MathDB

1

Part of 2005 AIME Problems

Problems(2)

Tangent Circles and Area

Source:

11/10/2005
Six circles form a ring with with each circle externally tangent to two circles adjacent to it. All circles are internally tangent to a circle CC with radius 3030. Let KK be the area of the region inside circle CC and outside of the six circles in the ring. Find ⌊K⌋\lfloor K \rfloor.
geometryfloor function
A Deck of Cards

Source:

11/13/2005
A game uses a deck of nn different cards, where nn is an integer and n≥6n \geq 6. The number of possible sets of 66 cards that can be drawn from the deck is 66 times the number of possible sets of 33 cards that can be drawn. Find nn.