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?

Guest Feb 5, 2021

#1**+1 **

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 10^{300} cards ( a whole bunch !!!! )

CPhill Feb 5, 2021