We are proud to announce that on June 19^{th} Celfocus will be at the JNation Event taking place in Coimbra.

The JNation Conference is about bringing together technology enthusiasts from all over the world with a passion for Java. For a full day, visitors will get the chance to hear well-known speakers talk about Java and JVM related technologies, frameworks, tools, programming languages, cloud, internet of things and many more.

Celfocus will be there to meet you all and introduce you to some of the latest and most innovative projects and solutions we have been working on in Telecom Operators across the globe.

**If you are attending JNation Event, don’t miss out on the Celfocus Oculus Go Challenge!**

To celebrate this initiative, Celfocus is giving away an Oculus Go VR Headset.

Here’s what you have to do!

### Exercise 1 (Easy) - Counting Sundays

**How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)?**

Use this information or more (should you decide to research):

- 1 Jan 1900 was a Monday.
- September, April, June and November has thirty days;

All the rest have thirty-one, Expect February;

Which has twenty-eight, rain or shine;

And on leap years, twenty-nine. - A leap year occurs on any year evenly divisible by 4, but not on a century unless it is divisible by 400.

*The correct solution of this exercise gives 1 entry for the challenge.*

### Exercise 2 (Medium) - Exploring the number of different ways a number can be expressed as a sum of powers of 2

**Define f(0)=1 and f( n) to be the number of different ways n can be expressed as a sum of integer powers of 2 using each power no more than twice. **

For example, f(10)=5 since there are five different ways to express 10:

- 1 + 1 + 8
- 1 + 1 + 4 + 4
- 1 + 1 + 2 + 2 + 4
- 2 + 4 + 4
- 2 + 8

What is f(10^{25})?

*The correct solution of this exercise gives 10 entries for the challenge.*

### Exercise 3 (Medium) - Path sum: two ways

In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by only moving to the right and down, is indicated in bold red and is equal to 2427.

Given a 20 by 20 matrix in a text file named matrix.txt, find the minimal path sum, from the top left to the bottom right by only moving right and down.

*The correct solution of this exercise gives 5 entries for the challenge.*

**Exercise 4 (Hard) - Path sum: four ways**

In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by moving left, right, up, and down, is indicated in bold red and is equal to 2297.

Given a 20 by 20 matrix in a text file named matrix.txt, find the minimal path sum, from the top left to the bottom right by moving left, right, up, and down.

*The correct resolution of this exercise gives 5 entries for the challenge*

All Exercices are taken from Project Euler.