8
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OEEE
XOOX
EXEX
XEOE

Exactly one letter needs to be exchanged into one of the other two. But where and which one?

I intended this to be part of Monthly Topic Challenge. This is sort of a hint.

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3 Answers 3

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I think it's

The 2nd E in the 3rd row, it needs to be an O

How come:

The whole grid looks like Tic-tac-toe on a 4x4 grid. Given there are 5 Xs and 4 Os, it should be O's turn to play. Playing in the 2nd empty (E) square in the 3rd row guarantees a win for the player with the Os, completing both a vertical 3 in a row and a diagonal one. $$ \begin{array}{cccc} \mathsf{\text{O}} & & & \\\mathsf{\text{X}}& \mathsf{\text{O}} & \mathsf{\text{O}} & \mathsf{\text{X}} \\ & \mathsf{\text{X}} & \color{lime}{\mathsf{\text{O}}} & \mathsf{\text{X}} \\ \mathsf{\text{X}}& & \mathsf{\text{O}} & \end{array}$$

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  • $\begingroup$ Another good one. This must be it. $\endgroup$
    – JLee
    Aug 2 at 13:04
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Not sure if this is the intention, but

X is present in rows 2,3,4 and columns 1,2,4
O is present in rows 1,2,4 and columns 1,2,3
E is present in rows 1,3,4 and columns 1,2,3,4

So

If the constraint is present in 3 rows/columns, the only way is to change the E in column 1 (all other columns have 2 Es). Can only be changed to X to not break constraint for O.

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  • $\begingroup$ @Jlee After seeing your answer, I'm fairly sure mine is a happy coincidence - TicTacToe reference makes a lot of sense, with E perhaps representing "empty" $\endgroup$ Aug 2 at 11:35
  • $\begingroup$ but yours is simpler, so I was actually thinking that it is probably correct. $\endgroup$
    – JLee
    Aug 2 at 11:45
  • $\begingroup$ This would be a good answer for an IQ test kind of question but it is missing the parody aspect, so it is not what I had in mind. $\endgroup$
    – quarague
    Aug 2 at 11:50
  • $\begingroup$ I think the progressive matrix tag made us think it was an IQ-style question, since we are used to seeing that tag on those questions, and that directed our focus away from the tic-tac-toe aspect. However, the tag is probably good, but my being misled was due to my incorrect narrow interpretation of the tag. $\endgroup$
    – JLee
    Aug 2 at 13:11
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Is it

the 2nd E in the 4th row needs to be an O.

Reasoning:

Tic-tac-toe comes to mind. There are 5 X's, but just 4 O's, so it seems we need to change one of the E's to an O, but which one?
The X's form 3 rows of 2, where 2 of those rows are connected at one point. Therefore we must place the O so that that setup holds true for O's also. That means the O must replace one of the E's on the bottom row.
To decide which one, we notice the number of columns and rows taken up by X is 3, so in order to match that, the O must replace the E in the 2nd column.

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  • $\begingroup$ Your reasoning starts out exactly as what I had in mind but you got to a different answer and the reasons for it to me look more complicated that what I was thinking. $\endgroup$
    – quarague
    Aug 2 at 11:48

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