[veli_joza]

Great read.

TLDR Shannon's approach to creativity and few mental tools for problem-solving:

  * simplify by eliminating everything from the problem except the essentials; cut the problem down to size
  * seek similar known problems, find analogies and apply solutions to your problem
  * try to restate the problem in just as many different ways as you can
  * generalize the building blocks by trying to apply them to broader class of problems
  * structurally analyse the problem - break it down into sequence of smaller mental leaps
  * invert the problem and see if it's solvable by retracing from solution to the start

[mettamage]

Mobile friendly version (I am on mobile now, I hope HN changes this part of their design, bullet points should be mobile friendly, enough users complain about this, what happened to make what users love?):

simplify by eliminating everything from the problem except the essentials; cut the problem down to size

seek similar known problems, find analogies and apply solutions to your problem

try to restate the problem in just as many different ways as you can

generalize the building blocks by trying to apply them to broader class of problems

structurally analyse the problem - break it down into sequence of smaller mental leaps

invert the problem and see if it's solvable by retracing from solution to the start

[mettamage]

@mods: this got 40+ upvotes as of writing this reply.

[Radim]

> invert the problem and see if it's solvable by retracing from solution to the start

This last bit I personally find tremendously useful. It works best on hard conceptual blocks (though not necessarily Shannon-hard).

I start by "explaining" to an invisible audience how I solved (past tense) the problem – without having a clue how to actually approach it. First the overall hand-wavy "feel" of the solution, then filling in more specific gaps as the imaginary audience prompts. Sometimes retracting and adjusting the narrative. Very top-down, back-to-front.

By the end of this, there's often a working outline. I call it "Solution by Bragging", as a more extreme form of rubber-ducking.

[theoh]

That's not what Shannon means. He just meant "solve the inverse problem".

[75dvtwin]

Thank you for the summary. Incidentally the above, is approximately what I try to get from my interviews for technical and non-technical roles.

Specifically, for technical roles I am interested if the person being interviewed can do ( 2 ).

I feel that algorithmic puzzles are the almost an anti-pattern to ( 2 ), and create a negative filter that eliminates applicants that are great at ( 2 ).

[namelosw]

Agreed. Most algorithmic puzzles are looking for very constrained ways of solving problems, that's why those so-called good solutions are fast. In real-world applications, this could be an anti-pattern because of most of the business model are dynamic. In contrast, general strategies like logic programming are underrated for a long time.

[joe_the_user]

It's a great list and by now a fairly standard list. You can find variations and extension of this in many places. I recall one of Feynman's standards tricks was seeing if he could get a desired result without going through the expected stepped. I think Douglas Hofstadter's analogy project was aim to construct an AI using this (an approach that hasn't gotten the attention (or research grants) it deserves imo).