There are three official counting systems and probably a dozen community proposals.
In real world languages, there are two number systems- exact and approximate. Even primative people like English speakers often have to resort to approximate number systems, counting "one, a pair, a trio, a few, a bunch, a lot, a whole lot, a crap load." When you see people note that such and such a society counts "one, two, many" what is being observed is an approximate number system. When people use an approximate number system with a so-called "five", often five means three to seven. On the other hand exact number systems are not universal, so the toki ponan with an exact numbering system at all, is a rather advanced.
Couting with approximates. ala, wan, tu, tu wan, tu tu, tu tu wan. This system is pretty bizzare. It corresponds to the English, "none, single, few, few single, few few, few few single" and so on. This system stops working at about six.
Couting with approximates and luka. "wan, tu, tu wan, tu tu, luka, luka wan, luka tu, luka tu wan, luka luka". Again, this is an approximate system that has been forced into exact counting. This system stops working at about 15.
Counting with ale, mute for 100 and 20 This is more of the same, except ale and mute have much more opportunity to be confused with a non-numerical meaning. The system breaks down at about 350, but is bearable to write if you use Roman style numerals. All that said, it looks like a Christmas tree if you list them centered.
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