# Can you solve this Masyu puzzle?

Hey guys, enjoy this Masyu puzzle!

For those unfamiliar with Masyu, here are some instructions:

The goal of Masyu is to connect the circles on the grid via a line that closes itself and also does not go over previously established portions of said line. The circles have special characteristics that dictate how the line must move:

• Once the line enters a black circle, it must turn left or right.
• The tiles approaching or leaving black circles can't have turns.
• Once the line enters a white circle, it must go straight.
• Of the tiles approaching or leaving white circles, at least one must have a turn.

I hope I understood the instructions correctly. If so, the correct answer is:

Yes, I can.

• Yeah that's right. Nov 17, 2016 at 13:36

There were a lot of little steps here, not any big ones, so I wasn't sure how to put a useful solution down. In the end I just explained everything - this answer should be a good resource for anyone who wants to see how many standard Masyu deductions can be applied to a real puzzle. Rows and columns (mentioned in RXCY format) are counted from the top left, with the top left cell being R1C1.

Basic deductions used repeatedly here:

• White circle on an edge (or effectively on an edge):

A line must go straight through the white circle, parallel to the edge. Since it is on an edge the required straight line cannot go perpendicular to the edge.

• White circle which needs to turn:

A white circle which has a double-length straight line segment extending out one edge, must immediately turn upon exiting the opposite edge to fulfil the white-circle turn requirement

• Black circle on/one away from an edge (or effectively on/one away from an edge):

A line must go straight out perpendicularly away from the edge, as it cannot go "backwards" into the edge and a turn is required to exist.

• Black circle with a nearby hanging end:

A "hanging end" (a line entering a square but not leaving it) entering a square directly orthogonally adjacent to a black circle, but not pointing at the black circle, prevents the black circle from having a line extending that way. This is because the black circle's lines cannot turn immediately, which would be a consequence of connecting with the hanging end. Therefore this acts as an "effectively an edge".

Step 1:

Initial basic deductions. R8C1 is a white circle on an edge. Many black circles are on/near an edge.

Step 2:

We will first be looking closely at the bottom area. The black circle in R8C5 is now effectively near an edge. Once a line is drawn for it, the white circles in R9C6 & C8 are effectively on an edge. Then the black circles in R8C5 & C9 have hanging ends near them.

Step 3:

The white circles in R9C6 & C8 both need to turn. Then the black circle in R9C3 is effectively on an edge. Finally, the lines coming out of the white circles can't connect (that would complete the loop too early) so they must escape up their respective ways.

Step 4:

Now we start working through the top area. The white circle in R3C2 is effectively on an edge. Then the black circle in R2C3 has a nearby hanging end. Extending its line runs into a white circle, and the line must run straight through the white circle (by the "no turning in a white circle" rule) and turn up (as it must turn, and it can't turn into the nearby R3C6 black circle). Said black circle is now effectively on an edge.

Step 5:

The white circle in R6C3 is effectively on an edge. Then the black circle in R5C2 has a hanging edge near it.

Step 6:

"Clean-up" of many small unconnected things.
- the white circle in R3C2 needs to turn
- the black circle in R5C5 has a hanging edge next to it
- the hanging edge in R4C3 has only one direction to go
- the white circle in R6C9 has a hanging end which can be extended through, which also allows the hanging end in R6C10 to escape one more up

Step 7:

We now work from the middle of the right-edge, towards the middle of the puzzle. The white circle in R6C9 must turn. Then the black circle in R5C8 is effectively on an edge. Then the white circle in R6C6 is effectively on an edge. Then the black circle in R5C5 is effectively on an edge.

Step 8:

There is only one way for the ends in R4C4 and R3C5 to connect, so they snake around and touch. Then the black circle in R3C6 is effectively on an edge. The black circle in R5C8 is effectively on an edge, and extending its line leave only one way to connect the ends there.

Step 9:

The hanging end in R6C4 has only one way to go. Then, the ends in R7C1 & C3 can't connect (that would close the loop too soon) so they must sneak around each other to allow one to escape out.

Step 10/solution:

We finish in the top right. The black circle in R3C10 and the white circle in R2C8 are effectively on edges. Then there is only way to make all the ends connect.

You may have reached the end of this answer and think it is too long, or I explained too much/went into too much detail. "bobble", you may say, "I got bored. All of that logic was trivial!". Well, yes it was, but I had fun explaining it :) Hopefully this answer helps some Masyu beginner.