Consecutive towers are built.
The $1^\text{st}$ tower has one floor made of two cards.
The $2^\text{nd}$ tower has two floors made of seven cards.
The $3^\text{rd}$ tower has three floors made of fifteen cards, and so on.
How many cards will the $1000^\text{th}$ tower have?
+128474 It appears that the number of "upright" cards in any tower N = (N) (N + 1)
And it appears that the number of "flat" cards in any tower N = 2^(N - 1) - 1
So.....my "guess" is that the 1000th tower should contain
(1000) ( 1001) + 2^(1000 - 1) - 1 ≈ 5.35 x 10300 cards ( a whole bunch !!!! )
