I have built twelve emoji-mutating machines, each of which changes one characteristic of an emoji—for example, adding glasses, removing a tear, changing a smile to a frown, and so on. Each machine has one and only one effect.

Each of the emojis on the left has passed through the three machines to their right, resulting in the emojis at the right. For example, the smiling, open-eyed, human emoji with a tear (at the bottom left) has passed through machines J, K, and L, resulting in the smiling, closed-eyed, human emoji with a heart (at the bottom right). Similarly, each of the emojis at the top has passed through the four machines below it, resulting in the emojis at the bottom.

What does each machine do?

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Note: The emojis at the left and top are semi-transparent because those are the “before” pictures. The machines don’t convert emojis from transparent to solid.

Source: My book (cited here for attribution, not self-promotion), adapted from puzzles by Barry R. Clarke, Challenging Logic Puzzles.

  • $\begingroup$ @WeatherVane yes, cat to human is one operation. I guess you can think of it as a set if you want, but my intention was to think of that as a unary operation, since there are cat-shaped emojis and human-shaped emojis -- but you are right, there are multiple differences between those two types of emojis. Sorry for any confusion. $\endgroup$ Commented May 7, 2019 at 23:23
  • $\begingroup$ The 9 changing features I see are: ears, eyes, mouth, whiskers, glasses, heart, outline, tear, chin. Which of those are grouped to make "cat" and "human", because 7 of those are changed in column 4 and only one in rows 2 and 3. $\endgroup$ Commented May 7, 2019 at 23:28
  • $\begingroup$ Each emoji either has a heart or no heart. Each emoji either has a tear or no tear. Each emoji either has a frown or a smile. Each emoji either has eyes open or eyes closed. Each emoji either has cat head or human head. Each emoji either has glasses or no glasses. And, each machine toggles one of those "either ... or..."s. $\endgroup$ Commented May 7, 2019 at 23:32
  • 1
    $\begingroup$ The generic human emoji is round faced and has no whiskers or cat-ears. The generic cat emoji has more pointed chin, whiskers, and cat-ears. This seems pretty self-evident and if you consider the "feature" to be a binary choice between "cat" and "human", the traits that accompany that feature seem clear to me. Other "feature" binaries are: glasses (y/n); heart (y/n); tear (y/n); eyes (open/closed); mood (happy/unhappy). I think that covers them all? $\endgroup$
    – Rubio
    Commented May 7, 2019 at 23:33
  • $\begingroup$ @WeatherVane You may be over-complicating this. Yes, it could have been stated more clearly, but I think the intent is (at least to me) pretty apparent. $\endgroup$
    – Rubio
    Commented May 7, 2019 at 23:34

1 Answer 1


I think this works:

A removes a heart
B opens eyes
C adds a tear
D adds glasses
E transforms to cat
F transforms to person
G makes unhappy
H makes happy
I removes glasses
J removes a tear
K closes eyes
L adds a heart


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