I noticed that the symbols are grouped into three blocks of each symbol.
Going from left to right, the blocks have the following number of tiles:
Circle: 29, 19, 13
Arrow: 20, 30, 10
Triangle: 15, 21, 33
I thought perhaps there was a significance between the size of the blocks. Like the difference in the size of the Arrow blocks is 10, if you align them in acending order. Perhaps if you could figure out a pattern for the other two, you'd know how many of the blank tiles would be needed to fill in the pattern.
As an aside, (and as a DM) I can't imagine allowing a campaign that I'd worked a *year* on to be unravelled by a silly puzzle. That's just wasting a year of your (and your players!) lives. It also shows a severe lack of attention to the #1 rule - keep the game fun. I'd be pissed if a game I'd played in for a year ended this way.