Keys, codes and patterns

My flatmate always forgets his key, so now we have installed a small locker outside the room where a spare is located. So that my flatmates doesn't forget the code we made this small riddle for him, if he can find the pattern he finds the missing number. The missing number is also the code for unlocking the locker. Please help him, he forgot his key (and the pattern) again....

Hint:

The pattern starts at the top left corner.

Hint:

If you sum first one number, secondly three numbers, thridly five numbers and lastly seven numbers the pattern should be clear!

The missing number is

131

The reason is that

as denoted by the red lines, each group sums to 311

Could it be

295

Reason

If we consider the top row being the sum of some of the 12 numbers below we get the following: where each number is being used precisely once and the different colors corresponds to one of the four numbers in the top row

• You're definitely in the right direction. The pattern includes the sum of numbers, but the numbers which are summed are arranged in a clear pattern and not randomly arranged over the grid.
– tyui
Apr 6, 2020 at 5:47

We start from the top. The sum of the first row is 315 + 165 + 145 +83 = 704. The sum of the second row is 133 + 13 + 3 + 1 = 150. The sum of the third row is 113 + 19 + 31 + 50 = 213. The sum of the fourth row is 12 + 2 + 32 = 46. If we subtract from the sum of the first row the sum of the other three rows, we have 704 - (150 + 213 + 46) = 295, so the missing number is 295.

• that's not the missing number, but you're getting closer!
– tyui
Apr 8, 2020 at 6:23

$$331$$

Because :

If we observe first column there is pattern :
311 ( $$three$$ one time and $$one$$ two times)
133 ( $$one$$ one times and $$three$$ two times )
113 ($$one$$ two times and $$three$$ one times)
So , as we can see above there is no $$3$$ two times in start so i think there should be
$$331$$

• Good try, but all sixteen numbers are needed to find the pattern which leads to the question mark!
– tyui
Apr 5, 2020 at 17:37
• @tyui rot13(jr arrq gb nqq nyy pbyhza fhz naq naq gura fhogenpg jvgu pbyhza 1 ,vs fb nafjre jvyy or 1 (557-556 = 1)) Apr 8, 2020 at 6:37
• rot13(fhogenpgvba vf abg arrqrq gb svaq gur cnggrea)
– tyui
Apr 8, 2020 at 8:34
• "Same result we will get if we add rows as well" No Shit Sherlock... rot13(V'z abg fnlvat: fhzz bs nyy ahzoref = ? )
– tyui
Apr 8, 2020 at 9:04
• rot13(v nz pbashfr yvggyr ovg , ohg yrg vg or fbzr bar ryfr jvyy tvir nafjre bs guvf v nz abg fb tbbq va znguf :C) Apr 8, 2020 at 9:29