IBM Ponder This #196 · August 2014

We are trying to solve an optimization problem,

Let's assume that correct answer is defined as an integer number between 51 to 150 cm (inclusive).

You can use a black box solver to answer the question: "is the correct answer at least X?"

If the answer is positive - it costs you one cent, but if not - it costs you 10 cents.

Assuming that the answer is uniformly distributed (i.e., every number has the same probability) and using the most efficient strategy, how much will it cost, on average, to solve the problem?

Solution

Best opened after a real attempt

To be added.