# SuperUserDo

## Problem Statement

Fox Ciel just used the command "sudo" (super-user do) to gain administrative privileges in the UNIX-based operating system on her computer. She now wants to install several new programs. Each program has some dependencies: in addition to the program, the package manager has to install some libraries used by the program.
The package repository contains exactly 1000 libraries. For simplicity, we will number them from 1 to 1000, inclusive.
You are given the information about the dependencies of the programs Fox Ciel wants to install. More precisely, you are given the int[]s A and B, both containing the same number of elements. For each valid i, one of the programs needs all libraries that have numbers between A[i] and B[i], inclusive. Note that the programs may have overlapping dependences: multiple programs may require the same library to be installed. Of course, in such cases it is sufficient to install such a library once.
Calculate and return the total number of libraries that need to be installed.

# CodeForce Round#275 Div.2

## A. Counterexample

Your friend has recently learned about coprime numbers. A pair of numbers {a, b} is called coprime if the maximum number that divides both a and b is equal to one.

Your friend often comes up with different statements. He has recently supposed that if the pair (a, b) is coprime and the pair (b, c) is coprime, then the pair (a, c) is coprime.

You want to find a counterexample for your friend's statement. Therefore, your task is to find three distinct numbers (a, b, c), for which the statement is false, and the numbers meet the condition l ≤ a < b < c ≤ r.

More specifically, you need to find three numbers (a, b, c), such that l ≤ a < b < c ≤ r, pairs (a, b) and (b, c) are coprime, and pair(a, c) is not coprime.

# AIO2006 Solution

## Fashion Statement

In the latest trend of skin-tight jeans and slimline handbags, having a bulging wallet or purse is simply a fashion crime. You are faced with a dilemma: either you find yourself disowned by your fashion-conscious friends, or risk carrying too little money for your taxi ride home.

You wish to carry the exact amount of money for your taxi ride (in case you are mugged or otherwise lose it). However, you also wish to use as few notes as possible to avoid being ridiculed by your friends. The notes available to you come in denominations of \$1, \$5, \$20 and \$100 (you never carry coins, which are simply far too bulky).

For example, if your taxi fare costs \$67, the smallest number of notes you can carry is six — this is achieved by carrying three \$20 notes, one \$5 note and two \$1 notes (20+20+20+5+1+1 = 67).

Your task is to determine the smallest number of notes you need to carry in order to make up a given taxi fare.

# AIO2009 Solution

## Travelling Salesperson

Even in uncertain economic times, no home can be without electrical appliances. Realising that there is still a sales opportunity, you have recently taken up a part-time job selling electrical appliances the old fashioned way--travelling door to door. However, your hometown of Perth is full of electrical salespeople who have cornered the market, and so you must travel across Australia to find customers.

You will start in your hometown, Perth, drive across Australia to Sydney, and then back again to Perth. There are three routes between Perth and Sydney. In your market research, you have counted the number of customers living along each route. You wish to plan your trip to Sydney and back so that you visit the greatest number of customers possible. You must take a different route on the return journey, otherwise you would simply end up visiting the same satisfied customers twice.

Your task is to write a program which, given the number of customers along each of the three routes between Perth and Sydney, determines the greatest number of customers you can visit by travelling from Perth to Sydney and back.