Project Euler

Quite recently, I stumbled upon this so called Project Euler, named after famed German Mathematician. It is a collection of challenging mathematical questions.
Here is the description from the website:

Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.

The motivation for starting Project Euler, and its continuation, is to provide a platform for the inquiring mind to delve into unfamiliar areas and learn new concepts in a fun and recreational context.

Good luck in trying some of the questions XD

Surprising Number Pattern

1 x 8 + 1 =9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

edit : taken from the book Math Wonders to Inspire Teachers and Students.

Interesting Pattern

Have you ever noticed this?

11^2 = 121

111^2 = 12321

1111^2 = 1234321

11111^2 = 123454321

...

111111111^2 = 12345678987654321

1111111111^2 = 1234567900987654321

and so on.

edit : taken from the book Math Wonders to Inspire Teachers and Students.

How true is this?

When I was bored enough during maths lesson, I jotted down some prime number and find something rather surprising. Prime number that is larger or equal to 7 can be re-represented as the sum of three prime numbers. in short, d = a+b+c where a,b,c and d are prime number and d≥7.

Some example up to prime number that is less than 100 would be :
7=2+2+3
11=2+2+7
13=3+3+7
17=5+5+7
19=7+7+5
23=11+5+7
29=23+3+3
31=23+3+5
37=31+3+3
41=31+5+5
43=31+5+7
47=37+5+5
53=43+5+5
59=53+3+3
61=31+13+17
67=61+3+3
71=61+5+5
73=67+3+3
79=73+3+3
83=73+5+5
89=79+5+5
97=41+37+19

Enough of spamming out of the blue.

Thanks to Mr Chew for correcting the mistake.