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The letters of the alphabet can be arranged in four different groups. The first 13 letters establish the categories:
AM
BCDEK
FGJL
HI
Place the remaining 13 letters in their proper categories.
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THE
SOLUTION
AMTUVWY=symmetry about vertical axis, BCDEK=symmetry about horizontal axis, FGJLNPQRSZ=no symmetry and HIOX=symmetry about both axes.