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Nicolas Kaiser
645 followers -
Open source enthusiast. Barbell addict.
Open source enthusiast. Barbell addict.

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Solutions to the Hindu cryptarithms challenge

"Maths puzzles" course at futurelearn.com, Weizmann Institute of Science
https://www.futurelearn.com/courses/maths-puzzles

Question number 1: Solving the cryptarithms

I recently took the Coursera course "Modeling Discrete Optimization", which is all about solving combinatorial problems by stating them in a modeling language, MiniZinc, and then computing the results with constraint solving software.
https://www.coursera.org/course/modelingoptimization

In MiniZinc, Hindu problem 1 can be modelled like this:
https://gist.github.com/nikai3d/bc7447b7ae8f626a14bc69b498a0a446

Computing all solutions gives a single result:
https://goo.gl/photos/utA9paxiqnJQp2rS8

Knowing that this is the only feasible result, we immediately can tell that the additional constraint in Hindu problem 2 causes the problem to become infeasible.
Computing all solutions with the additional constraint confirms that this problem is unsatisfiable.

For me, the biggest challenge with Hindu problem 3 was to figure out how exactly the long division is performed. Thanks to Khan Academy for the nice videos on the topic:
https://www.khanacademy.org/math/arithmetic/multiplication-division/long-division/v/division-2
https://www.khanacademy.org/math/arithmetic/multiplication-division/long-division/v/dividing-by-a-two-digit-number

In MiniZinc, the problem can be modelled like this:
https://gist.github.com/nikai3d/4351b39e0bd42a387ae82da8e64c721a

Computing all solutions gives 47 results. This is one of them:
https://goo.gl/photos/hRUerSDcJwTDpVqX7

Question number 2: Creating your own Hindu cryptarithm

This is a Hindu cryptarithm I created. It is small enough to brute force a solution if necessary. I think it has a cute solution. Have fun.
https://goo.gl/photos/FQqdBFLbYTepTLm96

EDIT:
Darn, this is exactly what happens when you model a problem that you don't completely grok. My solution to Hindu problem 3 is not acceptable, and even Salman Khan mentions the relation that I overlooked in his video.

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My favorite song in the 2016 +Eurovision Song Contest comes from Switzerland.

Best of luck to Rykka for the second semi final!

https://www.youtube.com/watch?v=96ENe3EYBE0

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Oh well, I'm searching a lot when I'm programming. Why hasn't this ever happened to me?

Probably because I'm using Hoogle.

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My favorite song in the first ESC 2015 semi final comes from Russia. Best wishes for the final, Polina Gagarina!

https://www.youtube.com/watch?v=jBVY7Glcd84

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Solar Eclipse, 20. 03. 2015, 10:39 in Kitzbühel, Austria

#SolarEclipse
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Solar Eclipse 2015
4 Photos - View album

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Looks like my +GitHub statistics turned to spooky colors.
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Protip: Don't forget to regularly update the firmware of your lightbulbs.
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