Painting New Construction

The construction foreman at Bayview is overseeing 20 houses arranged in 4 rows of 5. It would take 1 full day to paint each house, and he has 20 days to paint all the houses. To avoid a buildup of toxic paint fumes, he wants to maximize the minimum number of days between which 2 adjacent (vertically, horizontally or diagonally) houses have been painted. What is the maximum number of days?

For example, if the above diagram indicates the day in which those houses were painted, then the minimum number of days in which 2 adjacent houses were painted is 2. The houses numbered 4 and 6 and were painted 2 days apart.

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