2007 North American Computational Linguistics Olympiad

Solution to the problem

The first thing to notice about this problem is that the document is a table of squares. You can infer this from the hints that this is an educational document dealing with the number system, plus inspection of the characters. The first two characters are missing, but in the second column you have a list of characters that can be construed as meaning "36" (3 left wedges = 30, and 6 down wedges = 6), then 49 (four left wedges plus 9 down wedges). Since 36 and 49 are perfect squares, AND the third character in the first column consists of 8 down wedges, we might infer that the first two characters in the first column represent 6 and 7 (see below). Then the third character in the second column must represent 64, since that is the square of 8. This character consists of one BIG down wedge on the left and 4 on the right. In order to get 6 from this, we hypothesize that a BIG down wedge on the right = 60. From this we can infer the rest of the characters, as indicated below.