March, 2005

The Last Digits

Find the last three digits in the number 3³⁸⁴¹.

Pack 7

A circle packing in a circle is an arrangement or packing of smaller circles inside the larger such that no two smaller circles overlap and some (or all) are mutually tangent.  It is known that the smallest diametered circle in which 6 unit circles can be packed is a circle with diameter 6 units.  Find the smallest diametered circle in which 7 unit circles can be packed.