The previous aliens have departed from Earth. Another group has arrived from the vicinity of Alpha Centauri or Sirius (it's not important which) to probe the human psyche.
Help humanity to score a perfect 10 by determining the organisational principle involved in the following sequence of figures, and hence the missing figure.


But wait, that's not all ...

There are a number of clues embedded in the problem description. You will either find them, or you won't.

  • 2
    $\begingroup$ A perfect 10 when they are only 8 figures of 9 squares ? D: $\endgroup$ Aug 27 '15 at 14:53
  • 1
    $\begingroup$ These problems are somewhat interesting the first time. After the third time, it's more of a "meh". $\endgroup$
    – GentlePurpleRain
    Aug 27 '15 at 15:04
  • $\begingroup$ @Therandomguy - I had to word it the way I did, and could not have written "perfect ten". $\endgroup$
    – Marconius
    Aug 27 '15 at 15:16
  • $\begingroup$ @GentlePurpleRain - I can see your point. However, this problem is very different to the other two. I think the clues in this one are better as well. Enjoy! $\endgroup$
    – Marconius
    Aug 27 '15 at 15:23
  • 1
    $\begingroup$ 'Aliens are continuing to probe the human psyche' oh no, don't tell me the aliens from the Maze are back!! I thought I handled them for good! $\endgroup$
    – NeedAName
    Aug 27 '15 at 16:22

On this grid of digits:

1 2 3
4 5 6
7 8 9

These layouts represent the digits of the powers of 2, starting at 512 and going down. The missing one is 64, which is the left and right squares in the middle row.

There are only 10 possible layouts (1,2,... 512) because 1024 contains a 0, which doesn't have a spot on the grid.

  • $\begingroup$ Ah! You beat me to it =) $\endgroup$
    – Hackiisan
    Aug 27 '15 at 18:37
  • $\begingroup$ 8192, 16384 and 32768 would also be possible, although there would have to be gaps left for 4096, 2048 and 1024. After that all powers of 2 either repeat a digit or contain a 0. $\endgroup$
    – Mike Scott
    Aug 27 '15 at 20:23
  • $\begingroup$ @MikeScott I didn't count those because of the gap. $\endgroup$
    – f''
    Aug 27 '15 at 20:53
  • $\begingroup$ Well solved! BTW the clues, e.g. binary star systems, were meant to indicate that binary (base-2, and hence powers of two) is important. The "10" indicates the binary digits (01 would be too obvious?), and is also a nod to sayings such as "There are 10 types of people in this world: those who understand binary and those who don't". But it's cool that you found another meaning that fits too! $\endgroup$
    – Marconius
    Aug 27 '15 at 21:03

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