Siteswap is the most commonly used juggling notation system. It is a useful tool for communicating between jugglers, discovering new patterns, and finding transitions between different patterns. It encodes the number of beats of each throw, which is related to their relative height, and the hand to which the throw is to be made. Throws are represented by positive integers that specify the number of beats in the future when the object is thrown again.
In basic siteswap patterns, each of the two hands throws in turn. A pattern can start with either hand, and then the throws alternate between hands: right-left-right-left-right-left... or left-right-left-right-left-right... Only one prop is thrown from one hand at a time, and only one prop is caught in one hand at a time. (More complex forms of siteswap notation that do not necessarily follow all of these rules exist, but are beyond the scope of this lesson.)
A siteswap pattern is a sequence of numbers (e.g. 531, 3, 91, 7441). Each number represents a type of throw to be done at that time or "beat" in the sequence. Odd numbers represent throws that cross from one hand to the other, and even numbers represent throws that are caught by the same hand that made the throw.
There are three numbers with special meanings: a "0" is a pause with an empty hand (the hand that would throw on that beat does nothing because it has nothing to throw), a "1" is a quick pass straight across to the other hand (also called a “handoff”), and a "2" is usually a pause with an object held in the hand that would otherwise throw on that beat (also called a “hold”).
Each of the numbers in a siteswap sequence corresponds to the number of beats later an object will be thrown again after the throw that number represents (including 1s and 2s as "throws"). This usually corresponds to how high it was thrown (higher siteswap number = higher throw). The throw heights are not proportional to the siteswap numbers, so a 6 is not just twice the height of a 3.
The sequence that defines a siteswap pattern can be repeated indefinitely, but a pattern is normally expressed in the shortest possible form (no repetition), so that the 5 ball cascade, which is tossed as "...5555555555...", is notated as just "5". Patterns containing more than one throw height, such as "...345345345...", can be written without repetition several different ways, but a siteswap is usually written so that it starts with the highest number, so the pattern is written as “534“, not "453".
Fun fact: the average of all the numbers in a site swap pattern = the number of objects that are juggled in the pattern (e.g. “7441” is a 4-object juggling pattern since (7+4+4+1)/4 = 4). All site swap patterns must therefore have a siteswap sequence that averages to an integer, or else the pattern is an invalid siteswap.
Let’s recap the various siteswap throws:
0 = "missing"/rest [empty hand]
1 = pass [crosses from one hand to the other]
2 = hold [no throw, stays in the same hand]
3 = a throw that crosses from one hand to the other, the same type of throw that you would use in a basic 3-ball juggling pattern (i.e. a 3-ball “cascade”)
4 = a throw that is thrown and caught by the same hand, the same type of throw that you could use in a basic 4-ball juggling pattern (i.e. a 4-ball “fountain”)
5 = a higher throw that crosses from one hand to the other, the same type of throw that you would use in a basic 5-ball juggling pattern (i.e. a 5-ball “cascade”)
6 = a higher throw that is thrown and caught by the same hand, the same type of throw that you could use in a basic 6-ball juggling pattern (i.e. a 6-ball “fountain”)
….and so on
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Geocache is not at the listed coordinates. In order to find this geocache, you will need to use the information above to analyze juggling animations in order to solve the puzzle. Feel free to reach out to me if you need a hint.
N38° A.BCD’ W94° E.FGH’
Identify the valid siteswap notation for each animation in order to solve for the coordinates:
A = [(
÷ 1111) + 
]-3
B = 
+ 5
C = 
(sum of the last 2 digits of the valid siteswap notation)
D = 
(2nd # in the siteswap notation for this pattern - bonus points if you can fully identify the proper siteswap notation just for fun 😜)
E = (
+ 
) ÷ 138.8
F = ( 
- 
) ÷ 16
G = The number following the *valid* siteswap
6316131 (0)
70304 (2)
H = 1+ [The number of objects juggled in the following siteswap pattern]
666060
A+B+C+D+E+F+G+H = 116