What is pencil mode?
Pencil mode is a way to visualize the values that can fit into the empty squares of a puzzle. These are the squares where it is not yet known, whether they will be blocks or numbers.
Pencil mode can also be used to set temporary blocks. This can be useful for trying out possible block positions.
Pencil mode can also be used to set temporary blocks. This can be useful for trying out possible block positions.
How is pencil mode activated?
To be able to activate pencil mode, it must first be enabled under Optional Features in the settings. The settings can be brought up while a puzzle is in play, by tapping the settings symbol in the top-right corner. Alternatively, just select Settings from any options menu:
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Once enabled, it is also possible to choose the background effect for squares with pencil markings.
In this example, the default selection is left unchanged. With this setting, pencil squares will have the same background as empty squares. |
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When pencil mode is enabled, an additional button with a pencil symbol is shown below the puzzle. Pencil mode is activated by tapping this button, as illustrated in the worked example below.
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How is pencil mode used?
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The puzzle shown here is an example of a difficult 5x5 puzzle generated by the puzzle generator in Expert play mode. This puzzle will be used to illustrate how to use pencil mode.
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Let's set about solving the puzzle. To start with, the squares in the middle of the first two columns cannot be blocks, because a clue of 5 and a clue of 4 both require 2 squares between the blocks. These squares can therefore be marked as number squares. The candidate values can also be reduced to 2 values in both cases:
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Now we're stuck! Let's use the help to show us where to look:
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The help has indicated that a step is possible in the first row, which has a clue of 3.
In order to perform an analysis of the values in this row, we activate pencil mode by tapping the pencil button |
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When pencil mode is activated, the pencil button glows orange and all empty squares are shown highlighted.
It is now possible to set candidate values on the empty squares, without committing them to being number squares. |
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The column with a clue of 5 can only begin with a block or a 1, because the only combination for a clue of 5 is 2+3.
With pencil mode active, the value of 1 is set as the only possible candidate on the first square of the row: |
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Similarly, the column with a clue of 4 can only begin with a block or a 2, because the only combination for a clue of 4 is 1+3.
With pencil mode still active, the value of 2 is set as the only possible candidate on the second square of the row: |
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The column with a clue of 2 cannot begin with a 2, because this single value will need to be sandwiched between the blocks.
With pencil mode still active, the values 1 and 3 are set as candidates on the last square of the row. The easiest way to do this is to tap the value 2 twice, to eliminate it. |
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For completeness, the values 1, 2 and 3 are set as candidates on the remaining two empty squares of the first row:
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Having completed our analysis of the values in the row, pencil mode can be de-activated by tapping the pencil button again.
When pencil mode is de-activated, empty squares without pencil markings go back to their normal appearance. The empty squares which do have pencil markings stand out in a couple of ways:
When pencil mode is de-activated, empty squares without pencil markings go back to their normal appearance. The empty squares which do have pencil markings stand out in a couple of ways:
- the candidate values are shown in bright orange
- the font resembles handwriting.
It is now much easier to work out where the blocks for the first row might fit, and where they do not fit.
How to work out what can be done next
For a clue of 3, there are two possible number combinations:
With pencil mode enabled, a temporary block is placed in the first square using double-tap:
- either, the two blocks will need to sandwich the single value of 3
- or, two squares will be needed between the blocks for the combination 1+2.
With pencil mode enabled, a temporary block is placed in the first square using double-tap:
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We can see immediately that the only combination which might work is 1+2.
Let's put in a second temporary block and set the combination 1+2 on the squares between the blocks. |
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This arrangement appears to work, but that doesn't necessarily mean, it is the only possible arrangement.
Let's undo back to before the first temporary block and repeat the process, this time by trying a block in the second square. |
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For the case of where the single number 3 is sandwiched between the blocks, the arrangement does not work, because there would be no square left outside the blocks that could take the value of 2.
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The other case of 1+2 doesn't work either, because if these values would be set between the blocks then it would not be possible to set a 3 on the remaining square outside the blocks (the first square).
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This investigation has therefore shown that the second square cannot be a block. The temporary blocks can be removed again using undo.
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If the second square cannot be a block then it must contain a number instead. With pencil mode de-activated, the square can be changed from a pencil square to a number square simply by tapping it (just as if it was still an empty square):
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Now that we know the second square of the first row is a number and not a block, we can make progress with solving the puzzle.
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First, the blocks for the column with the clue of 4 can be placed and the square outside the blocks can be confirmed as having the value of 2:
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Next, the squares either side of the block in the second row (having a clue of 3) can be marked as number squares:
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Now the first column (with a clue of 5) can be updated.
The first square is changed from a pencil square to a block by tapping it twice, just as if it was still empty. |
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Now the first row (with a clue of 3) can be completed.
As before, the fourth square is changed to a block by tapping it twice, just as if it was still an empty square. |
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And so on! The puzzle is considered to be complete when there are no empty squares left and when squares with candidate values only have one remaining candidate:
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Pencil squares do not need to be converted to number squares if they only have one candidate value left and if the right number of blocks are present.
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I have enabled pencil mode, but the pencil button is inactive. Why?
The pencil button is inactive if there are no empty squares left.
To recap, pencil mode is used to visualize the values which can fit into empty squares. As soon as there are no empty squares left, pencil mode is no longer useful so the button turns inactive.
To recap, pencil mode is used to visualize the values which can fit into empty squares. As soon as there are no empty squares left, pencil mode is no longer useful so the button turns inactive.
Is there a quick way to clear all pencil markings?
Yes. Tap "clear all pencil markings", which is shown just above the puzzle grid (or just below the grid if you have opted to have the clues for columns shown above the grid).
If you would like the pencil markings back again, you can undo the clear by tapping the undo button.
If you would like the pencil markings back again, you can undo the clear by tapping the undo button.
How can I mark a square as being a possible block?
If a square can be a possible block then just don't set candidate values on it, because this marks it as a number square. However, you can use pencil mode to pencil-in the candidates instead.
The main purpose of pencil mode is to allow the candidate values for a square to be visualized, without committing the square to being a number. This means, the square can still be a block too. To recap:
To elaborate a bit more, the screenshot below shows a 5x5 puzzle in the process of being solved.
The main purpose of pencil mode is to allow the candidate values for a square to be visualized, without committing the square to being a number. This means, the square can still be a block too. To recap:
- If you know a square will be a block -> set a block.
- If you know a square will be a number -> set candidate numbers.
- If a square might still be a block or a number, but you want to see the candidates -> use pencil mode to set the candidates.
To elaborate a bit more, the screenshot below shows a 5x5 puzzle in the process of being solved.
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A square which had pencil markings is now showing the outline of a square. What does it mean?
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This indicates that all the pencilled candidates have been eliminated.
The outline is a hint that the square might be ready to receive a block, because no candidate values are left. |
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The pencil markings just add confusion! What is the best way to use pencil mode?
Too many markings can in fact obscure the puzzle. This may make it more difficult to solve the puzzle than if the empty squares had just been left empty.
Here are some suggested guidelines on how to use pencil mode effectively:
Here are some suggested guidelines on how to use pencil mode effectively:
- Only use pencil mode if you need to. This is when you want to be able to see the candidate values for squares that can potentially still be either a block or a number.
- Use the help to show you where to look, then focus on the row or column it indicates.
- Try out the different background effects for squares with pencil markings, to find the setting that works best for you.
- Clear away all pencil markings once you have been able to make progress. Remember that the clear can be undone by tapping the undo button. So if you find you still need the pencil markings after all, just undo the clear again.