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I have been attempting for the past few days to figure out the order for giant crystal on Learning #22 (the end of the world). Although the presence of seven fruits makes an intimidating 5040 possible combinations in which to kill them, after repeated trials of the technique of hiding enemy (thank you Kaha), I was able to discern the following information:

(They are labeled according to these images.)

1) The last four to be killed are (in this order): M, L, LU, R.
2) RD is to be killed before RU.

These two bits of information (which can be confirmed through trials of Kaha's technique) yield only three possibilities for order:

a) RD RU LD M L LU R
b) RD LD RU M L LU R
c) LD RD RU M L LU R

Since it is impossible for LD to mix with RD or RU, we cannot select one of these three without actually trying them out. Hence, I tried all three out.

All this said, I regret to announce that there is no giant black crystal (or any, for that matter) at the end of the world. (This was to some extent expected, considering there is no giant crystal on any other level in the first half of Learning Mode.

(I thank the famous Kahakatashi for discovering the technique used here, and I thank my friend ameoba940550 for showing me how to find the end of the world.)