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Last evening, in France, at a friend's art exhibition, I came across this intriguing and enigmatic artwork which had a few square shaped boxes.

My friend asked - "So, what do you think? How many squares do you see?"

I counted, and recounted just to make sure I am not counting it wrong. With a grin on my face, I replied "Ah! Easy...There are 17 squares."

My friend laughingly said - "Non! Look carefully, can you see the 18th square?"

I was left confused and baffled. I rechecked but no luck. Finally, I gave up and asked for a hint.

My friend handed me a note which said -

Hidden behind the shadows is a mystery you need to see.
Moving five boxes is the only key.

Can you help me find the hidden 18th square? enter image description here

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  • $\begingroup$ Are the shadows important? $\endgroup$ May 2, 2023 at 14:08
  • $\begingroup$ @1357924680a Very important. :) $\endgroup$
    – Techidiot
    May 2, 2023 at 14:37
  • $\begingroup$ Well, important. I am doing a key. $\endgroup$ May 2, 2023 at 14:59
  • $\begingroup$ are the directions of the shadows important? $\endgroup$
    – RonnieChen
    May 3, 2023 at 18:42
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    $\begingroup$ @MOehm I suspect its this $\endgroup$
    – Billyb
    May 4, 2023 at 22:06

2 Answers 2

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Merci, for this brain teaser! After hitting many rabbit holes it struck me. Reminds me of my days of studying arts at Rennes studying artists using lights and shadows for their artwork... Reminds me of Trompe-l'œil. Here is the 18th Square...

enter image description here i.e. 324 displayed on 7-segment display enter image description here

The artwork summary...

You are asked to find the 18th square by moving 5 boxes..Shadows are important...Hmm...Good. I was able to find 5 boxes i.e. squares which spell out boxes going from left to right and top to bottom....
enter image description here
I tried to fit in all the possible places to see if I can build something but it went in vain until I started to see numbers being formed...specifically here it looks like a 7 segment display of number 3... enter image description here

Aha, and the rest was a cake walk then.... 18th square is $18^2 = 324$ enter image description here

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    $\begingroup$ Great Job! Wonderful explanations :) $\endgroup$
    – Techidiot
    May 9, 2023 at 9:09
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This is not an answer.

Here is a key to the 17 squares on the picture of the puzzle, with the direction of the shadows pointing to with the squares. Semicolons represent new lines.

B-UP NULL NULL I-NONE NULL O-LEFT NULL; NULL NULL NULL NULL NULL NULL M-NONE NULL; NULL NULL NULL K-UP NULL NULL NULL NULL; NULL T-RIGHT NULL NULL NULL NULL NULL R-RIGHT; F-DOWN Y-RIGHT NULL G-DOWNRIGHT NULL NULL U-DOWN W-RIGHT; NULL P-NONE NULL NULL X-RIGHT NULL NULL NULL; NULL NULL NULL NULL NULL NULL NULL NULL; E-DOWN NULL NULL S-DOWN NULL NULL R-NONE NULL
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    $\begingroup$ I don't know how helpful this is to the solvers but definitely helpful for me to know that there's nothing wrong with the visuals. +1 for the efforts :) $\endgroup$
    – Techidiot
    May 2, 2023 at 15:26
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    $\begingroup$ Shouldn't that be «Ceci n'est pas une réponse»? :) (I know, I know, he was Belgian, not French.) $\endgroup$
    – M Oehm
    May 2, 2023 at 15:59
  • $\begingroup$ @MOehm Exactly lol $\endgroup$
    – Techidiot
    May 2, 2023 at 16:06

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