Advance Weaving | Woven Pixels

advance Weaving

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Weaving Technique

Double cloth or double weave (also double cloth, double-cloth, double-weave) is a kind of woven textile in which two or more sets of warps and one or more sets of weft or filling yarns are interconnected to form a two-layered cloth. The movement of threads between the layers allows complex patterns and surface textures to be created.

In contemporary textile manufacturing, the term "double cloth" or "true double cloth" is sometimes restricted to fabrics with two warps and three wefts, made up as two distinct fabrics lightly connected by the third or binding weft, but this distinction is not always made, and double-woven fabrics in which two warps and two wefts interlace to form geometric patterns are also called double cloths.

Double-faced fabrics are a form of double cloth made of one warp and two sets of wefts, or (less often) two warps and one weft. These fabrics have two right sides or faces and no wrong side, and include most blankets, satin ribbons, and interlinings.

Double weaving is an ancient technique.

Surviving examples from the Paracas culture of Peru have been dated to before AD 700.

Modern applications of double cloth include haute couture coats, blankets, furnishing fabrics, and some brocades.

Common Use: > Clothing > Accessories > Home Decor WHAT IS DOUBLE CLOTH WEAVE? The fundamental principle of the double cloth weave is very simple. To weave a layer of plain weave cloth, you need two shafts threaded alternately. So to weave two layers, you need 2 x 2 = 4 shafts. I find that this is the easiest Way

to think about and plan a four-shaft double cloth weave: group the shafts into pairs and assign one pair to each layer of cloth.

UNDERSTANDING DOUBLE CLOTH WITH THIS SAMPLE DEVELOPMENT The important points to note are: We alternate the threading, taking one end from each layer in turn.

Shafts 1 & 2 carry one layer, shafts 3 & 4 carry the other.

You can test the second point by lifting shafts 1 & 2: you should be able to separate the two layers completely.

SETT The sett for double weave is very dense: twice the normal sett for plain weave with your yarn.

TIE-UP When planning a double weave tie-up, you need to think about what you want to achieve.

You will be handling several different tasks: Choosing which layer is on top and which is on the bottom Weaving in the top layer Weaving in the bottom layer Let’s say we want to start with layer 1 (shafts 1 & 2) on top and layer 2 on the bottom. To weave plain weave on shafts 1 & 2, we need to lift shaft 1 for the first pick and shaft 2 for the second.

Similarly, to weave plain weave on shafts 3 & 4 we need to lift shaft 3 for the first pick and shaft 4 for the second. However, this won’t give us double weave unless we take an extra step: we also need to lift the top layer out of the way.

Every time we weave the layer on shafts 3 & 4, we also need to raise shafts 1 & 2 to keep those ends clear of the shuttle.

Each X shows where a shaft is tied in order to be raised, while each O shows where a shaft is tied in order to be lowered. The blanks indicate that those shafts are not tied to those treadles at all.

TREADLING As with the threading, we need to alternate the treadling, inserting one pick into each layer in turn. By progressing the two layers at the same rate, you ensure that the beater can always reach the fell on both layers.

We can use the same reasoning to derive a tie-up, which works for weaving layer 2 on top and layer 1 on the bottom.

Putting these together to make the complete tie-up it makes sense to keep the "weaving lifts" separate from the "out-of-the-way lifts: so that we can mix and match during the treadling. For a jack-type loom, the tie-up looks like this

If you are weaving on a countermarche loom, then you will need eight treadles, tied up like this:

On a jack-type loom you will need to press two treadles whenever you are weaving the bottom layer: one foot presses the "weaving" treadle and the other the "out-of-the-way" treadle. On a countermarche loom, you will need to press two treadles for every pick – top and bottom layers – so that the shafts for the inactive layer are either raised (to weave the bottom layer) or lowered (to weave the top layer).

The theory sounds complicated, but once you are at the loom you will find that the freedom to mix and match the treadles in this way encourages you to try all kinds of patterns! For those of you weaving on table or dobby looms, the lift-plan looks like this:

MANAGING THE SHUTTLES You can weave many kinds of double cloth with a single shuttle, but to explore all the possibilities of color and structure you are likely to want to use two. How you handle those shuttles makes an important difference to the finished cloth.

By keeping the two layers separate in the body of the cloth (i.e. always weaving the same layer on top), but joining them at the edges, you can weave a tube. This is a great way to weave a small bag, for example. To link the edges together, start with both shuttles at the same side of the loom and weave the top layer first. After you have woven the first pick, place the shuttle on the face of the cloth in front of you. After you have woven the second pick, place the second shuttle in front of the first one, i.e. further from your body. Then pick up the first shuttle again and so on.

If you are interchanging the two layers – weaving one on top and then switching over to weave the other on top – stitching the ends together allows you to introduce padding into the pockets you create. The switching of the layers closes the pocket and secures the Pad-

ding.

Keeping the ends open at one side but closed on the other makes a series of tubular pockets, which could become a caddy for knitting needles or crochet hooks, for instance.

To keep the ends open, weave as above but place the second shuttle behind the first one, i.e. nearer to your body. To keep one end open and one closed you need to place the shuttle behind its partner at one side of the loom and in front at the other. Be sure to check every now and then that you have the openings where you want them, as it is easy to slip up! I find it easiest to keep track of where I am if I always weave the top layer first, whichever one it is. It is a good idea to experiment in order to discover what effects you get from different sequencing and placing of the shuttles – nothing will fix it in your mind so well as actually trying it.

Properties of Double Cloth Fabrics Available in many different colors Can be made reversible Can be patterned No lengthwise or crosswise stretch, only bias Frays easily Drapes well Versatile Flexible Improved thermal properties Warm to wear Uniform face, nothing to give away it is a double cloth

TECHNICAL DETAILS

NID | TEXTILE DESIGN | ADVANCE WEAVING | SPECIFICATION SHEET | DOUBLE CLOTH | STYLE NO. : Final warp

WARP DETAILS TYPE PATTERN RATIO 1:1 BEAM 01 no. Palette 1 2 3 4 5 6

MATERIAL COTTON YARN COUNT 2/20S EPI 80

WARP LENGTH 5 MTR REED 40 DENTING 8/D

WARP COLOR PATTERN

Name Group no. of ends per color in the warp 08 08 08 08 White A 12 Black B 08 08 Green C 08 Red D 08 Yellow e 08 08 08 White F 12

Repeat the same 32 times Repeat the same 32 times Repeat the same 32 times Repeat the same 32 times Repeat the same 32 times Repeat the same 32 times

Odd EVEN EVEN EVEN EVEN Even

WARP PATTERN

WEFT DETAILS TYPE PATTERN COLOR SINGLE

MATERIAL COTTON YARN COUNT 2/40S

PPI 160 SAMPLE SIZE 30 Inches

WEFT COLOR PATTERN no. Palette 1

Name White

no. of ends in the weft 160 ENDS PER INCHES

TOTAL WARP & WEFT TOTL ENDS OF WARP 1600

TOTL ENDS OF WEFT 3340

Total 576 256 256 256 256 576

NID | TEXTILE DESIGN | ADVANCE WEAVING | SPECIFICATION SHEET | DOUBLE CLOTH | STYLE NO. : Final warp

DRAFTING AND DENTING & SPEC PLAN

01 02 03 04

01 02 03 04 05 06 07 08

01 02 03 04 05 06 07 08

01 02 03 04 09 10 11 12

01 02 03 04 13 14 15 16

01 02 03 04 17 18 19 20

01 02 21 22 23 24

NID | TEXTILE DESIGN | ADVANCE WEAVING | SPECIFICATION SHEET | DOUBLE CLOTH | STYLE NO. : final warp

DRAFTING AND DENTING & SPEC PLAN

03 04

01 02 03 04 42 32 22 12

01 02 03 04 02 91 81 71

01 02 03 04 6 1 5 1 41 31

01 02 03 04 21 11 0 1 90

01 02 03 04 80 70 60 50

01 02 03 04 80 70 60 50

EVEN SHAFT PLAIN WEAVE ODD SHAFT PLAIN WEAVE STITCHING OF ODD AND EVEN WEAVE PLAIN WEAVE

LIFTING ORDER

2 6 10 14 18 22 4 8 12 16 20 24 1,2,4 5,6,8 9,10,12 13,14,16 17,18,20 21,22,24 2,3,4 6,7,8 10,11,12 14,15,16 18,19,20 22,23,24 2 6 4 8 1,2,4 5,6,8 2,3,4 6,7,8 1 5 3 7 1,2,3 5,6,7 1,3,4 5,7,8 2 6 4 8 1,2,4 5,6,8 2,3,4 6,7,8 2 6 4 8 1,2,4 5,6,8 2,3,4 6,7,8 2 6 4 8 1,2,4 5,6,8 2,3,4 6,7,8

10 12 9,10,12 10,11,12 9 11 9,10,11 9,11,12

14 16 13,14,16 14,15,16 13 15 13,14,15 13,15,16

18 22 20 24 17,18,20 21,22,24 18,19,20 22,23,24 17 21 19 23 17,18,19 21,22,23 17,19,20 21,23,24

10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12

14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16

18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24

1 5 3 7 1,2,3 5,6,7 1,3,4 5,7,8 2 6 4 8 1,2,4 5,6,8 2,3,4 6,7,8 2 6 4 8 1,2,4 5,6,8 2,3,4 6,7,8 2 6 4 8 1,2,4 5,6,8 2,3,4 6,7,8 6 1 8 3 5,6,8 1,2,3 6,7,8 1,3,4 1 5 3 7 1,2,3 5,6,7 1,3,4 5,7,8 6 1 8 3 5,6,8 1,2,3 6,7,8 1,3,4

9 11 9,10,11 9,11,12

13 15 13,14,15 13,15,16

17 19 17,18,19 17,19,20

21 23 21,22,23 21,23,24

10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12 9 11 9,10,11 9,11,12

14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 13 15 13,14,15 13,15,16

18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 17 19 17,18,19 17,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 21 23 21,22,23 21,23,24

10 14 18 22 12 16 20 24 9,10,12 13,14,16 17,18,20 21,22,24 10,11,12 14,15,16 18,19,20 22,23,24

2 6 4 8 1,2,4 5,6,8 2,3,4 6,7,8 2 6 4 8 1,2,4 5,6,8 2,3,4 6,7,8 6 1 8 3 5,6,8 1,2,3 6,7,8 1,3,4 1 5 3 7 1,2,3 5,6,7 1,3,4 5,7,8 6 1 8 3 5,6,8 1,2,3 6,7,8 1,3,4

10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12 9 11 9,10,11 9,11,12

14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 13 15 13,14,15 13,15,16

18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 17 19 17,18,19 17,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 21 23 21,22,23 21,23,24

10 14 18 22 12 16 20 24 9,10,12 13,14,16 17,18,20 21,22,24 10,11,12 14,15,16 18,19,20 22,23,24

6 2 10 14 18 22 8 4 12 16 20 24 1,2,4 5,6,8 9,10,12 13,14,16 17,18,20 21,22,24 2,3,4 6,7,8 10,11,12 14,15,16 18,19,20 22,23,24 6 1 8 3 5,6,8 1,2,3 6,7,8 1,3,4 1 5 7 3 1,2,3 5,6,7 1,3,4 5,7,8 1 5 3 7 1,2,3 5,6,7 1,3,4 5,7,8 1 5 3 7 1,2,3 5,6,7 1,3,4 5,7,8 6 1 8 3 5,6,8 1,2,3 6,7,8 1,3,4 2 6 4 8 1,2,4 5,6,8 2,3,4 6,7,8 6 1 8 3 5,6,8 1,2,3 6,7,8 1,3,4

10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12 9 11 9,10,11 9,11,12

14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 13 15 13,14,15 13,15,16

18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 17 19 17,18,19 17,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 21 23 21,22,23 21,23,24

10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12

14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16

18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24

1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4

2 4 1,2,4 2,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4

5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 6 8 5,6,8 6,7,8

10 12 9,10,12 10,11,12 9 11 9,10,11 9,11,12

14 16 13,14,16 14,15,16 13 15 13,14,15 13,15,16

18 22 20 24 17,18,20 21,22,24 18,19,20 22,23,24 17 21 19 23 17,18,19 21,22,23 17,19,20 21,23,24

10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12

14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16

18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24

6 10 14 18 22 8 12 16 20 24 5,6,8 9,10,12 13,14,16 17,18,20 21,22,24 6,7,8 10,11,12 14,15,16 18,19,20 22,23,24 5 18 22 10 14 7 20 24 12 16 5,6,7 9,10,12 13,14,16 17,18,20 21,22,24 5,7,8 10,11,12 14,15,16 18,19,20 22,23,24 5 9 22 14 18 11 7 20 24 16 5,6,7 9,10,11 13,14,16 17,18,20 21,22,24 5,7,8 9,11,12 14,15,16 18,19,20 22,23,24 9 13 17 21 5 15 7 11 19 23 5,6,7 9,10,11 13,14,15 17,18,19 21,22,23 5,7,8 9,11,12 13,15,16 17,19,20 21,23,24 9 5 14 18 22 7 11 16 20 24 5,6,7 9,10,11 13,14,16 17,18,20 21,22,24 5,7,8 9,11,12 14,15,16 18,19,20 22,23,24 5 10 14 18 22 7 12 16 20 24 5,6,7 9,10,12 13,14,16 17,18,20 21,22,24 5,7,8 10,11,12 14,15,16 18,19,20 22,23,24

2 6 10 14 18 22 4 8 16 20 24 12 1,2,4 5,6,8 9,10,12 13,14,16 17,18,20 21,22,24 2,3,4 6,7,8 10,11,12 14,15,16 18,19,20 22,23,24 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4

5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8

9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12

14 16 13,14,16 14,15,16 13 15 13,14,15 13,15,16

18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24

1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4

5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8

9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12

13 15 13,14,15 13,15,16 13 15 13,14,15 13,15,16

17 19 17,18,19 17,19,20

21 23 21,22,23 21,23,24

18 20 17,18,20 18,19,20 14 18 16 20 13,14,16 17,18,20 14,15,16 18,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24

2 6 10 14 18 22 4 8 12 16 20 24 1,2,4 5,6,8 9,10,12 13,14,16 17,18,20 21,22,24 2,3,4 6,7,8 10,11,12 14,15,16 18,19,20 22,23,24 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4

5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8

9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12

14 16 13,14,16 14,15,16 13 15 13,14,15 13,15,16 13 15 13,14,15 13,15,16 13 15 13,14,15 13,15,16

18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 17 19 17,18,19 17,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 21 23 21,22,23 21,23,24

18 20 17,18,20 18,19,20 18 14 16 20 13,14,16 17,18,20 14,15,16 18,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24

2 6 10 4 8 12 1,2,4 5,6,8 9,10,12 2,3,4 6,7,8 10,11,12 1 5 9 11 3 7 1,2,3 5,6,7 9,10,11 1,3,4 5,7,8 9,11,12

14 18 22 16 20 24 13,14,16 17,18,20 21,22,24 14,15,16 18,19,20 22,23,24

1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4

13 15 13,14,15 13,15,16 13 15 13,14,15 13,15,16

5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8

9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12

14 18 22 16 20 24 13,14,16 17,18,20 21,22,24 14,15,16 18,19,20 22,23,24

18 22 20 24 17,18,20 21,22,24 18,19,20 22,23,24 17 21 19 23 17,18,19 21,22,23 17,19,20 21,23,24

1 3 1,2,3 1,3,4

5 7 5,6,7 5,7,8

9 11 9,10,11 9,11,12

13 15 13,14,15 13,15,16

1 3 1,2,3 1,3,4

5 7 5,6,7 5,7,8

9 11 9,10,11 9,11,12

14 18 22 16 20 24 13,14,16 17,18,20 21,22,24 14,15,16 18,19,20 22,23,24

18 22 20 24 17,18,20 21,22,24 18,19,20 22,23,24

18 22 20 24 17,18,20 21,22,24 18,19,20 22,23,24 17 21 19 23 17,18,19 21,22,23 17,19,20 21,23,24

5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8

9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12

13 15 13,14,15 13,15,16 13 15 13,14,15 13,15,16 13 15 13,14,15 13,15,16

18 22 20 24 17,18,20 21,22,24 18,19,20 22,23,24

1 3 1,2,3 1,3,4

5 7 5,6,7 5,7,8

9 11 9,10,11 9,11,12

14 18 22 16 20 24 13,14,16 17,18,20 21,22,24 14,15,16 18,19,20 22,23,24

13 15 13,14,15 13,15,16 13 15 13,14,15 13,15,16 13 15 13,14,15 13,15,16

1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4

5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8

9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12

18 22 14 16 20 24 13,14,16 17,18,20 21,22,24 14,15,16 18,19,20 22,23,24

14 18 22 16 20 24 13,14,16 17,18,20 21,22,24 14,15,16 18,19,20 22,23,24 14 18 22 16 20 24 13,14,16 17,18,20 21,22,24 14,15,16 18,19,20 22,23,24 14 18 22 16 20 24 13,14,16 17,18,20 21,22,24 14,15,16 18,19,20 22,23,24 13 15 13,14,15 13,15,16 13 15 13,14,15 13,15,16 13 15 13,14,15 13,15,16

14 18 22 16 20 24 13,14,16 17,18,20 21,22,24 14,15,16 18,19,20 22,23,24

1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4

1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4

9 1 5 11 3 7 1,2,3 5,6,7 9,10,11 1,3,4 5,7,8 9,11,12 2 6 10 4 8 12 1,2,4 5,6,8 9,10,12 2,3,4 6,7,8 10,11,12 1 5 9 11 3 7 1,2,3 5,6,7 9,10,11 1,3,4 5,7,8 9,11,12

9 11 9,10,11 9,11,12

18 22 14 20 24 16 13,14,16 17,18,20 21,22,24 14,15,16 18,19,20 22,23,24

18 22 14 16 20 24 13,14,16 17,18,20 21,22,24 14,15,16 18,19,20 22,23,24

9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12

5 7 5,6,7 5,7,8

2 6 10 4 8 12 1,2,4 5,6,8 9,10,12 2,3,4 6,7,8 10,11,12 1 5 9 11 3 7 1,2,3 5,6,7 9,10,11 1,3,4 5,7,8 9,11,12

2 6 10 4 8 12 1,2,4 5,6,8 9,10,12 2,3,4 6,7,8 10,11,12 1 5 9 11 3 7 1,2,3 5,6,7 9,10,11 1,3,4 5,7,8 9,11,12 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8

1 3 1,2,3 1,3,4

18 22 20 24 17,18,20 21,22,24 18,19,20 22,23,24 17 21 19 23 17,18,19 21,22,23 17,19,20 21,23,24 18 22 20 24 17,18,20 21,22,24 18,19,20 22,23,24

18 22 14 16 20 24 13,14,16 17,18,20 21,22,24 14,15,16 18,19,20 22,23,24

22 18 24 20 17,18,20 21,22,24 18,19,20 22,23,24 17 21 19 23 17,18,19 21,22,23 17,19,20 21,23,24 18 22 24 20 17,18,20 21,22,24 18,19,20 22,23,24

2 6 10 14 18 22 4 8 12 16 20 24 1,2,4 5,6,8 9,10,12 13,14,16 17,18,20 21,22,24 2,3,4 6,7,8 10,11,12 14,15,16 18,19,20 22,23,24 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4

5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8

9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12

14 16 13,14,16 14,15,16 13 15 13,14,15 13,15,16 13 15 13,14,15 13,15,16 13 15 13,14,15 13,15,16

18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 17 19 17,18,19 17,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 21 23 21,22,23 21,23,24

18 20 17,18,20 18,19,20 14 18 16 20 13,14,16 17,18,20 14,15,16 18,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24

2 6 10 14 18 22 4 8 12 16 20 24 1,2,4 5,6,8 9,10,12 13,14,16 17,18,20 21,22,24 2,3,4 6,7,8 10,11,12 14,15,16 18,19,20 22,23,24 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4

5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8

9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12

14 16 13,14,16 14,15,16 13 15 13,14,15 13,15,16 13 15 13,14,15 13,15,16 13 15 13,14,15 13,15,16

18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 17 19 17,18,19 17,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 21 23 21,22,23 21,23,24

18 20 17,18,20 18,19,20 18 14 20 16 13,14,16 17,18,20 14,15,16 18,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24

2 6 10 14 18 22 4 8 12 16 20 24 1,2,4 5,6,8 9,10,12 13,14,16 17,18,20 21,22,24 2,3,4 6,7,8 10,11,12 14,15,16 18,19,20 22,23,24 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4 1 3 1,2,3 1,3,4

5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8 5 7 5,6,7 5,7,8

10 12 9,10,12 10,11,12 9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12 9 11 9,10,11 9,11,12

14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 13 15 13,14,15 13,15,16

18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 17 19 17,18,19 17,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 21 23 21,22,23 21,23,24

14 16 13,14,16 14,15,16 10 14 12 16 9,10,12 13,14,16 10,11,12 14,15,16

18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24

2 6 10 14 18 22 4 8 12 16 20 24 1,2,4 5,6,8 9,10,12 13,14,16 17,18,20 21,22,24 2,3,4 6,7,8 10,11,12 14,15,16 18,19,20 22,23,24

6 1 8 3 5,6,8 1,2,3 6,7,8 1,3,4 1 5 7 3 1,2,3 5,6,7 1,3,4 5,7,8 1 5 3 7 1,2,3 5,6,7 1,3,4 5,7,8 1 5 3 7 1,2,3 5,6,7 1,3,4 5,7,8 6 1 8 3 5,6,8 1,2,3 6,7,8 1,3,4 2 6 4 8 1,2,4 5,6,8 2,3,4 6,7,8 6 1 8 3 5,6,8 1,2,3 6,7,8 1,3,4 5 1 7 3 1,2,3 5,6,7 1,3,4 5,7,8 5 1 7 3 1,2,3 5,6,7 1,3,4 5,7,8 5 1 7 3 1,2,3 5,6,7 1,3,4 5,7,8 6 1 8 3 5,6,8 1,2,3 6,7,8 1,3,4 2 4 1,2,4 2,3,4 1 3 1,2,3 1,3,4

10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12 9 11 9,10,11 9,11,12

14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 13 15 13,14,15 13,15,16

18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 17 19 17,18,19 17,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 21 23 21,22,23 21,23,24

10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12 9 11 9,10,11 9,11,12

14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 13 15 13,14,15 13,15,16

18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 17 19 17,18,19 17,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 21 23 21,22,23 21,23,24

10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12

14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16

18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24

6 10 14 18 8 12 16 20 5,6,8 9,10,12 13,14,16 17,18,20 6,7,8 10,11,12 14,15,16 18,19,20 6 10 14 18 8 12 16 20 5,6,8 9,10,12 13,14,16 17,18,20 6,7,8 10,11,12 14,15,16 18,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24

1 5 3 7 1,2,3 5,6,7 1,3,4 5,7,8 6 1 8 3 5,6,8 1,2,3 6,7,8 1,3,4 2 6 4 8 1,2,4 5,6,8 2,3,4 6,7,8 2 6 4 8 1,2,4 5,6,8 2,3,4 6,7,8 6 1 8 3 5,6,8 1,2,3 6,7,8 1,3,4 1 5 3 7 1,2,3 5,6,7 1,3,4 5,7,8 6 1 8 3 5,6,8 1,2,3 6,7,8 1,3,4

9 11 9,10,11 9,11,12

13 15 13,14,15 13,15,16

17 19 17,18,19 17,19,20

21 23 21,22,23 21,23,24

10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12 10 12 9,10,12 10,11,12 9 11 9,10,11 9,11,12

14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 14 16 13,14,16 14,15,16 13 15 13,14,15 13,15,16

18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 18 20 17,18,20 18,19,20 17 19 17,18,19 17,19,20

22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 22 24 21,22,24 22,23,24 21 23 21,22,23 21,23,24

10 14 18 22 12 16 20 24 9,10,12 13,14,16 17,18,20 21,22,24 10,11,12 14,15,16 18,19,20 22,23,24