Let us choose the start point. Then for each k=1..670 we take 3k numbers from start point. For each sequence we have characteristic (a1,a2,a3), where a1 = number of "1" in sequence - k a2 = number of "2" in sequence - k a3 = number of "3" in sequence - k. a1 + a2 + a3 = 0. -10 < a1,a2,a3 < 20 How many does there exist such sets of a1, a2, a3? a3 depends on a1 and a2. It means that we can consider only a1 and a2. The total number is 31^2 = 961, but only part satisfies to our conditions. For example, if a1 = 20, then a2 = a3 = -10 is the only combination. So we can estimate the number of (a1, a2, a3) where: a1, a2, a3 > 0 is 0; only two numbers greater than 0 is 300; only one number greater than 0 is 330; all numbers equal 0 is 1; a1, a2, a3 < 0 is 0. Total 631 < 2010/3 = 670. It means that we have two equal sets (a1, a2, a3). Then difference between such sequences is the sequence which satisfies to the condition.