Prove that for all circle of radius $3^n$ we can have $7^n$ circles inside with a radius of 1 Prove that for all circle of radius $3^n$ we can have $7^n$ circles inside with radius of 1 and neither of them intersect.
For me, it sounds like using mathematic induction, but I have no clear idea or answer.

Yes, induction should work. The picture below should give you a hint why:

 

(the radius of the green circles is three times those of the red ones; the radius of the blue circle is three times those of the green ones)
