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### Solutions for Act IV Scene 4 - In Shufflin Feet

Let's begin by making a few observations. We have 48 frames containing a stick figure in various positions. There are numerous frames where the figure's positions are quite similar, so maybe it's possible for these to string together to form an animation. Of course, the order in which the frames are initially presented does not give any meaningful animation - so perhaps there's a little more be done. Separating the frames into groups which appear to be from the same type of animation may appear promising at first but there would be too much uncertainty in deciding exactly which ones fit where and in what order. We need something with a bit more certainty. Also, the letters and numbers obtained by doing this grouping do not appear to give anything meaningful.

One plausible method of physically animating a sequence of stick figures drawn on paper is to create a flip-book. This is done by stacking the frames on top of one another to create a book, then flipping an edge with the thumb to create an animation by seeing the frames change in rapid succession. Notice that each frame is the same size, possibly with one or two tabs hanging off the right-hand side, so forming a flip-book appears to be a viable option. As pointed out above, flipping through every frame is unlikely to give anything meaningful, so perhaps there could be a way of only viewing some of the frames? We can see that there are tabs on the top, middle or bottom of the right edge. So what happens when we try to flip with our thumbs on the tabs? (It might be helpful to use a bullclip to hold the left-hand edge together while flipping.)

Flipping through using the top or bottom tab does not appear to give any meaningful animation. However, the middle tab produces the following:

This looks like the HAKA! (More specifically, "Ka Mate" - the most well known haka.) Let's also take a glance at the front of the flipbook to see if there's anything useful. This is what we see:

What could the dot and arrow mean? Well, recall that the only meaningful animation appeared when we flipped the middle tab forwards. Hence, it is reasonable to assume that these are instructions: flip the dotted tab in the direction of the arrow. (An interesting observation is that when flipping forwards, the visible frames are those with that particular tab. However, when flipping backwards, the visible frames are in fact the ones behind the tabbed frame.)

OK, so that's one dance using just 10 frames. Surely there are others - but how would we get them? Flipping the three tabs, either forwards or backwards, doesn't give anything else useful. The key step is hinted in the title: we need to perform an in-shuffle on the frames. This is a type of perfect riffle shuffle where the deck is split into two halves and the frames are interweaved. For example, if we wanted to in-shuffle the digits from 1 to 10 in that order, we'd do the following:
Split the numbers into two halves:
1 2 3 4 5 - 6 7 8 9 10
Interweave the numbers using the second half first:
6 1 7 2 8 3 9 4 10 5

So if we perform in-shuffles on the frames then flip according to the symbols visible from the front, we get the following:

Number of In-ShufflesFront of bookAnimation
1

Flip bottom tab backwards.

Ballet

2

Flip bottom tab backwards.

Can-Can

3

Flip top tab backwards.

Moonwalk

4

Flip top tab forwards.

YMCA

5

No more flipping.

There are no more symbols! What do we do now? Well, our helpful friend on frame 23 is giving us a little nudge - he's pointing to the letter U in the bottom left-hand corner! Maybe now the letters will make sense. In the current order, it reads:

UNSHUFFLETHENAMEOFEACHDANCETHERIGHTNUMBEROFTIMES

How should we do this? First, we need to determine how to unshuffle. A reverse in-shuffle is performed by taking all the even-positioned objects in order then following that with all the odd-positioned objects in order. For example, an in-shuffle performed on the digits from 1 to 10 in order gives:
6 1 7 2 8 3 9 4 10 5
It is not hard to see that the above procedure will recover the original order.
The next thing we need to do is unshuffle the names of each dance the right number of times. Observe that the names of each dance found above contain an even number of letters, thus reverse in-shuffling is definitely possible. It is quite conceivable that "the right number of times" refers to the number of in-shuffles required to reach that particular dance. So, for example, since we in-shuffled 3 times to get the MOONWALK, we should reverse in-shuffle the word 3 times. Doing so produces the following:
HAKA

BALLET
ALTBLE

CANCAN
ACNCNA
CCAANN

MOONWALK
ONAKMOWL
NKOLOAMW
KLAWNOOM

YMCA
MAYC
ACMY
CYAM
YMCA

Taking the first letter of each result gives us the word HACKY, a reference to Hacky Sack, a well-known trademark name for a type of footbag - which is undoubtedly played with shufflin' feet!