In how manys can we select three of six lengths 1,2,3,2001,2002,2003 to build a triangle?

Question

Math kangaroo competition question

Answer 1

|b-c|<a<b+c where a, b and c are the sides of the triangle. |...| means absolute value. In words, this is: the length of any side must lie between the sum and difference of the other two sides.

The number set {1 2 3} does not satisfy the condition, so a triangle cannot be made.

The number set {a b c}={2001 2002 2003} satisfies the condition and so do:

{2 2001 2002}; {2 2002 2003}; {3 2001 2002}; {3 2002 2003}; {3 2001 2003}.

6 different sets of 3.