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So in this puzzle the goal is to come up with an answer that consist of 9 letters. Without giving away anymore info (atleast for now) on how to approach this puzzle I'll let you try make sense of it first.

Good luck!

enter image description here

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The 'family of 7' clued in this puzzle is:

the family of 7 Tetris shapes - otherwise known as tetrominos!

How? First notice that the bottom-right corner shows:

a key, giving the initial letter of what each of the other non-blank squares represents. These are (row by row):

Primes (clued by the top cube of this pyramid, where top is a synonym for prime - though I spent far too long looking at pyramidal numbers!),
Roman numerals (the Roman empire is mapped),
Square numbers,
Chemical elements with 1-letter symbols,
Vowels (the 5 crossed spaces correspond to the positions of the 5 vowels in the alphabet if counting from 1 to 26),
Binary numbers,
Hexadecimal numbers (clued by 'base 16'!).

If we shade the spaces in each box which correspond to these categories, we see the following:

enter image description here

These are the Tetris pieces! (Note that the vowel box uses Braille representation.) In other words, these are the 7 unique shapes (excluding reflection) that can be made from an arrangement of 4 squares.

This means the final 9-letter answer is:

TETROMINO i.e. a shape which can be made from an arrangement of 4 squares.

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    $\begingroup$ Well done :) rot13(Nf sbe gur cevzrf, V whfg gubhtug ohvyqvat oybpxf bs ahzoref!) $\endgroup$
    – Prim3numbah
    Commented Nov 18, 2020 at 10:15
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    $\begingroup$ @Prim3numbah Ah, that's quite poetic actually! I'll leave in the explanation I finally settled on because I think that's also valid - but I seriously went round the houses with pyramids for a loooong time! Nice puzzle, thanks :) $\endgroup$
    – Stiv
    Commented Nov 18, 2020 at 10:16
  • $\begingroup$ I don't understand how the Roman Empire maps to those 4 letters. Mind explaning a bit? $\endgroup$
    – iBug
    Commented Nov 18, 2020 at 17:50
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    $\begingroup$ @iBug Sure - the map is of the Roman Empire. The hash symbol overlaid on it means 'number', so we're looking for Roman numbers, which are commonly known as 'Roman numerals'. The letters in the Roman numeral system are I (1), V (5), X (10), L (50), C (100), D (500) and M (1000). Shade the letters in the box which are in this list (CIDL) but leave those which are not, and voila! :) $\endgroup$
    – Stiv
    Commented Nov 18, 2020 at 18:09

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