Ponder This Challenge:

What is the minimal number, X, of yes/no questions needed to find the smallest (but more than 1*) divisor of a number between 2 and 166 (inclusive)?

We are asking for the exact answer in two cases:

In the worst case, i.e., what is the smallest number X for which we can guarantee finding it in no more than X questions?

On average, i.e., assuming that the number was chosen in uniform distribution from 2 to 166 and we want to minimize the expected number of questions.

* For example, the smallest divisor of 105 is 3, and of 103 is 103.

Update (11/05): You should find the exact divisor without knowing the number and answering “prime” is not a validCitation-

http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/pages/index.html

A maths challenge by the boys in Blue above and also in employement news, the parent company of SPSS is opening a centre of advanced analytics right here in Washington D.C.

WASHINGTON - 10 Nov 2009:IBM (NYSE: IBM) today announced the opening of the sixth in a network of analytics solution centers – this one dedicated to helping federal agencies and other public sector organizations extract actionable insights from their data.The new IBM Analytics Solution Center in Washington, D.C., will draw on the expertise of more than 400 IBM professionals. These will include IBM researchers, experts in advanced software platforms, and consultants with deep industry knowledge in areas such as transportation, social services, public safety, customs and border management, revenue management, defense, logistics, healthcare and education. IBM also plans to add an additional 100 professionals, through retraining or new hiring, as demand grows.