# Find The Largest X

Number Theory Level 5

Find the largest positive integer $$X$$ for which there exist $$X$$ triples $$(a_1, b_1, c_1), (a_2, b_2, c_2), \cdots , (a_X, b_X, c_X)$$ consisting of non-negative integers such that:

• For all $$1 \leq i \neq j \leq X,$$ $$a_i \neq a_j, b_i \neq b_j, c_1 \neq c_j.$$

• For all $$1 \leq i \leq X,$$ $$a_i+b_i+c_i= 2014.$$

Details and assumptions

• This problem is not original.
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