MathDB

5

Part of 2005 AIME Problems

Problems(2)

Coin Arrangements

Source:

11/10/2005
Robert has 4 indistinguishable gold coins and 4 indistinguishable silver coins. Each coin has an engraving of one face on one side, but not on the other. He wants to stack the eight coins on a table into a single stack so that no two adjacent coins are face to face. Find the number of possible distinguishable arrangements of the 8 coins.
countingdistinguishabilityfactorial
Ordered Pairs and Logarithms

Source:

11/13/2005
Determine the number of ordered pairs (a,b)(a,b) of integers such that log⁡ab+6log⁡ba=5\log_a b + 6\log_b a=5, 2≤a≤20052 \leq a \leq 2005, and 2≤b≤20052 \leq b \leq 2005.
logarithmsfloor function