A 5 by 5 grid of semi-opaque white squares over a golden radial gradient background. Some squares are filled with numbers, and others are left blank. The top row reads blank, blank, blank, blank, and 8. The second row reads 8, 8, 2, blank, and 8. The third row reads blank, 4, 6, 4, and blank. The fourth row reads 6, 8, 8, blank, and 4. The final row reads blank, 4, blank, 8, and blank.

Fill in this grid of numbers and explain your reasoning. Warning: this is a very mean puzzle! No hints will be provided.

... or maybe they will :)

Hint #1: Observe the dimensions of the image

The template for this puzzle was provided by 🌮Taco🌮 and can be found here. Thank you!

Text version:

8 8 2 8
4 6 4
6 8 8 4
4 4


Just using the text version will provide too few details to reliably solve this puzzle. There are important details relevant to the image version that make this puzzle easier to solve.

  • 3
    $\begingroup$ Oh, glad to see you enjoyed the template! 🙋‍♀️ $\endgroup$ Oct 3 '21 at 21:47
  • $\begingroup$ The more I stare at this, the more it looks like "adluaf mvyaf lpnoa", only problem is, that's typically a 4x4. You'd also have to fail to fill it. $\endgroup$ Oct 4 '21 at 14:37
  • $\begingroup$ There wouldn't be rot19(lbqxl) in the puzzle then - that's not it. $\endgroup$
    – Avi
    Oct 4 '21 at 16:44

This puzzle suddenly clicked into place when I realized that

this puzzle is colored gold!

The mean-ness of this puzzle comes from

the golden mean, phi,

and the contents of the grid are

the digits of phi, spiralling clockwise from the lower left corner:
0 3 3 9 8
8 8 2 0 8
1 4 6 4 7
6 8 8 5 4
1 4 9 8 9
where the emboldened digits, which were given beforehand, are precisely the nonzero even digits.

  • $\begingroup$ rot13(Naq gur engvb bs qvzrafvbaf bs gur vzntr ner nccebkvzngryl guvf) :) $\endgroup$
    – Avi
    Oct 10 '21 at 18:08
  • $\begingroup$ I can't view that on mobile, I think :p $\endgroup$ Oct 10 '21 at 19:10
  • $\begingroup$ Ah, very unfortunate - I tried to keep the necessary hints within the elements of the puzzle that you identified, though, so it wouldn't be device-dependent to be able to solve it :) $\endgroup$
    – Avi
    Oct 10 '21 at 19:13

Here's my answer:

An average square

And my reasoning:

- Title: Grid of Odds and Evens - the grid started with even numbers only, so I sprinked in some odd ones for this to be true.

- "This is a very mean puzzle!" - Taking the mathematical definition of the word "mean" to (ahem) mean, "average" I chose a mostly arbitrary number (in this case 7) and found numbers to fill in the grid such that the mean of every row and column matched this number. I'm looking for clues to see if 7 isn't so arbitrary after all, but the closest I have is that the average of the supplied numbers is 6.14... which if you take the mathematical ceiling you get seven. Thin thread that.

I'm afraid I didn't have any particular method of determining those missing numbers given my chosed criteria, other than using a bit of eye-logic and excel formulas to make sure I was keeping track of everything.

  • $\begingroup$ Unfortunately, this is not correct. Using this logic could produce an arbitrary number of correct grids for different goals. There is only one correct answer and none of the numbers can be different in any way with the correct reason. $\endgroup$
    – Avi
    Oct 3 '21 at 23:46

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