*There is no need to be a scary monster with 31 fingers/legs to count to 31 you can actually do it using only 5 fingers and the power of mathematics.*


<center>
![centipede-562036_640.jpg](https://cdn.steemitimages.com/DQmdnA2YKbPMrjQiLp8SQtvxepGbaQs8jHtYkEoTfcEsZXa/centipede-562036_640.jpg)
</center>


Methods that come natural to us are usually not the most efficient/best. This also concerns counting with the fingers on your hand(s).   


## Counting to 5 
Most of us will count from 1 to  5 in the following way:
<center>
![output_Lsg3qi.gif](https://cdn.steemitimages.com/DQmNgbGMy5hg4BMNksnchVkfKJBXBrksHsbag7m6eUWkqeg/output_Lsg3qi.gif)
</center>
From a symbolic point of view each finger represents the numer one, adding those number ones, or equivalently, those number of fingers, will give you the number represented by my hand. This is an easy to understand rule. But it is not very efficient. For example, alternatively, I could count to 5 in the following way: 

<center>
![output_dVCucK.gif](https://cdn.steemitimages.com/DQmdYFg3AksK7sD66i1red5QAxh6hP31qbJ3B1JbAyYXaDs/output_dVCucK.gif)
</center>

It might look a bit strange but the idea is exactly the same as in the first gif. First I lift one finger, then two fingers, etc.  The problem with this hand counting method is that a number can be represented in several ways by your hand. For example, the number 1 can be represented by lifting any one of your five fingers. Similar case is true for 2,3,4. The exception is 5 since you only have five fingers on one hand. So there are no fingers to pick from.  


## Counting to 31:

To take counting to the next level you can define a counting method where a specific configuration of lifted fingers corresponds to a single number. In this way you can count all the way to 31: 

<center>
![output_ePSlei.gif](https://cdn.steemitimages.com/DQmPNHfVnEoB9UGeDAixveipbroaLJd3iVfpHagLoTwM3Mr/output_ePSlei.gif)
</center>

**A bit of math:** You have five fingers which have two states, lifted or not-lifted, so there are 2<sup>5</sup>=32 combination possible. However,  since we don't consider 0 we end up with 32-1=31 possible states.   

## Converting configurations back to to numbers.

Memorising stuff is a drag. For this new way of counting we need to memorise  31 configurations so that is not nice. There is actually a pretty nice way to convert the configurations back to numbers through the magic of mathematics. I will represent a finger state by 0 or 1, where 0 corresponds to an unlifted finger and 1 corresponds to a lifted finger. A whole hand will then be represented by 5 of these 0s and 1s, where the first number represent your first finger, which is your thumb, the second number represents your second finger, etc. So for example, 11111 is a whole hand and 00001 is only thumbs up.   An expression in 0s and 1s seems familiar from all those  hacker movies. Yes indeed. We have been counting like a computer. The last gif is actually the same as counting in binary, which is nothing else then counting with two different states. 

**WARNING BIT OF MATH AHEAD TO EXPLAIN THE CONVERSION RULE:** Let  a<sub>i</sub> be 0 if the i-th finger is not-lifted and 1 if the i-th finger is lifted (where i=1,2,3,4,5) then  a hand configuration a<sub>5</sub>   a<sub>4</sub>   a<sub>3</sub>   a<sub>2</sub>   a<sub>1</sub> corresponds to the number

<center>
      a<sub>1</sub>  + a<sub>2 </sub> x  2  + a<sub>3</sub> x  4  + a<sub>4</sub> x  8 + a<sub>5</sub> x  16, 
</center>

or equivalently, 

<center>
  a<sub>1</sub> x  2 <sup>0</sup> + a<sub>2</sub>  x 2 <sup>1</sup> + a<sub>3</sub>  x 2 <sup>2</sup> + a<sub>4</sub>  x  2 <sup>3</sup> + a<sub>5</sub> x  2 <sup>4</sup> .
</center>

For example, 00011 corresponds to 1+2=3, and indeed it is the third image in the gif (the starting image is 00001) and 11111 corresponds to 1+2+4+8+16=31, which is the last image so it has to be 31.


 ## In conclusion  
01000010-01101001-01101110-01100001-01110010-01111001-00100000-01101001-01110011-00100000-01100001-1110111-01100101-01110011-01101111-01101101-01100101-00100000-01100010-01101001-01110100-01100011-01101000-01100101-01110011 

1 steemitbasicincome for the first to translate this message :D

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**Source:** Top image from [Pixabay - CC0 - inactive account](https://pixabay.com/en/centipede-insect-macro-arthropod-562036/)


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<h2> Merchandise :D </h2><br />
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<p><img src="https://steemitimages.com/0x0/https://cdn.steemitimages.com/DQmdwbunfcePxAncstQN21fDefS97B3ofRrAABmi29zD26B/g7592-1-9.png" alt="2018-06-07 (2).png" /><br />
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