MathDB

2

Part of 2010 Malaysia National Olympiad

Problems(3)

OMK 2010

Source: Malaysia National Olympiad 2010 Bongsu Category Problem 2

6/4/2011
A student wrote down the following sequence of numbers : the first number is 1, the second number is 2, and after that, each number is obtained by adding together all the previous numbers. Determine the 12th number in the sequence.
inductioncombinatorics unsolvedcombinatorics
OMK 2010

Source: Malaysia National Olympiad 2010 Muda Category Problem 2

6/4/2011
A meeting is held at a round table. It is known that 7 women have a woman on their right side, and 12 women have a man on their right side. It is also known that 75% of the men have a woman on their right side. How many people are sitting at the round table?
combinatorics unsolvedcombinatorics
OMK 2010

Source: Malaysia National Olympiad 2010 Sulung Category Problem 2

6/4/2011
Find xx such that 2010log⁡10x=11log⁡10(1+3+5+⋯+4019).2010^{\log_{10}x}=11^{\log_{10}(1+3+5+\cdots +4019).}
logarithmsalgebra unsolvedalgebra