Four Fours/Table of 4s - Revision history

Unknown user: /* One 4 */

2025-04-04T03:15:29Z

One 4

2019-03-10T03:18:52Z

One 4

← Older revision		Revision as of 03:18, 10 March 2019
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	\dfrac{1}{24} = \dfrac{1}{4!}		\dfrac{1}{24} = \dfrac{1}{4!}
	</math>		</math>

			but these can't appear with 1 in the denominator.

	Could possibly add constants (harmonic number), possibly special functions.		Could possibly add constants (harmonic number), possibly special functions.

2019-03-09T22:05:19Z

Three 4s

← Older revision		Revision as of 22:05, 9 March 2019
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	where <math>n</math> is any number expressible with two 4's.		where <math>n</math> is any number expressible with two 4's.

			Once we can add three 4's, we can start to write expressions like

			<math>
			\dfrac{ \ln{P} }{ \ln{Q} }
			</math>

			where P and Q are any expressions involving 1 or 2 fours. If we choose carefully, P and Q will have the same base and different exponents, so we can start to combine integer powers to obtain new integers. This trick will get us out of at least a few jams when constructing the integers from 1 to 100 using only four fours.

	<math>		<math>

2019-03-09T22:02:48Z

Three 4s

← Older revision		Revision as of 22:02, 9 March 2019
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	==Three 4s==		==Three 4s==

	These lists blow up pretty fast... as you can see, focusing on using a smaller number of 4s can force you to be creative. This makes it possible to combine 4 4's beyond the integers from 1 to 20, and keep on going...		These lists blow up pretty fast... as you can see, focusing on using a smaller number of 4s can force you to be creative. This makes it possible to combine 4 4's beyond the integers from 1 to 20, and keep on going.

			One useful template for representing powers of 2 is:

	<math>		<math>

2019-03-09T22:02:02Z

Two 4s

← Older revision		Revision as of 22:02, 9 March 2019
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	281,474,976,710,656 = 4^{4!}		281,474,976,710,656 = 4^{4!}
	</math>		</math>

			<math>
			1,333,735,776,850,284,124,449,081,472,843,776 = {4!}^{4!}
			</math>

			(For those keeping score at home, that's 1 decillion 333 nonillion 735 octillion 776 septillion 850 sextillion 284 quintillion 124 quadrillion 449 trillion 81 billion 472 million 843 thousand 776)

	==Three 4s==		==Three 4s==

2019-03-09T21:54:41Z

Two 4s

← Older revision		Revision as of 21:54, 9 March 2019
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	==Two 4s==		==Two 4s==

	Note: we aren't using fourth roots ~~anywhere~~, e.g., <math>\sqrt{2} = \sqrt[4]{4}</math>. Adding this would greatly expand the possibilities.		Note: we aren't using fourth roots or one-quarter powers very much, e.g., <math>\sqrt{2} = \sqrt[4]{4} = 4^{\frac{1}{4}}</math>. Adding this would greatly expand the possibilities.

	<math>		<math>

2019-03-09T21:54:01Z

Two 4s

← Older revision		Revision as of 21:54, 9 March 2019
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	==Two 4s==		==Two 4s==

			Note: we aren't using fourth roots anywhere, e.g., <math>\sqrt{2} = \sqrt[4]{4}</math>. Adding this would greatly expand the possibilities.

	<math>		<math>

2018-01-14T14:49:36Z

Three 4s

@@ Line 340: / Line 340: @@
 <math>
 = (\sqrt{4})^{4 + \sqrt{4}}
 </math>
@@ Line 345: / Line 367: @@
 = (4F)_{4 \cdot 4}
 </math>
 <math>

2018-01-14T14:48:21Z

Three 4s

← Older revision		Revision as of 14:48, 14 January 2018
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	64 = (\sqrt{4})^{4 + \sqrt{4}}		64 = (\sqrt{4})^{4 + \sqrt{4}}
	</math>		</math>

			<math>
			79 = (4F)_{4 \cdot 4}
			</math>

			(That is, 79 is 4F in hexidecimal, or base 16 = 4 * 4)

	<math>		<math>

2018-01-14T12:55:39Z

Two 4s