The Pencil Predicament

The Flaming Chickens
Topic: Number Theory
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A bandit takes Faith's pencils and the Detective goes in to investigate. Faith doesn't remember how many pencils she had, but does remember one was always left over when she grouped them into groups of 3, 4, 5 ,and 6. Can the Detective solve the case and catch the bandit?

Common Core Standards: SMP
Problem #: 
249 (2015-2016)
Problem Difficulty Level: 6 [?]