## How To Play Vaki Puzzles

### and some tactics for solving them

This is a 4x4 vaki puzzle with both letters and numbers

 D3 B2 D4 C1

Vaki puzzles are solved by completing the grid so that there is a letter and a number and in each cell, each letter and each number appears once in each column and once in each row, and each pair appears only once in the grid.

Two basic tactics for solving vaki puzzles are also used in sudoku

#### Tactic One: which letters or numbers can be placed in this cell?

Look for a cell which can only be filled by one letter or number because only one possibility remains in that row and column.

In this vaki puzzle where the letters A,B,C,D form pairs with the numbers 1,2,3,4 there must be a 1 in row one column three as row one already contains 3 and column three already contains 2 and 4. If any number other than 1 was placed in that cell, it would appear twice in that row or twice in that column.

#### Tactic Two: Where can this letter or number can be placed?

 D3 1 B2 D4 C1

Identify where a particular letter or number can go in a row or column in the hope that there will only be one possibility. The letter or number can then be placed in that cell. So, while tactic one answers the question 'Which letters or numbers can go in this cell?" tactic two answers the question "Which cell can this letter or number go into?"

In the puzzle we are working on, the only place where a 3 can go in the bottom row (row four) is column one row four. Columns three and four already contain numbers and there is already a 3 in column two.

There must be a C in column three, and the only cell a C can go into in that column is in row three (rows two and four already contain letters and if the C goes in row one, the pair C1 would occur twice)

The same tactics allow us to place a few more symbols

 D3 1 B2 C3 3 2 D4 C1

In our partially solved vaki puzzle, the letters A to D form pairs with the numbers 1 to 4. All the possible pairs are formed, which means there is a C1, C2, C3, and C4 in the puzzle.

Where can the C2 go?

#### Tactic Three: Where can the pairs be placed?

The only possible cell for the C2 is row one, column one as C already occurs in rows three and four and two already occurs as part of a pair in row two.

 C2 D3 1 B2 C3 3 2 D4 C1

This leaves only one possible cell for the C4

Now, using tactics one and two it is possible to solve this vaki puzzle
This is the solution

 C2 D3 A1 B4 D1 C4 B2 A3 A4 B1 C3 D2 B3 A2 D4 C1