How to Solve Milk Tea Puzzles

Nobody seems to be certain who invented Mirukuti, or “Milk Tea” puzzles, but the first known appearance was on a Japanese puzzle blog. The goal of a Milk Tea Puzzle is to group the circles into sets of 3 by connecting two white “milk” circles with one black “tea” circle, each group in a vaguely “T” shape.

Two white circles within the same row or column are connected by one line. These circles may not be in immediately adjacent cells.
One black circle is connected with a line that is perpendicular to some point along the line between the white circles, forming a “T” that may be upright, sideways, or upside down. This stem from the black circle does not have to be centered along the top of the T between the white circles.
Circles are always the endpoints of a line – lines never pass all the way through a circle.
Lines from different groups may never touch or cross each other.

The best way to locate groups is usually to start with the pairs of white milk circles. Look for individual white circles that only have one possible circle they can connect with.

In this case, each of these circles are the only white circle in their column, which means they can only be the endpoint of a horizontal line. In both cases, there is only one circle in the same row they can connect to.

Yes, there is more than one white circle in row 4, but remember that a line can’t pass through a circle, so the line leading from the circle at the border will stop at the first white circle it reaches.

Now that we’ve established the tops of a couple Ts, we can start looking at our options to complete the set.

With this pair at the top, we look along the path a perpendicular line would take. It can only go one direction, since we’re right up against the border. Notice that three of these potential paths lead to another white circle, but only one connects with a black tea circle. Since we already have two white, and just need our black circle, this must be the correct path.

The other pair of white circles still has two possible black cells, so we’ll look for another pair of white circles we can connect.

Here we have another milk circle that’s the only one in its row, so it must pair up vertically. There isn’t a circle below it, so that means the line goes up to connect to the other white circle.

Now, there’s only one space between them, so we only have one row to check for the proper placement for the stem of the T. there are no circles to the left, so the black tea circle to complete the group must be the one just to the right.

That means that the leftover pair of white cells from earlier has only one remaining tea circle you can connect to complete the group.

We can also consider the possible groupings in reverse. Here, we have a black tea circle. The stem of the T can’t extend to the left or up, since there are no circles there.

It also can’t extend to the right, because it would simply run into a milk circle, not intersect a line running between a pair of them.

So we know the line of the T will point down, and we can see there is only one possible pair of white circles that could form a line before that stem simply hits another black circle. Therefore, we’ve found the correct grouping.

In general, though, it’s usually much easier to find the pairs of milk circles before looking for the tea. Take this black circle, for example.

We know the line can’t extend downward, because it would run directly into a white circle, which isn’t allowed. It also can’t go toward the right, because there’s another black circle there.

You might look up and see another black circle, assume the line can’t go that way and match this tea with the milk pair to the left, but notice that before you hit that tea circle above it, there is a potential pair of white circles.

Our saving grace here, though, is that we can look at the pattern of white circles.

We’re going to look at some potential pairings and talk about why they only work one way. Let’s start with the green cell at the bottom of the grid.

This white circle only has one direction to go to form a pair. It can’t pair with the circle to its right, because there wouldn’t be space between them for a black circle to connect. So we know the green pairing of circles must be true. Looking to the right, we see there is only one possible black circle to complete the group.

Looking at it another way, we can see that neither black circle could connect to a theoretical purple pair of white circles, because that would then leave the other black circle with no available pair of white circles.

We can make the same deductions if we started from the blue cell at the top. It only has one possible white circle to pair up with, and then together, they only have one available tea circle to complete the group.

So the solution to the rest of the puzzle is apparent from here. The highlighted black circle connects to the green pair of white circles. The tea circle above it connects to the blue pair of milk circles, and that leaves only one remaining grouping to the right of the yellow cell. The final black circle connects to the pair of white circles at the bottom of the grid.