NaYBR
The Grid Coloring Logic Puzzle
Neighbors are Yellow Blue or Red

The Contest Center
59 DeGarmo Hills Road
Wappingers Falls, NY 12590

       NaYBR is the new grid coloring logic puzzle from the Contest Center. The object is to color every box in the grid according to the clues that are provided.

       Each clue consists of a letter and a number. The letter refers to one of the three colors that you will use to color the grid. R stands for Red, Y stands for Yellow and B stands for Blue. The number tells you how many neighbors of that box have that color. For example R2 means that two of its neighbors are red, while Y0 means that none of its neighbors are yellow.

       Each box can have up to 4 neighbors. A box in a corner of the grid will have 2 neighbors, a box along an edge of the grid will have 3 neighbors, and a box in the middle will have 4 neighbors. Boxes that touch only at a corner are not neighbors.


THE BASICS

       The basic technique for solving a NaYBR puzzle is to mark the colors that can appear in each box. Use R for Red, Y for Yellow and B for Blue. To avoid confusion, list these possibilities at the top of the box. If the box also contains a clue, mark that at the bottom of the box. Then you solve the puzzle by eliminating possibilities until there is only one possible color for each box.

RYB R1	RYB	RYB	RYB B2	RYB	RYB
RYB	RYB	RYB	RYB	RYB	RYB
RYB	RYB	RYB Y3	RYB	RYB	RYB
RYB	RYB	RYB	RYB	RYB	RYB
RYB	RYB	RYB	RYB	RYB	RYB

ALL OR NOTHING

       The easiest deduction you can make is when the clue says that ALL of the neighbors must be a certain color, or that NONE of the neighbors can be that color. In these cases you can mark all of the neighbors that color, or you can eliminate that color from the possibilities.
       The box in the upper left corner has the clue R2. Since a corner box has only 2 neighbors, both of them must be red.
       The fourth box along the top row has the clue B3. Since an edge box has only 3 neighbors, all 3 must be blue.
       The third box on the third row has the clue Y0. That means none of its 4 neighbors can be yellow.
       You can mark all of these deductions at the top of the neighboring boxes.

RYB R2	R	B	RYB B3	B	RYB
R	RYB	RB	B	RYB	RYB
RYB	RB	RYB Y0	RB	RYB	RYB
RYB	RYB	RB	RYB	RYB	RYB
RYB	RYB	RYB	RYB	RYB	RYB

Here is another simple deduction. The box at the center of the top row cannot be red, and it also cannot be blue. So it must be yellow.

YB	RYB R0	Y	RYB B0	RY
RYB	YB	RYB	RY	RYB
RYB	RYB	RYB	RYB	RYB

When there is only one possible color in a box, that box may be colored in.

RYB R2			RYB B3		RYB
	RYB	RB		RYB	RYB
RYB	RB	RYB Y0	RB	RYB	RYB
RYB	RYB	RB	RYB	RYB	RYB
RYB	RYB	RYB	RYB	RYB	RYB

MAN IN THE MIDDLE

       When a box is surrounded on all sides by boxes of the same color, then it cannot be connected to boxes of any other color. This leaves two possibilities, either (1) that box is the only box of the other color, or (2) that box is the same color as its neighbors.

       If you know that there are more boxes of the other colors elsewhere in the grid, then the surrounded box must be the same color as its neighbors. In the next grid the box in the upper left corner is surrounded by red boxes. Since there must be at least one yellow box near the bottom of the grid, the upper left box cannot be yellow. Since there must be at least two blue boxes near the right side of the grid, the upper left box cannot be blue. It must be red.

R R2	R	RYB	RYB	RYB	RYB
R	RYB	RYB	RYB	RYB	RYB
RYB	RYB	RYB	RYB	RYB	RYB B2
RYB	RYB	RYB	RYB	RYB	RYB
RYB	RYB	RYB	RYB Y1	RYB	RYB

WHAT'S LEFT?

       In this grid the box with the clue R3 shares two neighbors with the box that has the clue B3.

RYB	RYB	RYB	RYB	RYB	RYB
RYB	RYB R3	RYB	RYB	RYB	RYB
RYB	RYB	RYB B3	RYB	RYB	RYB
RYB	RYB	RYB	RYB	RYB	RYB
RYB	RYB	RYB	RYB	RYB Y1	RYB

       There are 6 neighbors altogether of the R3 and the B3 boxes. Since there must be 3 red boxes and 3 blue boxes among these 6 neighbors, the two unshared neighbors of R3 must be red, the two unshared neighbors of B3 must be blue, and the two shared neighbors must be one red and one blue.

RB		RYB	RYB	RYB	RYB
	RYB R3	RB	RYB	RYB	RYB
RYB	RB	RYB B3		RYB	RYB
RYB	RYB		RYB	RYB	RYB
RYB	RYB	RYB	RYB	RYB Y1	RYB

       Since there must be at least one yellow box in the lower right area, the upper left corner cannot be yellow, so it must be red. Similarly, the R3 and B3 boxes are completely surrounded by red and blue boxes, so they also cannot connect to the yellow box in the lower right. So they cannot be yellow, either.

		RYB	RYB	RYB	RYB
	RB R3	RB	RYB	RYB	RYB
RYB	RB	RB B3		RYB	RYB
RYB	RYB		RYB	RYB	RYB
RYB	RYB	RYB	RYB	RYB Y1	RYB

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