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(So I made this puzzle, and I wanted it to be fun rather than difficult! I hope it’s original enough)

Given a 5x5 grid as input, here’s an algorithm:

  • randomly select any 3x3 grid within the 5x5 grid
  • randomly select a number
  • add that number to all numbers within the 3x3 grid
  • repeat for a random amount of times

Now here are two grids:

Grid A:

39174 39174 85267 46093 46093
39174 39174 85267 46093 46093
102625 102625 219841 117216 117216
63451 63451 134574 71123 71123
63451 63451 134574 71123 71123

Grid B:

53329798 53329798 116037282 62695584 62695584
53329798 53329798 116037282 62695584 62695584
106466735 106466735 219003633 112558698 112558698
53125437 53125437 102987951 49852814 49852814
53125437 53125437 102987951 49852814 49852814

Question 1: if grid A is given as input to the algorithm above, is grid B a possible output?

Question 2: in the process of finding an answer to question 1, you should find a set of numbers. But that is not just any set! A specific permutation of this set can be translated into a piece of ASCII text. But that is not just any piece of ASCII text! It is the code that can unlock the meaning of life! Find that code, and enlighten the masses!

Hint:

if you found a somewhat obvious selection of numbers that can’t be translated to ASCII or utilized otherwise, you either found the wrong selection of numbers, or you will have to perform a somewhat obvious modification on those numbers (for example if you come across the number "444444" and you think it’s too long, you could try removing some digits from that number, since the digit "4" is very clearly a pattern there).

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  • $\begingroup$ In tha step 2: Randomly select a number: Is a number from the grid or just any random number? $\endgroup$
    – nadapez
    Oct 27 at 15:50
  • $\begingroup$ any number (to simplify things a little, let's say any random non-negative integer) $\endgroup$ Oct 27 at 15:58
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The only things that actually matter

are the total amounts you add to each of the nine possible square positions. (Adding 3 top the top-left square, then doing some other stuff, then adding 5 to the top-left square, is just the same as adding 8 to the top-left square and doing that other stuff -- that is, the order doesn't matter.)

In addition, the starting values don't matter - you can just subtract them away from the ending values. So it's easy to do the calculations:
image of 5×5 grids

The left grid here shows the "areas of influence" of 3×3s centered on points a and f. The right grid shows the total values of each of the numbers once you've subtracted away the starting values.

But it's actually even easier than that in this particular case:

The subtraction shows that you only chose the four corner grids, and so it's easy to read off the total amounts each were modified by.grid differences

You only actually chose the corner 3×3s. Since each of those is the only one to hit its corresponding corner, the adjustments can just be read off directly from the difference between the grids.

But the edge numbers don't add up to the right amounts, then - so it's not possible. Specifically, the top two are off by 11900, the bottom two by 9700, the left two by 11500, and the right two by 10300.

Dividing each of these by 100 and converting to ASCII, they read swag (in the order ←↑↓→).

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  • $\begingroup$ (Heavy spoilers ahead!) Very well said, I added 53290624 to the top-left subgrid, and 53061986 to the bottom-left subgrid! But the middle leftmost number is 106466735, and 106466735-(53290624+53061986)=114125≠102625, so it is actually not possible! But just how different are those numbers? 114125-102625=11500. Hmm this number sure looks suspicious, but it doesn't quite translate to ASCII text. If only we could make something out of it... The "0" digits are kinda suspicious, let's remove them! The decimal number "115" translates to the ASCII character "s", which could be part of the code! $\endgroup$ Oct 27 at 17:17
  • $\begingroup$ Ah, of course, I didn't check the math as thoroughly as I should've. (The rest of that hint was really not necessary.) $\endgroup$
    – Deusovi
    Oct 27 at 17:39
  • $\begingroup$ You're right, this hint was way too much... So, the answer to the meaning of life is to be swaggy, haha! I'm probably way more amused by this than I should be (but in my defense, "swag" is the only funny 4-letter word in the context of this puzzle). Anyway, well done! $\endgroup$ Oct 27 at 18:05

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