As I started crocheting the 65th square of my Granny blanket, I was struck by the fact that I had not yet used the colour combination I'd chosen for that particular square!
I have 13 colours (plus cream for the centres). Does that mean 13x13=169 different colour combinations? Now, maths was never my forte at school so the clever-with-numbers people out there can laugh at me! But then since you can also reverse the order of colours - ie. which colour you choose for the second & third and the fourth & fifth rounds (there are 5 rounds altogether - first round being always cream), does that mean 169x2???
Come on guys help me out here! I'd like to know how many different squares I can make with two colours per square, 13 colours, and the variation of using which colour first and which second. Does that make sense, can anyone give me an answer??
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| With the same two colours, you can make two different squares |
Meanwhile the blanket grows…
and it's already nice to snuggle under as I work on it.
...That's when my son's not stealing it!
The mix of cheerful colours
brightens up our grey January…
Best wishes,
Frivole
That's beautiful, what a wonderful afghan. I'm not a math expert either, but here's my guess. If you use Color #1 as the inner round, you can make 12 squares using all the others as the outer round. So, 12 x 13 is my guess.
ReplyDeleteThose beautiful colors would liven things up around here with all the huge white piles of snow! :) Beautiful blanket!!! :)
ReplyDeleteI think you have it correct, because of the combinations of all thirteen colors I do believe it is 169 X 2 this is really nice and looks warm too! :}
ReplyDeleteI am no good at maths but I think you are right, your blanket looks lovely and really colourful in this dull wet winter.
ReplyDeleteMargaret
As a statistician, I can assure you that if you have 13 choices of color and want to use two without repeating them but order matters, that you have 13 X 12 = 156 squares possible. If you did not want to repeat a pair (that is Red/Blue would be equivalent to Blue/Red), you would have half that number or 78 possible combinations. What you are seeing is a permutation of 2 items from 13 for the first scenario and a combination of 2 items taken from 13 in the second. Blessings, Susie
ReplyDeleteThat sounds pretty official coming from a statistician! Thank you Susie. I'll go for 156 then. Which means I could make the whole blanket without repeating a single square! It also means there are still many square combinations I've not tried! How exciting.
DeleteI think your number is going to be 13x12 or 156 combinations. You start by picking any of the 13 colors. To make it 2-colored you only have the other 12 colors to choose from. Combinatorics says you multiply 13 by 12 making 156 possibilities. I think this number covers doing the reverse order because either could come up first in the original pool of 13 leaving the unchosen color of a given pair still in the pool of 12. It's a little confusing. I'd have to draw a diagram to see if my reasoning is correct. There is a chance you need to multiply the 156 by 2 to account for the order of use. I'll take a few minutes and work it out.
ReplyDeleteYes, I still can't quite get my brain around this problem! It seems to me the number should be doubled to account for the order of use… and I don't know why it isn't!
DeleteI just made myself a chart-- the original 13x12=156 accounts for all combinations including reversing the order in which you use the colors. The tan in the center is constant and so is not included in the calculation.
ReplyDeleteWhew! I'm definitely not a mathemetician, but that's a LOT of possibilities. The blanket looks lovely. Working on something *warm* during cold weather is nice, too. ;-)
ReplyDeleteNot adding to the helpful comnents here, but if you are still stuck after all the input, shoot me an email. : ))
ReplyDeleteIt is a gorgeous Granny -Square blanket!
Fox : )
Thank you guys, I knew you'd come to the rescue!
ReplyDeleteYou're looking for combinations and permutations. There is a formula for both - handy for working out your chances of winning Lotto as well. For example:
ReplyDeletehttp://www.mathwords.com/c/combination_formula.htm
(Which also has a link to permutations at the bottom).
Here's a link to a calculator that works out both for you at once:
http://easycalculation.com/statistics/permutation-combination.php
You have 156 permutations and 78 combinations if you want to choose every which way there is of 2 colours from 13 - depending on whether colours, say, 9 and 3 count as different to colours 3 and 9.
(I thought you may as well get the formula and a calculator in case you need to do this again). :-D