What's going on with the math?
Color groups for a perfect shuffle of 278 cards (mod 279)
Did you get...
1 color group of size 2
1 color group of size 6
6 color groups of size 5
8 color groups of size 30
The factors of 279 are 3² · 31. From the prime modulo table we know that the factor 3 will contribute
a color group of size 2, and the factor 31 will contribute 6 color groups of size 5.
Because there is a second power of 3, there is also a color group 3 times the size of the original
color group created by the factor 3. So there is a color group of 6.
The remaining cards divide into color groups the size of the least common multiple of the color groups
already included. The least common multiple of 2 and 5 and 6 is 30, so the remaining cards form 8
color groups of 30.
Now if you have been following my explanation of the math, I imagine two questions are coming to mind.
How the heck did you figure all that out?
Good question. See the who came up with this brilliant idea page to learn more about me, my math
senior project, and how I came to knit math scarves.
Ok, so now I can determine the how many color groups of what sizes will be created by a perfect shuffle
of a given number of cards. But if I want to knit a perfect shuffle scarf how do I know which color
goes where?
Another great question. See the knit your own perfect shuffle scarf. to learn how I actually design the scarves I knit.
Page 1 2 3 4 5
Color groups for a perfect shuffle of 278 cards (mod 279)
Did you get...
1 color group of size 2
1 color group of size 6
6 color groups of size 5
8 color groups of size 30
The factors of 279 are 3² · 31. From the prime modulo table we know that the factor 3 will contribute
a color group of size 2, and the factor 31 will contribute 6 color groups of size 5.
Because there is a second power of 3, there is also a color group 3 times the size of the original
color group created by the factor 3. So there is a color group of 6.
The remaining cards divide into color groups the size of the least common multiple of the color groups
already included. The least common multiple of 2 and 5 and 6 is 30, so the remaining cards form 8
color groups of 30.
Now if you have been following my explanation of the math, I imagine two questions are coming to mind.
How the heck did you figure all that out?
Good question. See the who came up with this brilliant idea page to learn more about me, my math
senior project, and how I came to knit math scarves.
Ok, so now I can determine the how many color groups of what sizes will be created by a perfect shuffle
of a given number of cards. But if I want to knit a perfect shuffle scarf how do I know which color
goes where?
Another great question. See the knit your own perfect shuffle scarf. to learn how I actually design the scarves I knit.
Page 1 2 3 4 5