# Sudoku Puzzle Triplets -- Identifying and Understanding

by Ed GLysson
(Morgan Hill, CA)

Sudoku Puzzle; Identifying and Understanding Triplets:

The “Sudoku Puzzle -- Triplets” example attached can be used as a visual aid to promote the the identification and understanding of a Sudoku Puzzle pattern that I call a “Triplet”. The black entries represent the original puzzle and the blue entries represent the puzzle challenges that were filled in by the puzzler. The Curtains and Belts highlighted in yellow identify the Triplets. As you may be able to determine, it is a valid puzzle. Also attached are four puzzles of differing degrees of difficulty that each have two Triplets to be discovered; then there is another attachment that contains the solutions to the Triplet puzzles as well as the highlighted Curtains and Belts containing the Triplets.

(Refer to my other article “Sudoku Square and Space Notation” for a full explanation of the terms: Belts, Curtains, Squares, and Spaces.)

How to identify a three Space pattern of entries called a Triplet:

Observe that in Curtain 1(D) (composed of Squares 1, 4, and 7) there exists a sequence of three Space entries that follow a diagonal pattern (which in this case is left to right, but can be either left to right or right to left). The 3 Triplets in Curtain 1 are 268, 347, and 159. Observe that the Triplet 268 “runs” diagonally from the
upper left of Curtain 1 to the lower right of Curtain 1 (Spaces 11, 14,17, 42, 45, 48, and 73, 76, 79). The second Triplet in Curtain 1, 347, “runs” through Spaces 12,15,18, 43, 46,49, and 71,74,77. And the third Triplet in Curtain 1, 159, “runs” through Spaces 13,16,19, 41,44,47 and 72,75,78.

Notice that Curtain 3(F) also has Triplets (137, 689, 245) (Squares 3, 6, and 9).

And that Belt 3(C) also has Triplets (146, 578, 239) (Squares 7, 8, and 9).

This is an unusual puzzle to have three sets of Triplets. Very few puzzles have one Triplet!

Understanding the benefit of recognizing a Triplet:

What's beneficial about Triplets is that when resolving a Sudoku puzzle if ANY two groups of diagonal three Spaces contain the same entries then the ENTIRE Belt or Curtain can be resolved with Triplets.

Perhaps its possible, but I have NEVER seen a puzzle with partial Triplets.

Try working the puzzles in the attachment Sudoku Triplet Examples. As you puzzle, look for any Triplets that develop as each example puzzle has two sets of Triplets.

Recognizing Triplets will definitely speed up your puzzle resolution time and they are just fun!

Ed Glysson, Morgan Hill, CA Spring, 2016

Attachments:
Sudoku Puzzle – Triplets
Sudoku Triplet Examples
Sudoku Triplet Examples and Solutions

References:
Article “Sudoku Square and Space Notation”