A Culturally Biased Number Puzzle

Below is a number series puzzle. I'll give the answer midway through this post.

1
11
21
1211
111221

What's the next number in the series? It's not as easy as it looks.

I'm guessing that Thais would find this puzzle more difficult than would English speakers. Here's the version that would probably be easier for a Thai, and more difficult for a Westerner:

1
11
12
1121
122111

Much ado is made of "cultural bias" in various psychometric tests. I don't have strong opinions on the issue. It seems reasonable to think that steps can be taken to minimize, if not remove, cultural bias. It should also be possible to make post-test adjustments to account for such bias. Sparks start to fly when someone implies that one ethnic group is brighter than another; this accounts for the intense academic interest in the subject.

I'm no linguist, but it seems that many languages in this part of the world make heavy use of "counters". The Thai language has about 200 of these words. Indonesian language has many. I've been told that Chinese does as well. English language has a few commonly used counters as well. If you say, "I'd like two loaves of bread", the word "loaves" is the counter. For many objects, English speakers forego the counter (e.g. "She has three stamps"). The Thais, however, use counters for virtually everything. In Thinglish, you'd say "She have stamp three flat thing". There's a special word that helps you count small flat things. In Thai, at least, the counter always follows the thing you're counting, so you wouldn't hear "She have three flat thing stamp".

So, coming back to the puzzle, if you ask a Westerner, "What do you see below?"...

1

...he would say "I see one one".

11

Ask him again, and he'll say, "I see two ones".

21

Etc.

But, try the same game with a Thai:

1

In Thinglish, he'd say, "I see one one tua". ("tua" is the Thai counter for letters and numbers)

11

Now he'll say, "I see one two tua".

12

Etc.

By now you probably understand the puzzle. The final number you see in the Western version of the puzzle is 111221. The number has three ones, followed by two twos, followed by one one.

312211

The final number in the Thai version is 122111. That number has one one tua, followed by two two tua, followed by one three tua.

112213

Interestingly, if you reverse the Western result, you get the Thai result!

Another question: given a "seed number" of 1 through 9, will any of the strings eventually converge? For example, if you start with 2, will these strings eventually merge with with the strings you get if you start with 3? If you use the Thai counting system, it will be easier to realize that the answer is "no"!

In any case, it seems reasonable to believe that one version of the puzzle would be easier/more difficult for Westerners/Thais, given their linguistic habits. A test maker could easily be ignorant of these differences.

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A Westerner might find the Asian use of counters to be inefficient. It certainly is, if you're talking about compressing information into the shortest possible sentence. But there are plenty of inefficiencies in the English language. Why say "This is a table" when you could simply say "This table", as you would in Thinglish? Language is not simply about compressing information. It's about offering up information in ways that other brains, with limitations on speed and capacity, can understand. Different languages deal with these limitations in different ways.

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