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Leftunknown 19 June
1

## Order function

Let's consider a function O(a), where 'a' is an array of numbers. The function then swaps two numbers at a time, using the most efficient method, ordering them from smallest to largest and outputs the amount of swaps it took.

O(5,3) = 1         (5,3 --> 3,5)

O(2,0,1) = 2      (2,0,1 --> 1,0,2 --> 0,1,2)

If we want to know what the largest output of a 3 element O(a,b,c) with a, b and c being equal to or smaller than n, we can write it as

or without tex, simply as O[n](a,b,c).

O[0](x elements) = 0 (trivial)

O[n](a) = 0 (trivial)

O[x](x elements)

x
1
2
3
4
5
=
0
1
2
3
4
O(x)

0

1

0,1

1,0

2,0,1

1,2,0

3,0,1,2

2,0,3,1

+ 6 more

...

to be continued

Leftunknown 14 June
0

## Dice and Coins

Bellow are the odds of guessing the outcomes of x dice rolls and n coin flips, in order of chance:

(combinations of dice and coins go up to 10:10, alone chances go up to 1 trillion)

1 coin flip - 1 in 2

2 coin flips - 1 in 4

1 dice roll - 1 in 6

3 coin flips - 1 in 8

1 coin flip, 1 dice roll - 1 in 12

4 coin flips - 1 in 16

2 coin flips, 1 dice roll - 1 in 24

5 coin flips - 1 in 32

2 dice rolls - 1 in 36

3 coin flips, 1 dice roll - 1 in 48

6 coin flips - 1 in 64

1 coin flip, 2 dice rolls - 1 in 72

4 coin flips, 1 dice roll - 1 in 96

7 coin flips - 1 in 128

2 coin flips, 2 dice rolls - 1 in 144

5 coin flips, 1 dice roll - 1 in 192

3 dice rolls - 1 in 216

8 coin flips - 1 in 256

3 coin flips, 2 dice rolls - 1 in 288

6 coin flips, 1 dice roll - 1 in 384

1 coin fli…

Leftunknown 28 January
2

## Unusual time units

Planck time - 1 lp Kilo planck time - 1000 lp Mega planck time - 1,000,000 lp Giga planck time - 1,000,000,000 lp Tera planck time - 1,000,000,000,000 lp Peta planck time - 1,000,000,000,000,000 lp Exa planck time - 1,000,000,000,000,000,000 lp

Yoctosecond - 539,100,000,000,000,000,000 lp

Zetta planck time - 53.91 yoctoseconds

Yoctominute - 60 yoctoseconds

Zeptosecond - 1000 yoctoseconds

Yoctohour - 3 zaptoseconds 600 yoctoseconds

Yotta planck time - 53.91 zeptoseconds

Zeptominute - 60 zeptoseconds

Yoctoday - 86 zeptoseconds 400 yoctoseconds

Yoctoweek - 604 zeptoseconds 8 yoctoseconds

Attosecond - 1000 zeptoseconds

Yoctomonth - 2 attoseconds 628 zeptoseconds

Zeptohour - 3 attoseconds 600 zaptoseconds

Yoctoyear - 31 attoseconds 540 zeptoseconds

Attominut…

Leftunknown 4 November 2019
1

## Omega power modulos

Thanks to the patterns of division, we can combine them and transfinite ordinals.

mod
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

0
0
1, 2
0
0
2, 4
1, 6
0
6*
0
5*
4, 8
12*
6, 8
5, 10
0
16*
7*
1
0
Leftunknown 2 November 2019
6