a programming puzzle for learning how to contemplate counting in different bases.

zlorpian

Good afternoon fellow space travelers, thanks for coming along on this mission.  We still have about a week
before we arrive at New Zlorpia, so please return your stasis tubes to their original upright position and
prepare for your mission briefing.

We are going to be negotiating a trade agreement with the Zlorpians for their supply of Farkle seeds.  They
have a much different way of counting than we do, and I'm concerned that if we don't have a good way to
work with their number system, we'll be at a disadvantage in negotiations.  Let me explain:

The zlorpians have a single arm that comes out of their forehead, with a hand that has 3 fingers.  As a
result, our base-10 way of counting (based on our ten fingers) is as alien to them as their way is to us.

In some ways, their numbering system is similar to ours.

They represent the value zero with a single horizontal dash, and call it "zlorp".

The represent the number one with a single vertical dash, and it it "borp".

The number 2 is represented with 2 crossed lines, similar to our letter "X", and is called a "daborp".

Their number 3 is represented with a hash of three lines... the closest character on our keyboards is "#",
and is called a traborp.

And thats it.  They only represent the numbers 0-3.

BUT, just like us, they use columns to represent bigger numbers, 'rolling over' into the next column when
it gets too big.  Counting this way, their numbers look like this:


 -
 |
 X
 #
 |-
 ||
 |X
 |#
 X-
 X|
 XX
 X#
 #-
 #|
 #X
 ##
|--

Thankfully, they also have a really predictable way of naming each of the columns. When there is only one
column, the numbers are pronounced exactly as we define them above.  When there is a second column, called
the 'ity' column, they add the ending 'ity' to the name of the number.  So the number "||" is called
"Borpityborp".  The number "X#" is called "Daborpitytraborp".  By convention, if the number in the last
column is a zlorp, as in "|-", then they drop the zlorp, simply calling it "borpity".  This same pattern
holds for as many columns as we have learned to translate.

the rightmost column does not modify the number's name, as we have already seen.
the second-rightmost column is named "ity", as we have already seen.
The third-rightmost is named "en"
the fourth rightmost is named "onk"
the fifth rightmost is named "iffa"

Your job is to write 2 functions.  The first one should take a decimal number and convert it to a zlorpinumeral.
It should work like this:

>> zlorpinumeral(0)
=> "-"
>> zlorpinumeral(1)
=> "|"
>> zlorpinumeral(2)
=> "X"
>> zlorpinumeral(3)
=> "#"
>> zlorpinumeral(4)
=> "|-"
>> zlorpinumeral(5)
=> "||"
>> zlorpinumeral(15)
=> "##"
>> zlorpinumeral(16)
=> "|--"
>> zlorpinumeral(17)
=> "|-|"
>> zlorpinumeral(200)
=> "#-X-"
>> zlorpinumeral(221)
=> "#|#|"
>> zlorpinumeral(237)
=> "#X#|"
>> zlorpinumeral(1001)
=> "##XX|"


The second one should convert a decimal number to zlorpanese.  It should work like this:

?> zlorpanese(0)
=> "zlorp"
>> zlorpanese(1)
=> "borp"
>> zlorpanese(2)
=> "daborp"
>> zlorpanese(3)
=> "traborp"
>> zlorpanese(4)
=> "borpity"
>> zlorpanese(5)
=> "borpityborp"
>> zlorpanese(6)
=> "borpitydaborp"
>> zlorpanese(7)
=> "borpitytraborp"
>> zlorpanese(8)
=> "daborpity"
>> zlorpanese(9)
=> "daborpityborp"
>> zlorpanese(10)
=> "daborpitydaborp"
>> zlorpanese(15)
=> "traborpitytraborp"
>> zlorpanese(16)
=> "borpen"
>> zlorpanese(17)
=> "borpenborp"
>> zlorpanese(21)
=> "borpenborpityborp"
>> zlorpanese(200)
=> "traborponkdaborpity"
>> zlorpanese(221)
=> "traborponkborpentraborpityborp"
>> zlorpanese(237)
=> "traborponkdaborpentraborpityborp"
>> zlorpanese(1001)
=> "traborpiffatraborponkdaborpendaborpityborp"


If as a side effect you have functions that convert a zorpinumeral to a zorpanese string, please share them.
Extra points for the ability to convert a zorpinumeral back to a decimal number.

If anyone wants to convert these examples to some acceptance tests, I'd appreciate the contribution back.

https://gist.github.com/sbjustin/7009514

However, it looks like one of our translators is incorrect. Mine fails to translate 17 and 200 to what you have translated because there is a zlorp in the middle. Shouldn't 17, |-| , be borpenzlorpityborp?

I think I need to write my description better... the code I have is doing what I want. Let me explain; I'm making it mirror some English rules.

For the number '101', we pronunce that "one hundred one" (or "one hundred and one"). We don't say "one hundred zeroty one", although we do pronounce '121' by saying 'one hundred twenty one'. That is, in English, when a zero is in a column, we don't actually pronounce anything for it.

In fact in English, the only times we pronounce zero is when the number actually IS zero, or when we need it for precision after the decimal place.

The strange things we notice when teaching our children...

@bokmann: We used this exercise at our local Ruby group last night (Rogue.rb). We wrote some rspec specs for it based on your examples above. If you're still looking for acceptance tests, you're welcome to them.

Thanks for sharing this exercise. It was a lot of fun.

https://github.com/roguerb/zlorpian