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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?

 

 Feb 5, 2021
 #1
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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   !!!! )

 

 

cool cool cool

 Feb 5, 2021
edited by CPhill  Feb 5, 2021

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