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# Stringing it Out

##### Age 14 to 16Challenge Level The invitation is for you to explore the following transformations and comment on what you find:

### First

T(x) = y
T(y) = xy

This transformation has the following successive effect (starting with x):

x
y
xy
yxy
xyyxy
...
...

### Next

R(x) = xy
R(y) = z
R(z) = xy

This transformation has the following successive effect:

x
xy
xyz
xyzxy
xyzxyxyz
...
...

### Then

S(w) = wx
S(x) = y
S(y) = wz
S(z) = y

This transformation has the following successive effect:

w
wx
wxy
wxywz
...
...