The power tower puzzle | Lockdown math ep. 8
A fun puzzle stemming from repeated exponentiation.
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Notes by Ngân Vũ:
twitter.com/ThuyNganVu/status/1261014161464516608?s=20
Play along on Desmos:
www.desmos.com/calculator/nul32eaaa9
Related videos.
Calculus series:
www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr
In particular look at:
youtu.be/CfW845LNObM
Numberphile on Grahms constant:
youtu.be/XTeJ64KD5cg
— Video timeline (thanks to user «noonesperfect»)
0:36 Question 1
1:13 Answer 1
1:29 Introduction to tetration
3:37 How exponentiation works in tetration
6:10 Python program for power tower iterations
8:40 Question 2
9:32 Python Program regarding question 2
10:37 Answer 2 and explanation
13:18 Power tower for infinite size converges or not? (Thumbnail question)
15:21 Question 3
16:28 Footage of Grants setup arrangement problem due to construction-work back at home.
16:49 Answer 3 and explanation
17:40 Checking logic behind 2 different problems of power towers whose answer converges to the same value (Is it even possible?)
19:42 Checking same logic using Desmos graph tool i.e. Cobweb Graph (Desmos graph link in description)
28:12 Question 4
28:51 Questions from audience tweets
29:15 Knuths Up Arrow Notation and Grahams Number (Check Numberphile video in description)
32:32 Answer 4 and explanation
37:29 Homework/Challenge Puzzle
39:20 Thumbnail question power tower logic
40:55 Audience questions from twitter
41:45 Power tower for complex numbers/Fractal set
45:19 Brainteaser
48:06 More questions from tweets
53:17 Notes for lock-down series in Grants Tweeter
— The live question setup with stats on-screen is powered by Itempool.
itempool.com/
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Music by Vincent Rubinetti.
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