Find the duplicate

You are given an array of 2n + 1 numbers. Out of these 2n + 1 numbers, 2n are duplicate. You are supposed to find the number which is not duplicate.

Inroduction to Statistics

Statistics is a commonly used word and also a commonly misunderstood one. Statistics in its full scope encompasses collection, organization, summarization, presentation, analysis of data, drawing valid conclusions and taking actions based on it. In this way, statistics provide a concrete and axiomatic way approach of interacting with our environment based on the observations. At the core, statistics is merely commonsense defined axiomatically, so that you don't require commonsense to understand commonsense.

In a more restrictive sense, statistics means the observations and numbers derived or based on the observations. Observations are also referred as data so we can regard statistics as data and the number based on the data.

We however prefer the former definition of statistics as it clearly highlightsnot only the means but also the ends of the statistics.

Breaking into pieces

You are given a iron rod, whose weight is 40 kg. You are supposed to make four pieces such that employing only those four pieces and a weight balance, you should be able to weigh all the integral weights from 1 to 40. What are the four weights ?

The problem is an interesting one and involves a subtle application. Please do not come up with a solution devised by combinatorial exhaustion of choice because as an adversory I can introduce heavier iron rods, which will sink the ship of combinatorial exhaustion.