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Work on an International Linguistics Olympiad Problem With Me!

Linguistics problems are very effective in developing problem solving techniques and tenacity. They're also fun and offer unexpected results.

Here is problem one from the fifth International Olympiad in Linguistics held in 2007:

(Source: )

We observe a dot at the beginning of every sentence. This may indicate capitalisation or act as a punctuation mark. In linguistics the term for this dot is a delimiter. Notice how there are two delimiters in the second sentence and one each in the first and third sentences. This corresponds to the number of capitalised letters in those sentences, so it is safe to assume (for now) that these delimiters denote capitalisation.

Each word in the Braille sentence corresponds to a word in the English sentence. It is safe for us to assume a one-to-one word mapping in the problem. Each Braille symbol likely represents a single word in English. We also observe a one-to-one character mapping. A character in Braille therefore likely corresponds to a letter in English.

There are three dots in some shape or form at the end of every sentence. The punctuation marks for all three sentences are different and so are the form of these three dots. We can assume that the arrangement of these dots reflects the punctuation marks at the end of the English sentences. So we have our exclamation mark. Sentence 2 is the only one to use a comma, it is safe to assume that the single dot in its Braille translation represents a comma.

We are required to write the number 40 in Braille. The only clue provided to us in the problem is the number 89. If we look carefully it is obvious that the four dots at the beginning of Braille 89 do not appear elsewhere. This is the only hint of segregation of numbers from letters. We have another assumption in our arsenal.

Now we have sufficient information to map each English letter to each Braille character. This is a strenuous task, but it isn’t hard. Look at all the places the letter A repeats. It is obvious that A is represented by a single top left dot. On observation we can see that the template for dotting is a grid of 6 dots, like a domino. Braille representations of letters C D E F H I J K L N O Q R S T U X and Y can be similarly found. As the hint says, the letter W does not exist in French orthography, so we will ignore it.

What pattern can you observe in your table of Braille Vs English characters? At this stage it would be wise to also number the letters from 1 to 26. Can you see something funny?

Look at letters E F G, the fifth, sixth and seventh letters respectively and O P Q, the fifteenth, sixteenth and seventeenth letters. What do you see?

For letters 11-20 the bottom left dot is a common feature. In fact, it’s their only distinguishing feature from the letters that are exactly 10 before them. That is, adding a bottom left dot to D, the fourth letter, makes it N, the fourteenth letter.

What about letters 21-26? We find that the bottom right dot is the distinguishing feature of this group from letters 11-20. But there’s a letter gap. Adding a bottom right dot to O, the fifteenth letter, doesn’t make it Y, the twenty-fifth letter- it makes it Z.

Did you strike your W yet? Removing W from the picture and renumbering from 21 to 25 solves all our problems.

Proceeding in this manner we can derive the Braille symbols for all the letters.

From 1-10 to 11-20 add a bottom left dot and remove it the other way round. From 11-15 to 21-25 add a bottom right dot and remove it the other way round.

We have all our letters, the capitalization mark and our punctuation marks. Now we need to lay out the Braille numbering system.

Remember how we numbered the letters? Notice how the numbers 8 and 9 and the letters H and I, the eighth and ninth letters, have the same symbols respectively. It is then safe to assume that the symbol for D represents 4. We use the marker to distinguish between letters and numbers, remember?

But what about zero? Zero could be A, the first letter, but that doesn’t fit into our analysis. The only other option is to visualise a keyboard. Zero comes after nine on a keyboard, maybe it does here too? Trust your intuition, especially when you can’t think of any other logical argument. Indeed, the symbols for J and zero are identical.

And there you have it. You have all the Braille characters to translate the problem’s sentence.

Here is my working for reference:

You’ll notice that we made a lot of assumptions while solving this problem. Often, in problems of this type, we have no choice but to try and generalise our observations. Sometimes just looking at the problem carefully can provide us our entire solution.

If you liked this problem, have a go at other linguistics problems. A repository of past IOL problems can be found here.

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