Solutions for Act II Scene 4 - Coordination

We are presented with seven different curves that don't seem to resemble anything in particular nor interact in any meaningful way. The title seems to be our biggest hint at the moment, and "Coordination" strongly implies we care about the coordinates these curves pass through. So let's draw in grid lines as indicated by the provided notched axes:

It becomes apparent that the curves each seem to go through a series of lattice points. (In creating this image, we focussed on making it clear when a curve did not go through a lattice point, as the points where they did were difficult to ensure precise crossings.) For example, the orange curve goes through lattice points (3,1), (8,7), (5,6), (9,0), (4,2), using the arrowhead to give a direction/order.

Once we have this list of coordinates, the next step is to work out what exactly they represent. Knowing we must eventually extract a word or phrase, it seems likely that they're an alphabetic encoding of some sort. Though in total, we have more than 26 different coordinates at the moment. This suggests one letter might have more than one corresponding coordinate, and the most logical association in this case would be between coordinates that are alternate orderings of each other (that is, associate (a,b) with (b,a)).

Another more important fact one should note is that in most cases, the numbers in each coordinate are close to each other. The exception to this is zero, which appears with 9, 8, and 7. This implies zero should be somehow considered "close to" the largest digits. In fact, in all coordinates, a number only ever appears with a second number that is at most 3 away from it. It furthermore seems that (between coordinate pairs) a difference of one appears more often than a difference of two, which in turn appears more often than a difference of three. And of course, no lattice points in which the first and second digit are the same appear at all. All these properties can be observed from the list of coordinates or by looking at the graph itself.

The big intuitive leap here is to realise that these coordinates are also acting as coordinates for the keys on a regular computer keyboard. In the keyboard case though, the coordinates both come from the top row of the keyboard, and we extrapolate their intended location/letter by observing where the two diagonal columns extended from each number intersect. e.g. (3,1) points to A, by following the right-diagonal column from 1 (QAZ) and the left-diagonal from 3 (WA). This explains many of the observations above - for instance, a difference of three is least frequent because the bottom row of a keyboard mostly contains least-used English letters, and zero appears paired with 9, 8, and 7 because it does indeed appear after 9 in a keyboard's top row. We can similarly see why coordinate order doesn't matter in this system. The title is a final weak attempt at referencing this theme, since good hand-eye coordination is needed to use a keyboard.

However we come to this conclusion, we can now use this new coordinate system to extract letters and thus words per coloured curve. Using the usual rainbow ordering, we get the following messages:

US brekkie chain
uneven gait
make tea

Some of these clues are vaguer than others, but "uneven gait" is likely to be describing a LIMP and to "make tea" is probably to BREW. There are also very few famous American breakfast chains, one of which is IHOP. Looking at these and some of the other candidates for the clues, and keeping in mind the keyboard theme, it's noticeable that the letters in each answer tend to be near each other on the keyboard. Also useful to note is that the answers appear to all be four letters long.

It seems likely that these four-letter words are each to be interpreted as their own two pairs of coordinates, where the pairs of letters this time indicate numbers in the same way numbers indicated letters in the previous step. We can use this guess to confirm any remaining ambiguous clued words. They are IHOP, CARS, THUG, WENT, LIMP, BREW, READ. Using the reversed coordinate rule, we have IH implying the number 8, since it lies on one of the diagonals through I and another though H. All up, each word contributes two numbers and we get the new coordinates (8,0), (3,4), (6,7), (3,6), (9,0), (5,3), (4,3).

Using the same coordinate trick one last time, we extract the letters KEYCODE, our thematic answer.

Puzzle Notes: This puzzle ended up being trickier on average for solvers than we had expected. This is almost certainly due to the big jump in logic required to associate the normal coordinates with this new keyboard encoding. It was hoped the various clues extracted from the large number of coordinates (as described above) combined with the fact most solvers would have a keyboard in front of them at the time would make the jump a little more conceivable. The visual representation was also supposed to help in this regard - in fact you can almost overlay a keyboard and its reflection over the crossed lattice points, excepting those corresponding to zero.

The original reason this puzzle was presented visually was so that each curve could look approximately like one of the letters in QWERTY(U), providing a bigger hint to the keyboard mapping. Unfortunately this ended up looking far too messy to extract the lattice points themselves, so was scrapped. You can still see the original intended shape in some of the curves though. A second idea was to have each curve cross the x-axis only once, at a point corresponding to the QWERTY letters (such that the red one would cross at x = 1.7, implying the 17th letter Q), but this still proved too messy and complicated.

Another solution to decreasing the inherent messiness of the image was to make the clues as succinct as possible. Unfortunately IHOP still proved difficult to describe, as did LIMP without being able to use the letters P or L. It is hoped the vagueness of some of these clues didn't prove too much of an obstacle, though based on the large number of guesses made starting with T, it's possible people interpreted the list of clues in a different way.

(Update: It turns out the many guesses beginning with T were based on the fact all other solutions to Act II puzzles began with T. We're suprised it took us this long to notice!)

The answer is: keycode