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We're the engineers behind.
We're building a free, world-class education for anyone, anywhere.
Subscribe Last week a mysterious double-sided puzzle appeared at.
To solve the puzzle you must fit all four pieces inside the recessed the pieces will not entirely fill the area.
We found a solution to the easy side after only a few days but nobody взято отсюда get close to solving the hard side.
So five of us at Khan Academy began writing own solvers.
The first question we each faced was how to best represent the positions of the pieces.
Laying a triangular grid over each side was intuitive enough, but it wasn't obvious how the cells should be addressed.
Naturally we all came up перейти different systems.
I had a problem though.
Once I manually input a piece into this coordinate system, I needed to rotate and reflect that piece https://produkt.space/karta/igrovie-plastikovie-karti-pro-poker-tactic-games.html 12 different alignments.
Reflection was easy, but despite my best efforts, I couldn't figure out to rotate the pieces once they were placed into my grid.
After smashing my head the problem for an hour and getting nowhere, I gave up and manually inputted the three rotations necessary for each piece all the other alignments could be expressed as reflections of those rotations.
Now just to write the logic to try every possible placement of the pieces, but I was behind.
Ben Eater had already finished and it was churning away.
His solver didn't do any pruning of the search space though and took some time to each placement he estimated that the solver would finish around 2 years.
To try and be a little faster I added in some logic to skip large parts of the search space where possible.
This worked by laying down a piece at a time, and only trying the other ones if there were no collisions.
For example, first my program would pity, Мобильный био-кондиционер Master CCX 2.5 sorry down Piece A somewhere.
If Piece A collided with a wall, my program would not try laying down Piece B yet, but would instead move Piece A somewhere else.
This ended up working well and soon I had that could brute force the puzzle in less than a minute.
The hard side of the puzzle was unsolvable.
Clearly there was a very evil puzzle master in our ranks.
He said our solvers all shared a fatal flaw.
After a few hints, Emily and I did find the answer.
Which was good, because none of us had gotten any work done for awhile.
If you want to spoil it for yourself, here is.
Ben Eater to side-step the issue by drawing the shapes directly onto the screen.
Cam Christensen came up with a coordinate system with two axes that formed a 60° angle and he convinced Emily Eisenberg to the same system.
You don't really want me to give you the answer do you?
That would be boring.