User:Viliusr/Tutorials

Tutorials - if you found those useful, please say so about it in my talk page! :)

Noob friendly - everything explained like to a noob :3!

^
A number multiplied * of itself a number of times.

First number says what number.

Second number says how many times.

Examples:
 * 3^5 = 3*3*3*3*3
 * 8^7 = 8*8*8*8*8*8*8
 * 4^2 = 4*4

When there are three numbers, you just put the last two in brackets and count them first, then sum it and then sum it all.

Examples:
 * 3^5^2 =
 * 3^(5^2) =
 * 3^(5*5) =
 * 3^25 =
 * 3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3
 * 8^7^4 =
 * 8^(7^4) =
 * 8^(7*7*7*7) =
 * 8^2401 =
 * 8*8*8*8*8*8*8*8*8*8*8*............(2401 times)
 * 4^2^1 =
 * 4^(2^1) =
 * 4^2 =
 * 4*4

Same with when there are four numbers or more.

Example:
 * 8^3^2^5^6 =
 * 8^(3^(2^(5^6))) =
 * 8^(3^(2^(15625))) =
 * 8^(3^(2^15625)) =
 * 8^(3^([a really big number]))

If there is more than one ^ and there is no numbers between them, the first number is the number used, and the second number is how many of it to do. The number of ^ lower one, example if there were three ^^^, then there will be two ^^.

Examples:
 * 3^^^3 =
 * 3^^3^^3 =
 * 3^^(3^^3) =
 * 3^^(3^3^3) =
 * 3^^(3^27) =
 * 3^^(3^27) =
 * 3^^7625597484987 =
 * 3^3^3^3^3^3^3^3^3^3^....... (7625597484987 times)
 * 2^^^^7 =
 * 2^^^2^^^2^^^2^^^2^^^2^^^2 =
 * 2^^^(2^^^(2^^^(2^^^(2^^^(2^^^2))))) =
 * 2^^^(2^^^(2^^^(2^^^(2^^^(2^^2))))) =
 * 2^^^(2^^^(2^^^(2^^^(2^^^(2^2))))) =
 * 2^^^(2^^^(2^^^(2^^^(2^^^(4))))) =
 * 2^^^(2^^^(2^^^(2^^^(2^^^4)))) =
 * 2^^^(2^^^(2^^^(2^^^(2^^2^^2^^2)))) =
 * 2^^^(2^^^(2^^^(2^^^(2^^(2^^(2^^2)))))) =
 * 2^^^(2^^^(2^^^(2^^^(2^^(2^^(2^2)))))) =
 * 2^^^(2^^^(2^^^(2^^^(2^^(2^^(4)))))) =
 * 2^^^(2^^^(2^^^(2^^^(2^^(2^^4))))) =
 * 2^^^(2^^^(2^^^(2^^^(2^^(2^2^2^2))))) =
 * 2^^^(2^^^(2^^^(2^^^(2^^(2^(2^(2^2))))))) =
 * 2^^^(2^^^(2^^^(2^^^(2^^(2^(2^(4))))))) =
 * 2^^^(2^^^(2^^^(2^^^(2^^(2^(2^4)))))) =
 * 2^^^(2^^^(2^^^(2^^^(2^^(2^(16)))))) =
 * 2^^^(2^^^(2^^^(2^^^(2^^(2^16))))) =
 * 2^^^(2^^^(2^^^(2^^^(2^^(65536))))) =
 * 2^^^(2^^^(2^^^(2^^^(2^^65536)))) =
 * 2^^^(2^^^(2^^^(2^^^(2^2^2^2^2^2^2^2^2^2^........ (65536 times))))) =

->
If there are two numbers, just change the symbol.

Example:
 * 3->2 = 3^2

If there are three numbers, the first number is the first number, the second is the second number, and the third is how many ^ are between the numbers.

Example:
 * 3->2->4 = 3^^^^2
 * 7->5->6 = 7^^^^^^5

If there is a 1, we cut off the line where the 1 is and all numbers after it.

Examples:
 * 4->9->7->1 = 4->9->7
 * 3->4->1->6 = 3->4

If there are 4 numbers,


 * a->b->c->d

we bracket the third number, delete it,


 * a->b->{}->d

copy the line which is out of the brackets,


 * a->b->{a->b->c->d}->d

then lower the 3 number (c) by one and the last number (d) out of brackets


 * a->b->{a->b->c-1->d}->d-1

and so until we reach 1 and we can cut it off to make it not to have 4 numbers.

Examples: and so on... and so on...
 * 2->2->2->2 =
 * 2->2->(2->2->2->2)->2 =
 * 2->2->(2->2->1->2)->1 =
 * 2->2->(2->2) =
 * 2->2->(2->(2->2)) =
 * 2->2->(2^2) =
 * 2->2->(4) = 2->(2->4) =
 * 2->(2^2^2^2) =
 * 2->(65536) =
 * 2->65536 =
 * 2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^...... (65536 times)
 * 3->3->2->2 =
 * 3->3->(3->3->2->2)->2 =
 * 3->3->(3->3->1->2)->1 =
 * 3->3->(3->3)->1 =
 * 3->3->(3^3) =
 * 3->3->(27) =
 * 3->3->27 =
 * 3^^^^^^^^^^^^^^^^^^^^^^^^^^^3 =
 * 3^^^^^^^^^^^^^^^^^^^^^^^^^^3^^^^^^^^^^^^^^^^^^^^^^^^^^3 =
 * 3^^^^^^^^^^^^^^^^^^^^^^^^^^(3^^^^^^^^^^^^^^^^^^^^^^^^^^3) =
 * 3^^^^^^^^^^^^^^^^^^^^^^^^^^(3^^^^^^^^^^^^^^^^^^^^^^^^^3^^^^^^^^^^^^^^^^^^^^^^^^^3) =
 * 3^^^^^^^^^^^^^^^^^^^^^^^^^^(3^^^^^^^^^^^^^^^^^^^^^^^^^(3^^^^^^^^^^^^^^^^^^^^^^^^^3)) =
 * 3^^^^^^^^^^^^^^^^^^^^^^^^^^(3^^^^^^^^^^^^^^^^^^^^^^^^^(3^^^^^^^^^^^^^^^^^^^^^^^^3^^^^^^^^^^^^^^^^^^^^^^^^3)) =
 * 3^^^^^^^^^^^^^^^^^^^^^^^^^^(3^^^^^^^^^^^^^^^^^^^^^^^^^(3^^^^^^^^^^^^^^^^^^^^^^^^(3^^^^^^^^^^^^^^^^^^^^^^^^3))) =
 * 3^^^^^^^^^^^^^^^^^^^^^^^^^^(3^^^^^^^^^^^^^^^^^^^^^^^^^(3^^^^^^^^^^^^^^^^^^^^^^^^(3^^^^^^^^^^^^^^^^^^^^^^^3^^^^^^^^^^^^^^^^^^^^^^^3))) =
 * 3^^^^^^^^^^^^^^^^^^^^^^^^^^(3^^^^^^^^^^^^^^^^^^^^^^^^^(3^^^^^^^^^^^^^^^^^^^^^^^^(3^^^^^^^^^^^^^^^^^^^^^^^(3^^^^^^^^^^^^^^^^^^^^^^^3))))
 * 2->2->3->3 =
 * 2->2->(2->2->2->3)->2 =
 * 2->2->(2->2->(2->2->1->3)->2)->2 =
 * 2->2->(2->2->(2->2)->2)->2 =
 * 2->2->(2->2->(2^2)->2)->2 =
 * 2->2->(2->2->(4)->2)->2 =
 * 2->2->(2->2->4->2)->2 =
 * 2->2->(2->2->(2->2->3->2)->1)->2 =
 * 2->2->(2->2->(2->2->(2->2->2->2)->1)->1)->2 =
 * 2->2->(2->2->(2->2->(2->2->(2->2->1->2)->1)->1)->1)->2 =
 * 2->2->(2->2->(2->2->(2->2->(2->2)->1)->1)->1)->2 =
 * 2->2->(2->2->(2->2->(2->2->(2^2)->1)->1)->1)->2 =
 * 2->2->(2->2->(2->2->(2->2->(4)->1)->1)->1)->2 =
 * 2->2->(2->2->(2->2->(2->2->4->1)->1)->1)->2 =
 * 2->2->(2->2->(2->2->(2->2->4)->1)->1)->2 =
 * 2->2->(2->2->(2->2->(2^^^^2)->1)->1)->2 =
 * 2->2->(2->2->(2->2->(2^^^2)->1)->1)->2 =
 * 2->2->(2->2->(2->2->(2^^2)->1)->1)->2 =
 * 2->2->(2->2->(2->2->(2^2)->1)->1)->2 =
 * 2->2->(2->2->(2->2->(4)->1)->1)->2 =
 * 2->2->(2->2->(2->2->4->1)->1)->2 =
 * 2->2->(2->2->(2->2->4)->1)->2 =
 * 2->2->(2->2->(2^^^^2)->1)->2 =
 * 2->2->(2->2->(2^^^2)->1)->2 =
 * 2->2->(2->2->(2^^2)->1)->2 =
 * 2->2->(2->2->(2^2)->1)->2 =
 * 2->2->(2->2->(4)->1)->2 =
 * 2->2->(2->2->4->1)->2 =
 * 2->2->(2->2->4)->2 =
 * 2->2->(2^^^^2)->2 =
 * 2->2->(2^^^2)->2 =
 * 2->2->(2^^2)->2 =
 * 2->2->(2^2)->2 =
 * 2->2->(4)->2 =
 * 2->2->4->2 =
 * 2->2->(2->2->3->2)->1 =
 * 2->2->(2->2->(2->2->2->2)->1)->1 =
 * 2->2->(2->2->(2->2->(2->2->1->2)->1)->1)->1 =
 * 2->2->(2->2->(2->2->(2->2)->1)->1)->1 =
 * 2->2->(2->2->(2->2->(2^2)->1)->1)->1 =
 * 2->2->(2->2->(2->2->(4)->1)->1)->1 =
 * 2->2->(2->2->(2->2->4->1)->1)->1 =
 * 2->2->(2->2->(2->2->4)->1)->1 =
 * 2->2->(2->2->(2^^^^2)->1)->1 =
 * 2->2->(2->2->(2^^^2)->1)->1 =
 * 2->2->(2->2->(2^^2)->1)->1 =
 * 2->2->(2->2->(2^2)->1)->1 =
 * 2->2->(2->2->(4)->1)->1 =
 * 2->2->(2->2->4->1)->1 =
 * 2->2->(2->2->4)->1 =
 * 2->2->(2^^^^2)->1 =
 * 2->2->(2^^^2)->1 =
 * 2->2->(2^^2)->1 =
 * 2->2->(2^2)->1 =
 * 2->2->(4)->1 =
 * 2->2->4->1 =
 * 2->2->4 =
 * 2^^^^2 =
 * 2^^^2 =
 * 2^^2 =
 * 2^2 =
 * 4
 * 3->4->5->6 =
 * 3->4->(3->4->4->6)->5 =
 * 3->4->(3->4->(3->4->3->6)->5)->5 =
 * 3->4->(3->4->(3->4->(3->4->2->6)->5)->5)->5 =
 * 3->4->(3->4->(3->4->(3->4->(3->4->1->6)->5)->5)->5)->5 =
 * 3->4->(3->4->(3->4->(3->4->(3->4)->5)->5)->5)->5 =
 * 3->4->(3->4->(3->4->(3->4->(3^4)->5)->5)->5)->5 =
 * 3->4->(3->4->(3->4->(3->4->(81)->5)->5)->5)->5 =
 * 3->4->(3->4->(3->4->(3->4->81->5)->5)->5)->5 =
 * 3->4->(3->4->(3->4->(3->4->(3->4->80->5)->4)->5)->5)->5 =
 * 3->4->(3->4->(3->4->(3->4->(3->4->(3->4->80->5)->4)->4)->5)->5)->5 =

{}
Numbers are in {} and seperated by commas.

If there is one number, the number is the same number, nothing changes...


 * {a} = a
 * {2} = 2

If there are two numbers, the action just changes to ^.


 * {a,b} = a^b
 * {2,3} = 2^3

If there are three numbers, the action changes to ->.


 * {a,b,c} = a->b->c
 * {2,3,4} = 2->3->4

If there is a 1, like with ->, the chain cuts off and all numbers after it.


 * {a,1,c,d} = {a} = a
 * {a,b,c,1} = {a,b,c} = a->b->c

However if the third number (c) is 1, it gets difficult.


 * {a,b,1,d}

The fourth number (d) gets minused by 1. Then instead of the third number (c) we put {}, and the chain outside the brackets are pasted, then the second number (b) gets minused by 1 inside the brackets. The b outside the brackets turns into same as the first number (a).


 * {a,b,1,d} =
 * {a,a,{a,b-1,1,d},d-1}

We do this until the second number turns to 1 and we can cut off.


 * {2,3,1,5} =
 * {2,2,{2,2,1,5},4} =
 * {2,2,{2,2,{2,1,1,5},4},4} =
 * {2,2,{2,2,{2},4},4} =
 * {2,2,{2,2,2,4},4}

Afer this, we get {2,2,2,4}, neither b nor c nor d is 1, so we have to follow another rule when there are 4 numbers and none of them are 1.

The rule is that instead of b, we bracket and paste the thing outside brackets, c outside brackets and b inside brackets get minused by one.


 * {a,b,c,d} = {a,{a,b-1,c,d},c-1,d}


 * {2,3,1,5} =
 * {2,2,{2,2,1,5},4} =
 * {2,2,{2,2,{2,1,1,5},4},4} =
 * {2,2,{2,2,{2},4},4} =
 * {2,2,{2,2,2,4},4} =
 * {2,2,{2,{2,1,2,4},1,4},4} =
 * {2,2,{2,{2},1,4},4} =
 * {2,2,{2,2,1,4},4} =

(now we have to use when c is 1 rule again)


 * {2,2,{2,2,{2,1,1,4},3},4} =
 * {2,2,{2,2,{2},3},4} =
 * {2,2,{2,2,2,3},4} =
 * {2,2,{2,{2,1,2,3},1,3},4} =
 * {2,2,{2,{2},1,3},4} =
 * {2,2,{2,2,1,3},4} =
 * {2,2,{2,2,{2,1,1,3},2},4} =
 * {2,2,{2,2,{2},2},4} =
 * {2,2,{2,2,2,2},4} =
 * {2,2,{2,{2,1,2,2},1,2},4} =
 * {2,2,{2,{2},1,2},4} =
 * {2,2,{2,2,1,2},4} =
 * {2,2,{2,2,{2,1,1,2},1},4} =
 * {2,2,{2,2,{2},1},4} =
 * {2,2,{2,2,2,1},4} =
 * {2,2,{2,2,2},4} =
 * {2,2,{2->2->2},4} =
 * {2,2,{2^^2},4} =
 * {2,2,{2^2},4} =
 * {2,2,{4},4} =
 * {2,2,4,4} =
 * {2,{2,1,4,4},3,4} =
 * {2,{2},3,4} =
 * {2,2,3,4} =
 * {2,{2,1,3,4},2,4} =
 * {2,{2},2,4} =
 * {2,2,2,4} =
 * {2,{2,1,2,4},1,4} =
 * {2,{2},1,4} =
 * {2,2,1,4} =
 * {2,2} =
 * 2^2 =
 * 4

Yes, that was very very very long, just to get 4...

Now, what about when there are 4 numbers and none of them are 1?

{a,b,c,d,}

We bracked the second number, and put the stuff that is outside the brackets.


 * {a,{a,b,c,d},c,d}

Second number inside the second number's brackets' gets minused by 1, as well as third number outside the brackets.

{a,{a,b−1,c,d},c−1,d}

So the rule is:

{a,b,c,d,} = {a,{a,b−1,c,d},c−1,d}

Example:
 * {2,2,2,2} =
 * {2,{2,2,2,2},2,2} =
 * {2,{2,1,2,2},1,2} =
 * {2,{2},1,2} =
 * {2,2,1,2} (Third number is now 1, now we use the rule when the third number is 1.) =
 * {2,2,{2,1,1,2},1} =
 * {2,2,{2},1} =
 * {2,2,2,1} =
 * {2,2,2} =
 * 2->2->2 =
 * 2->2->2 =
 * 2^^2 =
 * 2^2 =
 * 4