Word distance metrics in one of the following databases:

• Corpus of Contemporary American English (COCA)
• American National Corpus

Make a definition of distance between words. For instance, you could use the number of occurrences of $A$ and $B$ exactly 9 words apart, divided by the number of occurrences of $A$ and $B$ at most 9 words apart.

Select 10 words (or more) and compute all distances between them.

Check whether your distance $d(A,B)$ satisfies the following axioms for a metric (if they don’t, your definition may still be okay if it has other nice features):

$d(A,A)=0$

$d(A,B)=d(B,A)$

$d(A,B)\le d(A,C)+d(C,A)$

Make a graphic representation of the 10 words so that words $A$ and $B$ are close to eachother in the graphic if $d(A,B)$ is small.

There are many articles available about Rubik’s cube but not as many about the simpler pocket cube (2x2x2).

Note 2021: This is not really true anymore, see https://www.rubiks.com/media/guides/RBL_solve_guide_MINI_US_5.375×8.375in_AW_27Feb2020_VISUAL.pdf

Here are some draft instructions:

First solve the white side.
Get two of same color in the layer
Face the opposite two and have white face up.
Do:
$$
R^{-1} D R L D^{-1} L^{-1} R^{-1} D R
$$
Now we have the layer.

Now to swap two corners (recall that yellow should be opposite white),
face them towards you and do
$$
L^{-1} U^{-1} L F U F^{-1} L^{-1} U L U^2
$$

Then finally do (with problem corners facing you and white at bottom)
$$R U R^{-1} U R U^2 R^{-1} U^2
$$
(possibly repeat)

But if two already solved put solved corners furthest away from you
do $R U …$

If not done yet,
put the newly solved bottom *right* in bottom *left* and repeat $R U…$ maybe twice (this may intermittently mess up the two solved ones!).

Added 2020: If you have one correct corner and three incorrect, face one correct and one incorrect, not two incorrect ones (maybe).

To complete this project, your write-up will have to show exactly how the algorithm works on a couple of random cubes that I provide.