Solving twins (separating sides). User created Dec 16 and 22

The “user created” puzzle on Dec 16, 2017 has been solved by 83 puzzlers till the moment, and the “user created” puzzle on Dec 22, 2017 has been solved by 123 puzzlers.

But

**I have not build these two puzzles**, they are the top (left) and bottom (right) sides of a 7x7 twin puzzle already published by Patrick Min in one of his books. I can not reveal in which one, since the solution is “eternal” and other puzzlers could still try both.

First of all I asked Patrick his approval to do this “experiment” (and his cooperation in order to insert both puzzles consecutively and separated by a small number of days). The 7x7 twin puzzle did not score originally any points in the book, so no problem was apparently arising for assigning now some points (in my particular case I am not going to score those 19 points, since for me it is enough satisfaction to have the opportunity of exposing, in this Section “Solving strategies and tips”, my “theory”).

So, what you have done, my good friends, Calcudokers,

**is solving independently both sides of a twin puzzle**. Those who have solved both sides, can verify this simply by checking that all numbers occupy the same positions (it seems that nobody had noticed this) (BTW, you have the solution of the other side, so those who did not solve both can now quickly solve the other side, I apologize for that).

Since a long time ago I have been “worried” and “obsessed” with the idea (I have not a formal demonstration) that

**the twin puzzles could have an independent (and unique solution) for both sides**, so making unnecessary the “cooperation” between both sides. Please refer to this other post (Oct 06, 2011) "The essential info in a puzzle":

viewtopic.php?f=3&t=77 .

That’s why I have tried this “experiment” to "prove" it. If this becomes finally true (I wait debate and surprises in the future), and of course the difficulty increases a lot when you solve both sides independently, as you have seen, any time you find a twin puzzle you can try it, making many “trivial” twins (specially in the range of the 5x5’s and the 6x6’s)

**much more challenging (this could be interesting for the advanced Calcudokers)**, while, if you are in a hurry, use both sides simultaneously. As an example, I have solved all the twin puzzles in one of the Patrick’s books following this process.

However, it must be said that there is an exception to this “rule”, that’s the case of the twins puzzles “

**fm 0**”, this has been found by

**frederick** (I had with him different PM’s / mails on the subject). I believe the reason is because the “

**fm 0**” puzzles have “

**less information**” since the multiplication rule, for instance, can not be applied (it produces a zero for any line), so having more “uncertainties” (in some way similarly to the case of the puzzles with negative numbers where, for instance, in the “symmetric” puzzles with negative numbers, you can not either apply the addition rule since it also produces a zero). The parity rule, in the other hand, can be applied (being more useful in puzzles “fm 0”).

Merry Christmas.