How to select groups of numbers with the same sum from an array

Question

Hi Guys , Well i have a probleme with some puzzles , However i want to solve this puzzle and i need your help , i have an array from ten Numbers(Or More),for example :

arr[1,2,3,4,5,6,7,8,9,10]

i want a method to check if 3 numbers from this arrays have the same sum to another 3 numbers (I want to get all the possibilities ! ) , for example :

{1.8.10} {2.10.7} {3.7.9} {4.9.6} {5.6.8} {The sum Is : 19}

{1.6.10} {3.10.4} {5.4.8} {7.8.2} {9.2.6} {The Sum Is : 17}

{6.3.5} {7.5.2} {8.2.4} {9.4.1} {10.1.3} {The Sum IS :14}

Update:

That's another example to what exactly i want to do !

Or :

N.B : This is not a home work !