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AMC / AIME · Floor and Ceiling · AIME / USAJMO / AMO

Floor and Ceiling: (Proof track.) Give a complete justification. How many pairs math of positive integers satisfy math and math?

Integer parts.

Try the problem

**(Proof track.)** Give a complete justification. How many pairs

(m,n)

of positive integers satisfy

\lfloor m/n\rfloor=2

and

m\le10,n\le10

?

Hint and answer

Concept to use

Contest floors.

Hint

Replace the floor or ceiling with its sharp bounding inequalities.

Answer

10

More Floor and Ceiling problems

(Proof track.) Give a complete justification. Find the greatest integer less than math.
(Proof track.) Give a complete justification. How many positive integers math have math?

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