motley

[mot-lee] Origin

mot·ley

[mot-lee] adjective, noun, plural mot·leys.
adjective
1.
exhibiting great diversity of elements: a motley crowd. heterogenous, varied, diverse, mixed, assorted, sundry; incongruous, disparate, diversified, dissimilar, divergent. homogeneous, uniform, identical; similar, like.
2.
being of different colors combined: a motley flower border. parti-colored, multicolored, variegated, polychromatic; pied, piebald, mottled, dappled. monochromatic; solid.
3.
wearing a parti-colored garment: a motley fool.
noun
4.
a combination of different colors.
5.
a parti-colored effect.
6.
the parti-colored garment of a jester.
7.
a heterogeneous assemblage.
8.
a medley. conglomeration, hodgepodge, jumble, miscellany; olio, potpourri, pastiche, gallimaufry, farrago.

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Motley is a TOEFL word you need to know.
So is formulate. Does it mean:
the act or manner of managing; handling, direction, or control
to express in precise form; to devise or develop, as a method to express in a formula

Origin:
1350–1400; Middle English; see mote1, -ly
Dictionary.com Unabridged

Mot·ley

[mot-lee]
noun
John Lo·throp [loh-thruhp] , 1814–77, U.S. historian and diplomat.
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2012.
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Collins
World English Dictionary
motley (ˈmɒtlɪ)
 
adj
1.  made up of elements of varying type, quality, etc
2.  multicoloured
 
n
3.  a motley collection or mixture
4.  the particoloured attire of a jester
5.  obsolete a jester
 
[C14: perhaps from mot speck, mote1]

Collins English Dictionary - Complete & Unabridged 10th Edition
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Etymonline
Word Origin & History

motley
late 14c., from Anglo-Fr. motteley, probably from O.E. mot "speck" (see mote). "Diversified in color," especially of a fool's dress. Hence, allusively, "a fool" (1600).
Online Etymology Dictionary, © 2010 Douglas Harper
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