First we have to agree on some notation.

(It was generated before I incorporated Olivier Grégoire's suggestion about checkingfor 8 digits, so note that any solution to this puzzle leads to another solution where the 1s and 7s are swapped.) But is this an intrinsicly hard puzzle?

5 4 1 7 |3 6 9 |8 2 5 B1 B2 B3| B4 B5 B6| B7 B8 B9 .

This implies that each squaremust have a different value from any of its peers.

6 3 2 |1 5 8 |9 4 7 C1 C2 C3| C4 C5 C6| C7 C8 C9 .


Politicians help solve the social problems of our time by making complicated decisions within the confines of the law, public opinion, and (hopefully) budgetary restraints.

8 2 5 |4 3 7 |1 6 9 E1 E2 E3| E4 E5 E6| E7 E8 E9 .

Someone has to fix all of those machines and robots.What are employers looking for?

Employers are looking for three basic traits.

Here are the names of the squares, a typical puzzle,and the solution to the puzzle:

We could code that strategy in a few lines by adding an test to .


Engineers (Chemical, Civil, Electrical, Industrial, Material) build products/structures/systems like automobiles, buildings, computers, machines, and planes, to name just a few examples.

Mathematics is no longer just a subject taken by the elite.

Building cases demands a strong sense of language with specific emphasis on hypotheses and conclusions.
Managers maintain schedules, regulate worker performance, and analyze productivity.

First, we could try a brute force approach.

They research illnesses, carefully administer the proper amounts of medicine, read charts/tables, and organize their workload and manage the duties nurses and technicians.

All other characters are ignored (including spaces,newlines, dashes, and bars).

So each of the following three grid stringsrepresent the same puzzle:

Although laziness, or what we call laziness is also a common trait across people, is hard to overcome, we are hoping, that you, like us feels and sees the difference it makes to your well being in times of being more creatively active. Concepts and ideas are funny things in the way that they often come when we are doing something completely different. What we mean is that often that thing that you’ve been working so hard on, that issue that so desperately needs resolving, the solution usually comes as an unrelated activity is performed. Perhaps during a walk, or whilst doing the dishes, or having a bath. Anything which is you relaxing and not trying to solve the issue can help you resolve it, mad as it may sound, the team here believes strongly that that is the case, and we assure you that it’s scientifically proven that it’s good to take a break.

One might think that a 9 x 9 arraywould be the obvious data structure.

Therefore, will be a dict with squares as keys.

On the quantitative account, verisimilitude is defined by assigningquantities to contents, where the index of the content of a giventheory is its logical improbability (given again that content andprobability vary inversely). Formally, then, Popper defines thequantitative verisimilitude which a statement ‘a’possesses by means of a formula:

Here is the code to parse a grid into a  dict:

We could implement this as , but we can do morethan just that.

Finnish mathematician Arto Inkala described his as "the most difficult sudoku-puzzle known so far" and his as "the most difficult puzzle I've ever created." My program solves them in 0.01 seconds each ( will bedefined below):