The Puzzler's Guide/Number/Special Number - Revision history

Doomsdayred at 11:52, 13 April 2007

2007-04-13T11:52:29Z

← Older revision		Revision as of 11:52, 13 April 2007
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	This indicates the sequence is a sequence of square numbers (all the numbers the same) but a the differences are '''2 times greater than normal''' (2) the square sequence has been '''multiplied by 2'''.		This indicates the sequence is a sequence of square numbers (all the numbers the same) but a the differences are '''2 times greater than normal''' (2) the square sequence has been '''multiplied by 2'''.

			== Cube numbers ==

	== Fibonacci numbers ==		== Fibonacci numbers ==

Arcysparky at 09:06, 7 April 2007

2007-04-07T09:06:55Z

← Older revision		Revision as of 09:06, 7 April 2007
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	This one's a complicated one, but basically each number in the sequence is defined by the sum of the previous two numbers in the sequence, with the first two numbers being 0 and 1. So following from that:		This one's a complicated one, but basically each number in the sequence is defined by the sum of the previous two numbers in the sequence, with the first two numbers being 0 and 1. So following from that:

	0		'''0'''
	1
	0 + 1 = 1		'''1'''
	1 + 1 = 2
	1 + 2 = 3		0 + 1 = '''1'''
	2 + 3 = 5... etc.
			1 + 1 = '''2'''

			1 + 2 = '''3'''

			2 + 3 = '''5'''... etc.


	If you are given more than three of the numbers in the seqence (which you undoubtedly will, if you are being asked to continue it) then it's simply a matter of adding the first two numbers and seeing if they sum to the third, if they do, then it is likely they are part of the fibonacci sequence.		If you are given more than three of the numbers in the seqence (which you undoubtedly will, if you are being asked to continue it) then it's simply a matter of adding the first two numbers and seeing if they sum to the third, if they do, then it is likely they are part of the fibonacci sequence.

Arcysparky: added short intro, added to fibonacci number section

2007-04-07T09:05:00Z

added short intro, added to fibonacci number section

← Older revision		Revision as of 09:05, 7 April 2007
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	Number Sequences feature regularly in ARG's and this section will detail some of the famous sequences that may occur in a puzzle		Number Sequences feature regularly in ARG's and this section will detail some of the famous sequences that may occur in a puzzle. It's important to learn a few of the most common sequences such as the first few fibonacci and square numbers, first few digits of Pi and Phi as they are not only very useful numbers when dealing with mathematics but also a lot of puzzle setters like to sneak them in here and there to see if you are paying attention.

	== Square Numbers ==		== Square Numbers ==

	1, 4, 9, 16, 25, 36, 49, 64, 81, 100		1, 4, 9, 16, 25, 36, 49, 64, 81, 100...

	=== What are they? ===		=== What are they? ===
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	=== Exceptions ===		=== Exceptions ===

	Sometimes the entire square sequence has been multiplied by a number. In this case the difference of the differences will be ~~multiplies~~ by that number		Sometimes the entire square sequence has been multiplied by a number. In this case the difference of the differences will be multiples by that number

	==== Example ====		==== Example ====
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	The difference between the numbers above are: '''4, 4, 4'''		The difference between the numbers above are: '''4, 4, 4'''

	This indicates the sequence is a sequence of square numbers (all the numbers the same) but a the differences are '''2 times greater than normal''' (2) the square sequence has been '''multiplied by 2'''		This indicates the sequence is a sequence of square numbers (all the numbers the same) but a the differences are '''2 times greater than normal''' (2) the square sequence has been '''multiplied by 2'''.
	~~== Cube numbers ==~~

	== Fibonacci ~~number~~ ==		== Fibonacci numbers ==

			0, 1, 1, 2, 3, 5, 8, 13, 21, 34...

			===What Are They?===

			This one's a complicated one, but basically each number in the sequence is defined by the sum of the previous two numbers in the sequence, with the first two numbers being 0 and 1. So following from that:

			0
			1
			0 + 1 = 1
			1 + 1 = 2
			1 + 2 = 3
			2 + 3 = 5... etc.

			If you are given more than three of the numbers in the seqence (which you undoubtedly will, if you are being asked to continue it) then it's simply a matter of adding the first two numbers and seeing if they sum to the third, if they do, then it is likely they are part of the fibonacci sequence.
	== Pi ==		== Pi ==

	== Phi / The Golden Ratio ==		== Phi / The Golden Ratio ==

Scribe: + Phi

2007-04-03T14:36:04Z

+ Phi

← Older revision		Revision as of 14:36, 3 April 2007
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	== Pi ==		== Pi ==

			== Phi / The Golden Ratio ==

Doomsdayred at 12:30, 3 April 2007

2007-04-03T12:30:19Z

← Older revision		Revision as of 12:30, 3 April 2007
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	This indicates the sequence is a sequence of square numbers (all the numbers the same) but a the differences are '''2 times greater than normal''' (2) the square sequence has been '''multiplied by 2'''		This indicates the sequence is a sequence of square numbers (all the numbers the same) but a the differences are '''2 times greater than normal''' (2) the square sequence has been '''multiplied by 2'''
			== Cube numbers ==

			== Fibonacci number ==

			== Pi ==

Tornan steel: /* Square Number */

2007-04-02T10:17:52Z

Square Number

← Older revision		Revision as of 10:17, 2 April 2007
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	Number Sequences feature regularly in ARG's and this section will detail some of the famous sequences that may occur in a puzzle		Number Sequences feature regularly in ARG's and this section will detail some of the famous sequences that may occur in a puzzle

	== Square ~~Number~~ ==		== Square Numbers ==

	1, 4, 9, 16, 25, 36, 49, 64, 81, 100		1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Tornan steel: Inofrmation about square numbers added..... tired now but may add more later ie. square + 1, cube, triangle, fibanachi, primes etc.

2007-04-02T10:17:27Z

Inofrmation about square numbers added..... tired now but may add more later ie. square + 1, cube, triangle, fibanachi, primes etc.

New page

Number Sequences feature regularly in ARG's and this section will detail some of the famous sequences that may occur in a puzzle

== Square Number ==

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

=== What are they? ===

'''Square numbers''' are numbers that are the result of squaring a particular number (multiplying it by itself). For example 36 is a square number because it is the result of 6 x 6. In a square number sequence the numbers created are usually consecutive - the example above is formed by the sequence 1 squared, 2 squared, 3 squared and so on all the way up to 10 squared.

=== Tell-tale signs ===

An easy way to tell if you are dealing with square numbers is to find the difference between the sequence of numbers. If the difference of these differences are all equal then you have a sequence of square numbers. Normal square numbers produce a sequence of 2's

==== Example ====

You are given the sequence: '''121, 144, 169, 196, 225'''

The difference between the numbers in the original sequence are: '''23, 25, 27, 29'''

The difference between the numbers above are: '''2, 2, 2'''

This indicates that the sequence is a sequence of square numbers as the difference of the differences are all 2

=== Exceptions ===

Sometimes the entire square sequence has been multiplied by a number. In this case the difference of the differences will be multiplies by that number

==== Example ====

You are given the sequence: '''2, 8, 18, 32, 50'''

The difference between the numbers in the original sequence are: '''6, 10, 14, 18'''

The difference between the numbers above are: '''4, 4, 4'''

This indicates the sequence is a sequence of square numbers (all the numbers the same) but a the differences are '''2 times greater than normal''' (2) the square sequence has been '''multiplied by 2'''