Greatest Integer Function

Floor and fractional-part identities, classic [.]-based olympiad problems.

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Q1 · Greatest Integer Function · EASY
What is the value of ⌊4.7⌋ + ⌊−2.3⌋, where ⌊·⌋ denotes the greatest integer function?
Q2 · Greatest Integer Function · MEDIUM
How many integers x satisfy the equation ⌊x/3⌋ = 5?
Q3 · Greatest Integer Function · HARD
Find the sum ⌊√1⌋ + ⌊√2⌋ + ⌊√3⌋ + ... + ⌊√100⌋.