Have you played around with
Well, you should.
Go ahead, mouse around with different buttons below this line:
A very simple interface:
The idea is that you move the mouse around,
and the keyboard acts like a very large number of mouse buttons,
generally taking an action at the current mouse location.
Tile placing commands
Press '1' to place a red triangle.
Press '2' to place a blue triangle.
Press '3' to place a rhombus.
Edge painting commands
Press 'b' to make the mouse location be a blue edge.
Press 'r' to make the mouse location be a red edge.
Press 'c' to to make the mouse location be a crossing edge (a rhombus).
Your three mouse buttons act the same as these three keys.
Hold down shift to only give a blue or red "hint". (defined below)
Holding down shift when laying a rhombus instead lays a "not-rhombus" tile boundary.
Press 'y' to mark an edge as being a boundary between a rhombus and a triangle,
oriented towards the blunt middle of the rhombus.
Press 'u' (or ',' or '<' or backspace) to undo the last information laid down.
Press 'z' to undo the restriction next to the mouse (will undo and then
redo all more recent restrictions -- do not be alarmed).
Press '?' to try all possible local configurations at the vertex where the mouse is,
and then apply any conclusions that are reached in all cases.
Press 'a' to search for a full solution automatically, starting where the mouse is.
(The screen will only update once every few seconds
if it takes a huge amount of trial and error.
Check the status bar to see how much it has tried and erred so far.)
Press 'q' to stop the search.
What do the markings mean?
Thick blue and red lines are the standard Knutson-Tao markings for the Knutson-Tao tiles:
red triangles, blue triangles, and rhombi which have a red line crossing a blue line (with
blue always slightly clockwise from red).
A blue or red dot on a tile boundary indicates that the two tiles meeting at that
boundary have that color on their shared edge.
A dark (as opposed to yellow) boundary between tiles
indicates that no rhombus crosses that boundary.
A thin blue line (a blue "hint") indicates that a blue line will pass there,
either as the center of a rhombus or as a blue line on a boundary.
A small blue (or red) dot indicates
that the tile that goes there must have some blue (or red) on it.
These markings fully indicate, for each triangle in the grid, what can go there.
A small cyan dot on a vertex means that there are some configurations of tiles
around that vertex which are not possible, but you can't tell just by looking at the
markings on that hexagon. That is, a cyan dot represents local knowledge about
combinations of tiles that is too complex to represent in terms of restrictions on
the placement of individual tiles.
A small hollow black circle on a vertex
means that you placed some information near there with the mouse.
(Yes, in a future version it will show the marking on the actual edge where you placed the
The black circles on the boundary are there because the boundary has been informed,
as if by shift-middle-clicking with the mouse, that no rhombi may cross it.
The cyan circles that blink
(and the thin green circles they leave behind until they are done)
show the places it is thinking about.
You won't see too much of these until you get to really complicated situations.
A big black dot indicates a place where an inconsistency has been noticed.
In this situation further actions will not take their usual action but will instead
backtrack and change the last-layed-down information,
which led to the inconsistency, rather than taking their own action -- but of course
the changed information might itself lead to a new inconsistency!
Welcome to the world of logic puzzles!