Puzzle series: Addition of Four Primes

Miguel — Sat, 05 Jan 2008 15:28:00 GMT

Ok, after a vacation week I am back, this is my first post of 2008 and also my first post with the new look&feel of the website. I wish all of you a Happy New Year and also hope you like the new website design...

Let's continue on our series about Algorithms and Math puzzles. I want to propose you to take a look at prime numbers.

There are some conjectures that state properties of these numbers. One of those conjectures is the Waring's prime number conjecture, it states that every odd integer is either prime or the sum of three primes.

Probably, the most famous conjecture about prime numbers is the Goldbach's Conjecture, and claims that every even integer is the sum of two primes.

Both problems have been studied for over 200 years...

In this problem, you have a little different task: You have to find a way to express a given integer as the sum of four primes (exactly four).

Consider an input of an integer (n<10000000), you should return a list with the four prime numbers. If it is impossible to represent that, you can give as output any illogical result (i.e: -1 -1 -1 -1)

Example:

Input: 24
Output: 3 11 3 7

As you can see, you can repeat prime numbers as factors for a given input, and it does not matter if the list of factors is ordered or not.

What kind of algorithm would you implement? Is it efficient? Remember: Most powerful weapons of human's mind are Mathematics and Logic ;-)

Enjoy and comment, good luck folks! :-)

Switching our Christmas tree bulbs

Miguel — Wed, 26 Dec 2007 00:55:00 GMT

Hi there,

I want to propose you a kind of algorithm/mathematics problem, mixed with some fun related with this Christmas period... :-)

Imagine that you have a big Christmas tree with 365 light bulbs, each one with a switch, tagged with correlative numbers from 1 to 365. During December 25th on 2006, you looked at the tree and saw all lights OFF, so you decided to switch them but in a particular way.

Each day of the year (assuming 365 days) you would change the state of each switch just one time, according to a certain rule. The rule is that during the day “n” I will only switch those bulbs tagged with a number multiple of this “n” value.

Giving you an example to clarify this criteria:

1^st day: All bulbs multiple of 1. So, all bulbs. (the tree was beautiful that night, completely lightened)

2^nd day: All bulbs multiple of 2. So… #2, #4, #6, #8… (notice that this day all bulbs multiple of 2 were switched off)

3^rd day: All bulbs multiple of 3. So… #3, #6, #9…

Last day: All bulbs multiple of 365. So… only the #365.

Assuming that anything strange happens and nobody except you touches the switchs, which bulbs will be ON today? How would you determine it?

Merry Christmas from the whole Channel 8 Team :-)

Entries tagged with puzzles - Channel 8

Puzzle series: Addition of Four Primes

Switching our Christmas tree bulbs