrac{5!}{5} - 5 + \sin{ \left( 5 \pi \right)}
			</math>

			<math>
			90 = \left( 5 + 5 \right) \left( 5 + 5 + \cos{\left( 5 \pi \right)} \right)
			</math>

			<math>
			94 = \dfrac{ \phi \left( \phi^{5+5} \right) - 55 }{ \phi } + 5
			</math>

2025-04-05T10:56:40Z

Five Fives

← Older revision		Revision as of 10:56, 5 April 2025
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	<math>		<math>
	80 = \left( \phi^5 - 5 \phi + 5 \right) \left( 5 + 5 \right)		80 = \left( \phi^5 - 5 \phi + 5 \right) \left( 5 + 5 \right)
			</math>

			<math>
			81 = \left( \phi^{5} - 5 \phi \right)^{\left(5 - \frac{5}{5}\right)}
			</math>

			<math>
			82 = 5 \left( 5 + 5 \right) + \dfrac{ \ln{\left(5\right)} }{ \ln{ \left( \sqrt{ \sqrt{ \sqrt{ \sqrt{ \sqrt{ 5 } } } } } \right) } }
	</math>		</math>

2025-04-05T10:13:37Z

Five Fives

← Older revision		Revision as of 10:13, 5 April 2025
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	<math>		<math>
	41 = \phi^5 - ~~\dfrac{1}{~~\phi^5} + 5 \times 5 + 5		41 = \phi^5 - \phi^{-5} + 5 \times 5 + 5
	</math>		</math>

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	<math>		<math>
	44 = \left( 5 - \dfrac{5}{5} \right) \left( \phi^5 - ~~\dfrac{1}{~~\phi^5} \right)		44 = \left( 5 - \dfrac{5}{5} \right) \left( \phi^5 - \phi^{-5} \right)
	</math>		</math>

2025-04-04T21:23:59Z

Five Fives

← Older revision		Revision as of 21:23, 4 April 2025
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	73 = 5!! + \phi^{5} - 5 \phi + 55		73 = 5!! + \phi^{5} - 5 \phi + 55
	</math>		</math>

			<math>
			74 = 55 - 5 + \frac{5!}{5}
			</math>

			<math>
			75 = 5 \times 5 \times \log_{5}{\left(5! + 5\right)}
			</math>

			<math>
			76 = \dfrac{ \ln{\left(5\right)} }{ \ln{\left(\sqrt{ 5 }\right)} } \left( 5!! + \frac{5!}{5} - \ln{e} \right)
			</math>

			<math>
			77 = \left( \phi^5 - \phi^{-5} \right) \left( 5 + \dfrac{ \ln{\left( 5 \right)} }{ \ln{\left(\sqrt{ 5 }\right)} } \right)
			</math>

			<math>
			78 = \left( \phi^{5} - 5 \phi \right) \left( \phi^5 - \phi^{-5} + 5!! \right)
			</math>

			<math>
			79 = 5 \left( \phi^5 - \phi^{-5} \right) - \frac{5!}{5}
			</math>

			<math>
			80 = \left( \phi^5 - 5 \phi + 5 \right) \left( 5 + 5 \right)
			</math>

2025-04-04T18:06:14Z

Five Fives

2025-04-04T17:40:05Z

Five Fives

2025-04-04T16:22:55Z

Five Fives

← Older revision		Revision as of 16:22, 4 April 2025
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	Extending the idea of [[Four Fours]], where the intention is to write each integer as a combination of 4 4's (any mathematical symbol is allowed except for digits that are not 4), we can create the game of Five Fives.		Extending the idea of [[Four Fours]], where the intention is to write each integer as a combination of 4 4's (any mathematical symbol is allowed except for digits that are not 4), we can create the game of Five Fives.

	It is ~~also~~ useful to build a table of different combinations of 5 to help out: [[Five Fives/Table of 5s]]		Write each integer as a combination of 5 5's - no other numerical digits allowed.

			(It is useful to build a table of different combinations of 5 to help out: [[Five Fives/Table of 5s]])

	<math>		<math>
Line 307:		Line 309:
	<math>		<math>
	70 = 5 \times 5 \times 5 - 55		70 = 5 \times 5 \times 5 - 55
			</math>

			<math>
			71 = 5! - \frac{5!}{5} - \left( 5 \times 5 \right)
	</math>		</math>