Pattern-Matching Puzzle

mmm4444bot

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How many triples can you locate, in the grid below?

In this puzzle -- from a Page-a-Day Calendar of brainteasers -- a triple is any set of three adjacent cells (running vertically, horizontally, or diagonally) that satisfy all three of the following conditions.

(1) From cell-to-cell, the shapes must be all the same OR they must be all different

(2) From cell-to-cell, the number of objects must be all the same OR they must be all different

(3) From cell-to-cell, the objects' shading must be all the same OR it must be all different


Shapes Shading Sizes.JPG


For examples:

Look at the first three cells in row four. These do not form a triple because the shading is neither all the same (one open, two dotted) nor all different.

Look at the last three cells in row four. These do form a triple because the shapes are all the same (squares), the numbers of cell objects are all different (1,2,3), and the shadings are all different (open, closed, dotted).
 
Hello, mmm4444bot!

A great puzzle . . . thank you!


How many Triples can you locate, in the grid below?

A Triple is any set of three adjacent cells (running vertically, horizontally, or diagonally)
that satisfy all three of the following conditions.

(1) From cell-to-cell, the shapes must be all the same OR they must be all different.

(2) From cell-to-cell, the number of objects must be all the same OR they must be all different.

(3) From cell-to-cell, the objects' shading must be all the same OR they must be all different.

View attachment 2909

Number the cells like this: .\(\displaystyle \begin{array}{ccccc}1&2&3&4&5 \\ 6&7&8&9&10 \\ 11&12&13&14&15 \\ 16&17&18&19&20 \\ 21&22&23&24&25 \end{array}\)

I found 11 Triples.

Horizontal: .\(\displaystyle \begin{Bmatrix} 3,4,5 \\ 8,9,10 \\ 18,19,20 \end{Bmatrix}\)

Vertical: . \(\displaystyle \begin{Bmatrix} 2,7,12 \\ 6,11,16 \\ 10,15,20 \\ 14,19,24 \end{Bmatrix}\)

Diagonal: .\(\displaystyle \begin{Bmatrix}6,12,18 \\ 4,8,12 \\ 5,9,13 \\ 14,18,22 \end{Bmatrix}\)
 
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