When two colours are used there are two combinations: AB, BA
For three colours there are six combinations:
ABC, ACB, BAC, BCA, CAB, CBA
Four colours combine in 24 ways:
ABCD, ABDC, ACBD, ACDB, ADBC, ADCB
BACD, BADC, BCAD, BCDA, BDAC, BDCA
CABD, CADB, CBAD, CBDA, CDAB, CDBA
DABC, DACB, DBAC, DBCA, DCAB, DCBA
Five colours are combined in the 120 ways - as shown in this afghan.
Mathematically, Take Five is closely related to Have It All Ways.
It is all the possible permutations of five colours.
The number of combinations for four colours is
4 x 3 x 2 x 1 = 24
For five colours the number of combinations is
5 x 4 x 3 x 2 x 1 = 120
If six colours were used there would be
6 x 5 x 4 x 3 x 2 x 1 = 720
It is essential to use a logical plan to make sure none of the combinations are missed. There is more than one way of doing this.
The method that we used can be seen by looking at the squares across the bottom, starting at the left-hand corner. A sequence was chosen for the first square and in the next four squares that sequence was kept the same but ‘rolled round’ so that the top stripe goes off the top and comes back on at the bottom. The ‘rolling round’ is complete on the fifth square. For the sixth square the order of the top three colours was kept the same, the other two colours were swapped over. This sequence was then ‘rolled round’ for the other four squares. A similar system was used for all the other rows. The colours of the rolling stripes can be seen as sloping gently up to the right.
Use any yarn, in five colours, and needles of your choice. The colours must be noticeably different.
The overall size of the afghan will vary according to the yarn chosen.