TECHNIQUES FOR SOLVING TENTS PUZZLES

The fundamental aim in solving a TENTS puzzle is to place a tent beside every tree (horizontally or vertically) without ever placing tents in contact (horizontally, vertically or diagonally). However, it is just as important to identify cells in which a tent cannot be placed, and the solution task will be much easier if such cells are marked in some way. In what follows, a dot will be placed in the center of each cell in which a tent cannot be placed.

When specific cells need to be referred to in this discussion, they will be designated as C4-R3 which means the 4th cell in row 3.

For a description of TENTS puzzles, refer to  Building Tents Puzzles 

Initial Steps.

   
The first move is to find any rows or columns in which there are no tents. In this puzzle, there are no tents in rows 1 and 3, so all of the cells which do not contain a tree can be marked with the dot which indicates no tent. This is an example of the "Row/Column Count" Strategy.

Next, we can use the fact that tents can only be placed in cells adjacent (horizontally or vertically) to a tree. Any cell which does not meet this criteria can be marked with a dot. This is the "No Adjacent Tree" strategy.

The right hand graphic above shows the situation after the above two steps have been completed.

One old and one new strategy.

   
We now have an opportunity to apply the "Row/Column Count" Strategy to row 2. We must insert 4 tents, but we vave 5 available cells. Two of these cells are adjoining, so only one of them can have a tent, but each of the single cells can certainly have a tent inserted. Sometimes you will even encounter a situation in which you have a group of three contiguous cells into which two tents must be inserted. In such a case, you can insert them directly into the first and last cells of the group.

We can also apply the "One Option Tree" strategy to cell C3-R1. There is only one vacant cell adjacent to this tree, and so a tent must be inserted into it. Whenever you insert a tent, you should, as a matter of course, insert dots into any vacant cells which are adjacent (horizontally, vertically or diagonally) to the newly inserted tent.

As usual, the right hand graphic shows the puzzle with these changes made.

More applications of Row/Column Count.

   
Column 9 requires 3 tents, and that is exactly the number of available vacant cells. Insert the three tents, being careful to mark any adjacent cells with a dot. This will also complete column 8, although column 8 could also have been completed directly by the applcation of "Row/Column Count".

Column 6 require 2 more tents, one of which clearly goes into C6-R4. The other will go into either C6-R6 or C6-R7. We don't yet know which, but regardless of which, the cells C7-R6 and C5-R7 can be marked with a dot. Can you see why?

The right hand graphic shows the puzzle with these changes made.

More Steps.

   
The following steps are presented without explanation. If you have understood the preceding information, you should have no problem in formulating a justification for each step.
  • A tent can be inserted at C7-R8.
  • A dot can be inserted at C6-R7.
  • A tent can be inserted at C6-R6.
  • A dot can be inserted at C5-R5.
  • A tent can be inserted at C5-R9.
  • A dot can be inserted at C4-R8.
The right hand graphic shows the puzzle with these changes made.

Completing the puzzle from this point should be a simple matter.

Astute solvers may find other, more obscure strategies which they can apply. However, the strategies listed here are guaranteed to solve any TENTS puzzle created by Magnum Opus.