The bold lines on the numbered side of each strip and the fact that the numbers are all between 1 and 9 strongly suggests that this puzzle is a sudoku. Teams quickly realized that although they had enough numbers to make a sudoku with just vertical or just horizontal strips, redundant numbers made that impossible.
Many teams got the reference from the puzzle that, like Penelope from Homer's Odyssey, they were supposed to weave. More specifically, they were supposed to weave the horizontal and vertical strips in an over-under-over-under fashion to make a valid sudoku.
Although this sounds like a Herculean task, it can actually be done in a straightforward and deductive manner. First teams can figure out which parts of each strip must face down. Every strip shows either the 1st, 3rd, 5th, 7th, and 9th places or the 2nd, 4th, 6th, and 8th places, with the rest covered. Repeated numbers in those places can eliminate one of the two orientations and therefore determine which part of the strip faces up.
From there teams could start figuring out the order of the strips. This was easier to do using the horizontal strips, since more of them had an easily determined orientation than the vertical strips. The determined orientation of a few of the horizontal strips helped to put the already oriented horizontal strips in order. That emerging order helped determine eliminate more possible orientations of vertical strips, which further helped finish the order of the horizontal strips. Once teams figured out the orientation of the horizontal strips, they could easily finish the vertical ones. Keeping it from falling apart was a bit of a challenge, but that's why teams were told to bring tape. The completed sudoku looks like this:
Now to read the message. Several teams pointed out that they were disappointed by the fact that the message wasn't immediately obvious when the finished the sudoku. I toyed with the idea of having the message written simply on the back, but ultimately decided against it. I was worried that teams might be able to read the message without finishing the weave. Rather, was was indicated by the letter from Boddy, teams had to use the front to figure out which letters to take from the back.
Specifically, teams had to find the letter on the back of the row number of each row and then on the back of the column number of each column. For the first row, they took the letter behind the 1. For the second row, they took the letter behind the 2. And so on. And the same for the columns. This works because each row and each column contains one and only one of each number 1 through 9. In each case, the letter taken was not on the same strip as the number read, which made careful construction important. Doing this yielded:
or "go to Union City's IHOP," which was the next location.