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Today I want to share with you a neat way to solve the towers of Hanoi puzzle
just by counting in a different number system,. and surprisingly this stuff relates to finding a curve that fills Sierpinski triangle.
I learned about this from a former CS lecturer of mine, his name is Keith Schwarz.
And I've got to say, this man is one of the best educators that I've ever met.
I actually recorded a bit of the conversation where he showed me this stuff,
so you guys can hear some of what he described directly.
It's weird, I'm not normally the sort of person who likes little puzzles and games,
but I just love looking at the analysis of puzzles and games,
and I love just looking at mathematical patterns and (ask): where does that come from?
In case you aren't unfamiliar,. let's just lay down what the towers of Hanoi puzzle actually is.
So you have a collection of three pegs, and you have these discs of descending size.
You think of these disks as having a hole in the middle, so that you can fit them onto a peg.
The set I pictured here has five discs, which I'll label 0, 1, 2, 3, 4,
but in principle you could have as many discs as you want.
So they all start up stacked up from biggest to smallest on one spindle,
and the goal is to move the entire tower from one spindle to another.
The rule is you can only move one disc at a time,. and you can't move a bigger disc on top of a smaller disk.
/rəˈkôrdəd/
set down in writing or some other permanent form for later reference. To put music, sounds onto a device to store it.
/ˈpadərn/
repeated decorative design. Colors or shapes which are repeated on objects. decorate with pattern.
/stakt/
put or arranged in stack or stacks. To be put on top of others. To arrange cards in a certain order, to cheat.
/ˈkoun(t)iNG/
taking account of when reaching total. To add things together to find the total number.
/(h)wətˈevər/
Referring to any particular kind, type, quantity. at all. Anything or everything needed; no matter what. said as response indicating reluctance to discuss something, often implying indifference. used for emphasis instead of 'what' in questions.
/ˈpik(t)SHər/
Shown or displayed in a photo or painting. represent in picture.
/ˈspindl/
Part of a tool used to wind thread or wool. impale piece of paper on metal spindle for temporary filing purposes.
/ˈfīndiNG/
Something you discover or find out; a result. To discover or meet by chance.