Andriiko has unlimited amount of chips painted in 6 colours. He wants to put some of the chips in one row so that for any two different colours in that row there are two adjacent chips of those colours. What is the minimum amount of chips he can put in a row?
Answer: 18.
Solution
The chip of each colour has to be adjacent at least 5 times, to each of other colour. But any chip has maximum 2 neighbours, thus there is at least 3 chips of each colour in a row. Here is an example that 18 is a correct answer: 123456246325164135.
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