# Two honeycomb hints (yet another 'find the next number in the sequence')

Find the next number in the sequence $1,7,74,\dots$

First hint:

Second hint:

To clarify: the 'hints' are really clues. They are hidden, because any of the two alone could be enough to solve the puzzle. So, anyone who is interested, can look up only one hint, or both.

There is a simple rule for both cases, all the blanks can be filled and the sequence can be continued ad infinitum.

• Refreshingly large clues/data ratio! (just 3 actual data and 2000 words worth of clues)
– humn
Commented Sep 20, 2016 at 19:44
• @humn, thanks then. This is my first post here Commented Sep 20, 2016 at 19:47
• @humn, I made it up, and I haven't seen this sequence (or the arrays as a whole) anywhere Commented Sep 20, 2016 at 20:10
• Looks like a new take on Minesweeper. :) Commented Sep 20, 2016 at 20:17
• If you want to post another puzzle, go ahead and do it in a new question!
– Deusovi
Commented Sep 20, 2016 at 21:22

1017.

Because:

The rule is that

you fill out the honeycomb by simply adding the sum of the surrounding cells into the next cell clockwise.

The second hint can be filled out analogously:

It would be interesting to see in another solution what is the mathematics behind this rule. I suspect nice recursions lurking behind the scenes.

• Indeed, as 129+12+14=155. Thanks. Commented Sep 20, 2016 at 20:02
• Now it is correct. Would you like to fill in the hexagons below as well? Commented Sep 20, 2016 at 20:12
• I see now that it follows (perhaps) exactly the same rule. I will do that. Commented Sep 20, 2016 at 20:14
• Matsmath, I added another case, I hope you don't mind Commented Sep 20, 2016 at 20:37
• If the answer to that puzzle is different from this, then I would suggest you to start another post on that. Perhaps there are others who would like to pursue that challenge. Commented Sep 20, 2016 at 20:41