This one needs its own post

President Obama hosts the MATHCOUNTS winners!

Question: If you start with $1 and, with each move, you can either double your money or add another $1, what is the smallest number of moves you have to make to get to exactly $200?

Mark Sellke, an 8th grader at Klondike Middle School in West Lafayette, Indiana, correctly answered this question in less than 45 seconds this past May to become the 2010 MATHCOUNTS individual champion.

Yesterday, President Obama met with Mark, the winning MATHCOUNTS team from California, and the individual runner-up of the competition. During their visit to the White House, these elated “mathletes” talked to the President about their aspirations—including working for NASA and becoming a math professor. The President congratulated the students on their accomplishments and emphasized the importance of science and math to the Nation’s economy, security, and competiveness. He also confessed to a more parochial pleasure in getting to know them, declaring that he would be calling upon them next time Sasha or Malia stumped him with a math homework question. [...]

That’s one reason why the President launched the “Educate to Innovate” campaign to motivate and inspire students to excel in science, technology, engineering, and mathematics (STEM). That campaign has already helped to raise more than $500 million from the private, nonprofit, and philanthropic sectors for the creation of innovative public-private partnerships to attract, develop, reward, and retain outstanding educators in STEM subjects.

Note: to answer the question, write 200 in binary and count the number of 2′s:

200 = 128 + 64 + 8 = 2^7 + 2^6 + 2^3 = 2^3(2^4+2^3 + 1)= 2^3(2^3(2+1)+1)
So, in all, this is
double, then add 1, then double thrice, add 1, double thrice which is 9 moves.

Easy, huh?

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