Clues by Sam: case analysis

• 19 November 2025
• notes,
• puzzles

If you haven’t already come across Clues by Sam and you enjoy puzzles, you’re missing out. It’s a daily logic problem in which you have to work out which cells in a 4x5 grid contain criminals and which contain innocents. Here’s an example grid from the tutorial, partially filled in:

The best day to start is a Monday, which usually has an easy puzzle. Puzzles get harder through the week.

On difficult puzzles, I find I have to use case analysis. I pick a cell, make an assumption about whether that cell is an innocent or a criminal and see where that leads.

RAA

If I’m lucky, my assumption about the initial cell (e.g. it’s a criminal) leads to a contradiction and so the assumption was wrong and I know the opposite is true (e.g. it’s an innocent).

This technique is known as proof by contradiction or reductio ad absurdum (RAA). For example, RAA worked for Tom in the evil puzzle in this week’s newsletter.

But if I pick a cell that doesn’t lead to a contradiction, what next?

Overlapping alternatives

In that case, I make as many deductions as I can from the initial assumption and record the results using tags.^[1][2] Then I screenshot (see “Feedback” for another option) the puzzle, clear the tags, and repeat the process with the opposite assumption about the same initial cell.

I then compare the puzzle with the screenshot. If any of the deduced cell values are the same, I know the values of those cells^[4], since they are the same for either of the two possible values of the initial cell.

I describe this technique as “overlapping alternatives”, since the alternative assumptions about the initial cell result in deductions which overlap on the same values.

To keep things tidy, I clear the tags and delete the screenshot before continuing with the puzzle.

Admittedly this might not be the fastest approach, but I’m generally more interested in getting a clean solution than breaking speed records.^[5]

Example

Let’s look at an example to make the approach more concrete. In the grid below, I tagged Alex and Tom with yellow because, by virtue of Denis’s clue, one must be a criminal and the other an innocent. Similarly, I tagged Isaac and Sam, by virtue of Ruth’s clue.

I picked Alex as a starting for a case analysis, since that will immediately lead to Tom and, in the case where Alex is a criminal, Sam.

I first analysed the case where Alex is a criminal and used bottom right tags to record the consequences (and to mark clues which have been used in the analysis):

Next I analysed the opposite case where Alex is an innocent:

Observe that Megan is a criminal in both cases, so we know for sure that Megan is a criminal and can fill that cell in and then proceed.

Aside: you may have noticed that a case analysis wasn’t needed in this example, but at least it illustrates the technique.^[6]

Picking an initial cell

I try to choose an initial cell which will produce the largest number of deductions, for at least one of its possible values. That seems to give the most scope for RAA or an overlap of alternatives.

How about you?

How do you do case analysis? Have you other tips for picking initial cells? Join the discussion thread on Reddit^[7] or email me if you prefer.

Feedback

After this was initially posted, TeemoIsStealthed described how they pick an initial cell:

I usually pick my starting cell out of a duo or trio of cells in which only one of them can be innocent/criminal, that then gives me a good starting point to start tagging.

They also mentioned an alternative to screenshots:

What I do now is open a second (or third, or…) tab, and tag the people there for the other possible scenarios. By then quickly swapping between the tabs it’s easy to see which tags don’t change between the scenarios and which ones do :p (admittedly, doesn’t work on mobile)

This works nicely on Firefox:

• Right click the tab and choose “Duplicate Tab”.
• Use command+option+← and command+option+→ to swap between the tabs.^[8]