Take the 4 aces, 4 twos, 4 threes, and 4 fours from an ordinary deck of playing cards.
Is it possible to place all 16 cards in a row on a table so that there is precisely 1 card between any 2 successive aces, 2 cards between any 2 successive twos, 3 cards between any 2 successive threes, and 4 cards between any 2 successive fours?
Can an analogous placement be achieved if the 4 fives are included?
_A_A_A_
(where blanks represent other cards) will not have precisely 1 card between the 1st and 3rd aces, etc. $\endgroup$