Then, the following Sunday and every Sunday thereafter, she removed one card from the deck, and either counted or calculated the number of points remaining in the deck. As a result, on Sunday, December 31, after she discarded the last card, there were zero points left in the pack, and zero days left to the year.
In fact, every alternate Sunday, starting January 1, then January 15, etc., she made the point count remaining in the pack equal to the number of days remaining still to be seen in the year. But it's the other Sundays that make the problem interesting. On those Sundays, starting with January 8, she made sure that the number of points remaining in the deck after the removal was either a palindrome, a perfect square or a perfect cube (including allowing fitting into more than one of these categories, possibly at times even also matching the count of remaining days in the year).
Each time she discarded the first king of a given color, the very next week she discarded the other king of the same color.
On which four dates did she discard the sixes?