In this video we not only solve the tricky submarine puzzle - we stumble upon one of mathematics' most fascinating results: the size of infinities. In fact, we will touch the very limit of mathematical knowledge. We then introduce a new puzzle about an infinite grid of mosquitoes and a laser pointer, to test our newly learnt skills. Can you solve this new puzzle before my next video?
Original puzzle statement:
A spy submarine is moving along an infinite number line at an unknown velocity. Your mission? Find it before it disappears forever. Each turn, you get to search one position - but the submarine keeps moving at its mysterious speed.
This puzzle is rumored to be an old Google interview question. Thanks to my former calculus teacher for showing me this puzzle.
Note on Cantor diagonalization proof: there is a detail related to 1 = 0.99... which needs to be adressed in a more formal proof.
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Timestamps:
00:00 Intro
00:22 The Submarine Puzzle
01:15 Solution pt 1: v=0
02:25 Solution pt 2: x0=0
03:45 Solution pt 3: Full Puzzle
04:31 Approach 1
05:32 Approach 2
06:15 Countable Infinities
07:52 Other Types of Infinities
10:19 Puzzle: Mosquitoes and a Laser Pointer
10:51 Outro