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What pattern could be placed in the last square to complete the sequence? 1:White circle in middle.2:White circles in middle, upper left, and bottom right.3:Blue circles in middle, upper left, and bottom right.4:Blue circles in middle, upper left, bottom right, and white circles in upper right and lower left.5:Blue circles in middle, upper left, upper right, lower left, and bottom right.6:"?".

This image from https://drive.google.com/file/d/1W0A2E2GIwi6mq9b94FzA7PhfXCae-VPB/view originally created by Daniel Rudansky

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  • $\begingroup$ Welcome to Puzzling! This looks like a puzzle you found elsewhere. For content you did not create yourself, proper attribution is required. If you have permission to repost this, please edit to include (at minimum) where it came from, then vote to reopen. Posts which use someone else's content without attribution are generally deleted. $\endgroup$ – Glorfindel Nov 7 at 21:28
  • $\begingroup$ Yup, Glorfindel's right. On hold pending attribution. (Sorry about the "off-topic" wording; we only have a fixed range of possible reasons for closing a question. Of course this isn't actually off topic.) $\endgroup$ – Gareth McCaughan Nov 7 at 22:15
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It seems that the pattern goes:

Add 2 blank dots, then colour them in, then add 2 blank dots, then colour them in, etc.

Therefore a suitable pattern for the last image would be:

dice with seven dots
Which is the usual pattern for a 7 dotted dice, often used in dice games.

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    $\begingroup$ why is not the white-blue-white line vertical? $\endgroup$ – balazs.com Nov 8 at 10:01
  • $\begingroup$ The dots could be placed on the diagonal too. $\endgroup$ – Conifers Nov 8 at 10:07
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    $\begingroup$ because this is the standard layout for a 7 dot dice $\endgroup$ – AHKieran Nov 8 at 13:58
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The pattern appears to build up, adding dots and colors, leaving the sequence "full" at the fifth square, with no room to add anything after that, so you could make an arbitrary choice as to what happens next, such as:

The sequence repeats, so the sixth square looks just like the first square. Or the sequence resets before it repeats, and the sixth square is empty. Or the sequence follows the pattern ABCDEDCBA, and the sixth square looks like the fourth square.

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If we take this pattern as a part of a bigger and complete pattern with a well defined rule, then this makes sense:

enter image description here

It is a complete palindrome-like pattern with "mirrored" operations (add-change-add- change-change-remove-change-remove). It eliminates the obscurity how to add white spheres after item 5. It involves operations that have already been used, so in this sense it is not arbitrary any more.

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