#math
7 problems

Return true if input is a Prime number
You are given n, a positive integer. Return true if n is a prime number, and false if it's not.

Extreme Recursion with Binary Tree Topologies
How many binary tree topologies are possible given n nodes?

Find the missing element in a randomized range of numbers
I take n consecutive integers, toss one of them out and mix up the remaining n1 integers as completely unsorted. Find the missing integer.

Prisoner's Dilemma With Blindfolds: a math teaser
Seven people are blindfolded and given unique colored hats at a roundtable. How should they cooperate for at least one to guess her own color?

MapReduce parallel processing of all known URLs for median length
You are given the data set of all Google crawled URLs on the Internet  that's a very large set. Write an algorithm to find the median URL length.

Getting paid for seven days with a single bar of gold
An employer hires you to work for 7 days and has a gold bar with 7 segments to pay you with. How do you get them to not break it to pieces?

Find the odd ball among eight balls
You are given eight balls that look exactly the same, and a balance to weigh them against each other. Find the odd ball by weighing only twice?