Masyu

[nickdeller]

Amended draft:

Draw a single closed loop passing through the centres of some grid cells using the following rules.

* In each white circle, the loop must pass straight through without turning, but must make a 90 degree turn immediately beforehand or immediately afterwards.
* In each black circle, the loop must make a 90 degree turn, but must NOT turn immediately beforehand and immediately afterwards.
* The loop must not intersect itself, and contains no diagonal segments.
* Apart from the above, the path has no restrictions and the loop does not need to pass through every square.

I believe that there may be some readers who would particularly appreciate some tips on this puzzle type.

[detuned]

The loop may not intersect itself! It might be worth mentioning the loop goes through the centre of each square in the grid too.

As for tips...I find myself scoring some really good masyu times on nikoli.com every now and again, but I don't think I could particularly explain how I do it. The beauty of this puzzle is in its simplicity and the intuitive nature of the solve. Every now and again you come across some crafty trick which you have to think through a bit, but these are worth considering on a one-off basis.

[nickdeller]

The loop may not intersect itself! It might be worth mentioning the loop goes through the centre of each square in the grid too.

I've amended accordingly, I thought at first that former point was specified by the phrase "single closed loop", but on reflection I see that it isn't.

As for tips...I find myself scoring some really good masyu times on nikoli.com every now and again, but I don't think I could particularly explain how I do it. The beauty of this puzzle is in its simplicity and the intuitive nature of the solve. Every now and again you come across some crafty trick which you have to think through a bit, but these are worth considering on a one-off basis.

I think even the basic patterns would be good to have noted down - things like:

* Start work on the outer edges of the grid - white squares on the outside edge can immediately be solved, black squares in the outside two rows must have an 'arm' pointing into the grid.
* A line of three (or more) white circles must be solved using multiple parallel lines, as the line would otherwise pass through the central circle(s) without an adjacent turn.
* Adjacent black circles must have 'arms' pointing outwards along their lines.
* Any path segment close to a black circle may force the direction of an 'arm'.
* Don't forget to ensure that the path doesn't short-circuit.

There are probably more interesting common patterns as well which force some path.

[Mephisto]

Missing: Diagonal line segments are not allowed (i.e. all line segments must be parallel to the grid lines).

Clarification: In all other cells the loop may turn by 90° or may go straights through.

In general: Some rules talk about squares, other rules talk about cells. This should be harmonized. Personally I prefer "cell" because it is more general and does not refer to the presentation. For example, "cell" works also for hexagonal grids, "square" does not. (For almost any puzzle type also a hexagonal variant exists.)

[ronaldx]

Assuming that the parallel/perpendicular rule is not stated, can you make a diagonal Masyu that is unique, i.e. that doesn't have an alternative solution with parallel/perpendicular lines?

Presumably it's possible to follow all the other rules and come up with a loop with lines at 45 degree diagonals.

But - I imagine that not having circles along the edge makes it difficult to constrain the possibilities for 'parallel' loops. Am I right?

[nickdeller]

Amended.

Interesting question regarding cells/squares, and as you can tell I don't have a strong view on it! What's the general view - is it better to use 'cells' or to use the shape in the particular grid we're working with?

[PuzzleScot]

I vote 'cell', to ensure consistency. eg, a Hex Masyu (or another variant I will reveal at 'The Gathering' ) should be able to follow the same basic rules with minimal additions thereto.

[drsteve]

Is is worth stating explicitly that the loop does not have to pass through every cell? I know you've used the phrase "some cells" but it might help to spell it out.

[nickdeller]

Steve - it's already there in the final line, but as you missed it, it might still not be obvious enough... Will probably do no harm to mention it more than once, so I'll formulate an amendment later in the weekend.

[Mephisto]

"Is is worth stating explicitly that the loop does not have to pass through every cell?" -- Yes. Some redundancy does not hurt, especially if the solver may have some expectations. That a loop must pass through every cell is more common than the oppisite.

Another example is "not even diagonally" in many rules. Strictly speaking it is redundant, but nevertheless it's often there.

[drsteve]

Steve - it's already there in the final line, but as you missed it, it might still not be obvious enough... Will probably do no harm to mention it more than once, so I'll formulate an amendment later in the weekend.

I'm a maths teacher, I not read too good. Sorry