Hakuna Matata

Problematized !!

The product I'm working on has its beta release somewhere in November. Design, Development, Testing & Debugging everything is going hand in hand in my module(having just two guys). Under such a hectic scene, my plan to goto Delhi has made the matters worse. Have been working late and during the weekend too :( trying to wrap things up before I leave.

In the middle of all this, I found myself killing a lot of time in some mathematical problems which came through Sundar last week. One of them was a fundoo programming excercise...

Let S = {1, 2, 3, …, 3n}. We define a sum-3-partition of S to be a collection of n disjoint 3-subsets of S, Ai = {ai, bi, ci}; i = 1, …, n such that the union :
A1 U A2 U…An = S. Within each triple Ai, some element is the sum of the other two.
For example: {1, 5, 6}, {2, 9, 11}, {3, 7, 10}, {4, 8, 12} is a sum-3- partition of {1, 2, 3, …, 12}.
(a) Find a sum-3-partition for {1, 2, 3, …, 15}.
(b) Prove that there exists no sum-3-partition for n = 1998.

Thanks Sundar,
**Its impossible to thoroghly enjoy solving such problems unless one has plenty of work to do.

posted by Praveer @ Wednesday, October 13, 2004