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Solutions for Act IV Scene 4 - Knit-Picking

The puzzle presents (lots of) images of knots and stitch markers hanging off knitting needles. And given the title of Knit-Picking, it certainly seems the puzzle is about knitting.

There are 6, 9, 14, 4, 25, ... , 19 hanging cords between each of the stitch markers. Using 1=a, 2=b, 3=c, etc. reveals the message "find your knitting pattern hiding in the khipus".

So you are looking for a knitting pattern and you need to know what khipus are!

A bit of research into khipus will inform you that the Incas tied different sorts of knots in cords to send messages and keep records. In particular, different kinds of knots were used to record numeric values in base 10. On any given pendant cord, simple overhand knots would indicate the number of 10s (and 100s, 1000s, ... etc.), figure-8 knots would indicate a single unit and long knots would indicate 2-9 units according to the number of turns. Knots could be made in two different orientations and the pendant cords could be attached in 'recto' or 'verso' to the primary cord (in this case the knitting needle). Pendant cords were often arranged in clear groups, perhaps marked by a change in colour, and they could have additional subsidiary cords hanging from them. These particular features of khipus are used in the puzzle to encode a knitting pattern.

A typical knitting pattern has one line per row of knitting and each row describes a sequence of stitches, the simplest of which are knits (K) and purls (P). This is abbreviated so that, for example, KKKPPKK would be written K3 P2 K2 and PPKKPPKK would be (P2 K2)*2. Knitting patterns that use more than one colour of wool also need to specify which colour needs to be used when. Lastly, when knitting on straight needles (like the ones shown in the puzzle) you knit back and forth along the needles. This means the first row (and all subsequent odd rows) of knitting produce stitches on what is called the right side (RS) of the piece and the second row (and all subsequent even rows) produce stitches coming back on what is called the wrong side (WS) of the piece.

Now for finding the knitting pattern hiding in the khipus.

The first pendant cord in the puzzle is white, is attached in recto, and indicates the number 47 with 4 (left, say) overhand knots and one (left) long knot with 7 turns. The next three are also white and represent the numbers 10 (recto), 27 (verso), 10 (recto) but with knots in the alternate right orientation. Given this totals 47, it strongly suggests each row of knitting has 47 stitches, with left knots indicating stitches made on the right side of the knitting (odd rows) and knots given in their alternate right orientation indicating stitches made coming back on the wrong side (even rows). Recto attached pendant cords indicate when stitches are knits and verso attached pendant cords indicate when stitches are purls - not only do the images of recto and verso attachments resemble knit and purl stitches on knitting needles, but knit would be considered the foremost stitch of knitting, with purl the stitch that is a knit from behind.

So the first two rows of knitting are in white (W) and are:

  • Row 1 (W): K47
  • Row 2 (W): K10 P27 K10.

The change in colour of the pendant cords indicates a change in colour of wool to black (B). The first black pendant cord is identical to one we have seen before, indicating the knitting instruction for the next row is

  • Row 3 (B): K47.

The next set of numbers indicated by the black pendant cords should then total 47 to indicate the stitches coming back in the 4th row, but in fact they represent P9 K13 P2 K2 P9 which don't total 47. However, given P2 K2 are joined by a subsidiary cord with a long knot of 4 turns, it is reasonable to assume P2 K2 are to be repeated a total of 4 times, a notation common in knitting patterns. This then gives a total of 47 stitches and the following instruction

  • Row 4 (B): P9 K13 (P2 K2)*4 P9.

There are 97 rows of knitting in total which can be decoded in the manner described above. Every odd row (right side) is K47 - in white for rows 1 mod 4 and in black for rows 3 mod 4. The knitting instructions for the even rows (wrong side) are as follows:

  • Row 2: (W) K10 P27 K10
  • Row 4: (B) P9 K13 (P2 K2)*4 P9
  • Row 6: (W) K8 P4 K8 P3 (K2 P2)*4 K8
  • Row 8: (B) P7 K3 P12 (K2 P2)*4 K2 P7
  • Row 10: (W) K6 P3 K4 P12 (K2 P2)*4 K6
  • Row 12: (B) P5 K3 P3 K15 (P2 K2)*4 P5
  • Row 14: (W) K4 P2 K4 P5 K9 P3 (K2 P2)*4 K4
  • Row 16: (B) P4 K2 P3 K4 P12 (K2 P2)*4 K2 P4
  • Row 18: (W) K3 P2 K3 P3 K4 P13 (K2 P2)*4 K3
  • Row 20: (B) P3 K2 P2 K3 P3 K15 (P2 K2)*4 P3
  • Row 22: (W) (K2 P2)*2 K4 P6 K8 P3 (K2 P2)*4 K2
  • Row 24: (B) (P2 K2)*2 P3 K4 P12 (K2 P2)*5
  • Row 26: (W) K2 P2 K1 P2 K3 P3 K4 P12 (K2 P2)*4 K2
  • Row 28: (B) P2 K2 P1 K2 P2 K3 P3 K14 (P2 K2)*4 P2
  • Row 30: (W) K2 P1 K1 P2 K2 P3 K3 P5 K7 P3 (K2 P2)*4 K2
  • Row 32: (B) P2 K1 P1 K2 P2 K3 P2 K4 P10 (K2 P2)*5
  • Row 34: (W) K2 P1 (K1 P2)*2 K3 P3 K5 P9 (K2 P2)*4 K2
  • Row 36: (B) P2 K1 (P1 K2)*2 P2 K3 P3 K12 (P2 K2)*4 P2
  • Row 38: (W) K2 (P1 K1)*2 P2 K2 P2 K4 P5 K5 P3 (K2 P2)*4 K2
  • Row 40: (B) P2 (K1 P1)*2 K2 P2 K2 P3 K5 P7 (K2 P2)*5
  • Row 42: (W) K2 (P1 K1)*2 P2 K1 P2 K3 P6 K7 (P2 K2)*5
  • Row 44: (B) P2 (K1 P1)*2 K2 P1 K2 P2 K4 P1 K2 P7 (K2 P2)*5
  • Row 46: (W) K4 (P1 K1)*2 P2 K2 P5 K2 P2 K5 (P2 K2)*4 P2 K3
  • Row 48: (B) P4 (K1 P1)*2 K2 P2 K3 P1 K1 P2 K2 P5 (K2 P2)*4 K2 P3
  • Row 50: (W) K4 (P1 K1)*2 P2 K1 P4 K1 P2 K2 P2 K3 (P2 K2)*4 P2 K4
  • Row 52: (B) P4 (K1 P1)*2 (K2 P1)*2 K1 P1 K2 P2 K2 P3 (K2 P2)*4 K2 P4
  • Row 54: (W) K6 P1 K1 P1 K2 P2 K1 P1 K2 P2 K2 P5 (K2 P2)*4 K5
  • Row 56: (B) P6 (K1 P1)*2 K3 P1 K1 P2 K2 P2 K4 (P2 K2)*4 P6
  • Row 58: (W) K6 (P1 K1)*2 P3 K1 (P2 K2)*2 P7 K1 (P2 K2)*2 P2 K7
  • Row 60: (B) P6 (K1 P1)*2 K3 P1 K2 P2 K2 P4 K3 (P2 K2)*3 P8
  • Row 62: (W) K8 (P1 K1)*2 P1 K2 P2 K2 P3 K3 P13 K9
  • Row 64: (B) P8 (K1 P1)*2 K1 P2 K2 P2 K3 P5 K11 P9
  • Row 66: (W) K8 (P1 K1)*2 (P2 K2)*2 P4 K12 P2 K9
  • Row 68: (B) P8 (K1 P1)*2 K2 P2 K2 P3 K4 P8 K4 P10
  • Row 70: (W) K10 P1 K2 P2 K2 P3 K2 P14 K11
  • Row 72: (B) P10 K1 P2 K2 P2 K3 P4 K9 P2 K1 P11
  • Row 74: (W) K10 (P2 K2)*2 P4 K12 P2 K11
  • Row 76: (B) P10 K2 P2 K2 P3 K4 P8 K4 P12
  • Row 78: (W) K11 P2 K2 P3 K2 P14 K13
  • Row 80: (B) P11 K2 P2 K3 P4 K9 P2 K1 P13
  • Row 82: (W) K12 P2 K2 P4 K12 P2 K13
  • Row 84: (B) P12 K2 P3 K4 P8 K4 P14
  • Row 86: (W) K13 P3 K2 P14 K15
  • Row 88: (B) P13 K3 P4 K9 P2 K1 P15
  • Row 90: (W) K14 P4 K12 P2 K15
  • Row 92: (B) P15 K4 P9 K3 P16
  • Row 94: (W) K16 P14 K17
  • Row 96: (B) P18 K10 P19

What does this actually look like when knitted?

From above, it simply looks like rows of black and white stripes:

However, when viewed on an angle, the effect of what is known as 'illusion knitting' or 'shadow knitting' is seen.

Knit and purl stitches have different profiles. From the front, a knit stitch is flat but a purl stitch is raised. So when knitted in rows of contrasting colours like this, and when viewed on an angle, black raised purl stitches are going to stand out against their flat counterparts to create an image, and white raised purl stitches stitches are going to stand out against their flat counterparts to create a neutral background. Flat knit stitches in either black or white serve to highlight the other colour's raised purl stitches to complete the effect.

Of course it is also possible to analyse the knitting pattern given to find the solution to the puzzle.

For an accurate analysis, one needs to have an understanding of the knitting process. In particular, when translating knitting instructions to a knitting chart (an actual grid diagram of what the knitting will look like), odd rows are knitted right to left but even rows are knitted coming back, so from left to right. Row 1 is at the bottom of the chart, row 2 above it, and row 3 above that etc., so knitting instructions get translated from bottom to top. Furthermore, as even rows are knitted on the wrong side, in such rows knits in the instructions will actually look like purls from the front and purls in the instructions will actually look like knits from the front!

So knitting is a bit confusing like this. But even if teams analysed the pattern without knowing these ins and outs of knitting, it is hoped they would still have been able to obtain the correct image, just perhaps reflected or upside down or back to front.

The odd rows are all K47 and are essential for actually knitting the square but not for obtaining the required image on paper, so these are omitted on the knitting chart below (indeed, it is not uncommon for knitting charts to omit rows like this). What is shown in the knitting chart are which stitches in the final product end up as raised purl stitches from the front (represented by '-'). In a typical knitting chart each row might also be coloured, but in order to add details to the image later, I have not done this here, but instead labelled row numbers that are 2 mod 4, W for white, and rows that are numbered 0 mod 4, B for black.

All that is left to do now is to realise what happens when such a pattern in two contrasting colours is viewed from an angle. As alluded to in Hint 3, and explained above, it is the black purls and the white knits that will reveal the illusion knit and these are coloured in (two different shades of) grey in the diagram below. Note that the white purls and black knits give the neutral background.

And so what is this image? Hint 1 stated that you might need to get out a ball of wool or two to find this solution. Indeed quality balls of pure wool are very likely to have this iconic symbol printed on their labels, as will many garments made of pure wool. Adorning wool products for over 50 years, it is one of the world's most recognizable textile symbols. What you are looking at is the Woolmark logo. And just as a watermark might feature on paper as a faint design that can only be seen at specific angles or when held against the light, a 'woolmark' hides in this square of knitting as the solution to this puzzle, only visible to knit-pickers who might be looking for it.

The answer is: woolmark