What is the rule for adjective order?
- I saw an abandoned cute little kitten.
- I saw a cute abandoned little kitten.
Which sentence is correct? What is the rule for using consecutive adjectives in English?
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As other answers have testified, the ordering of adverbs and adjectives in English is much down to personal taste. My favoured order would be "abandoned cute little kitten" because it lets you tie "cute little kitten" together (which is probably what you want), and then tagging that whole description with "abandoned".
There is a degree of flexibility in the ordering of adjectives, but a frequent order is this, given in ‘An A-Z of English Grammar and Usage’ by Leech and others:
Cute expresses objective feeling towards the kitten, so would come first according to that schema. Little clearly expresses size and would come second. Abandoned classifies the kitten, and so can be considered defining and would be last. This analysis produces the sentence that Flexo has provided.
I wouldn't use either of those options. I would say:
I'm not sure why, that's just my intuition.