An anagram of a siteswap is another siteswap that can made by rearranging the numbers in the siteswap. 630 and 603 are both valid siteswaps that are made from exactly the same set of numbers, so they are anagrams.

Some siteswaps, such as 534, don't have any anagrams. There are 6 different ways to arrange those three numbers, but three of them (354, 435, and 543) are not valid patterns, and the other three (345, 453, and 534) are just three different ways of writing the same pattern, not actual anagrams.

If the average of a set of whole numbers is a whole number, the numbers can be arranged at least one way to form a valid siteswap. The siteswap simulator JuggleSim has an anagram finder that will list all the permutations of a given string of numbers and letters that are valid siteswaps.

If the difference between two numbers in a siteswap is a multiple of the period of the siteswap, the pattern will remain valid if those two numbers are switched. For example, the period of 741 is 3, and the difference between 4 and 1 is 3, so those numbers can be switched to make another valid siteswap: 714. The difference between 7 and 4 and the difference between 7 and 1 are also multiples of 3, so there are actually three pairs of numbers in 741 that could be switched (7 and 4, 7 and 1, and 4 and 1), but these all result in the same anagram.

Juggling a siteswap in reverse often results in the same siteswap pattern, but sometimes the time-reverse of a siteswap is a different pattern, which is always an anagram of the original siteswap. To find the time-reverse of a siteswap, move each number in the siteswap that number of places to the right (move a 1 one place to the right, or a 2 two places to the right, etc.), and then read the resulting sequence backwards.

Example: Start with 12345, and move the numbers to the right to get 31425 (the 3 was moved three places to the right, to the spot just after the 5, which is the position of the 1 in the original pattern, and the 5 moving five places to the right in a period 5 pattern puts it back where it started), then read 31425 backwards to get 52413.

Anagram Siteswaps

Anagram Siteswaps

5 ball anagram siteswaps by Phillip Edwards

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