# No, It's Not A Polynomial

There is a simple way to generate every one of the thirty-seven numbers below. They form a closed set; that is, there are no more numbers with this property. My apologies in advance if this doesn't go as planned. This is my first number pattern and my puzzles tend to be either impossible to solve or trivially easy. Good luck!

3   5  17  27  29  33
35  37  43  50  60  62
69  74  82  96 100 115
117 121 129 135 153 169
181 193 210 235 242 258
262 270 272 276 288 297
312

Hint:

These numbers represent a pattern of which you all should be aware. In one sense I can definitely say that this puzzle can be solved with ease. As stated in the comments, it does not depend on any national or cultural pre knowledge. The order and arrangement of the numbers is not important. No special equipment is needed to derive these numbers. Again, good luck!

• You say they have a property. does that mean that the order of this sequence of numbers is irrelevant? Mar 16, 2016 at 8:58
• Could have something to do with the days of the year. If so, is it an international property? Mar 16, 2016 at 12:26
• @HughMeyers. You were right. this is damn impossible Mar 16, 2016 at 15:08
• Gah. I need a tool so that everytime I open this page, the numbers are in a random arrangement. I keep forgetting that it's arbitrary! =D Mar 21, 2016 at 17:50
• I (unironically, genuinely) love that Hugh's hints are always like "[restatement of something already noted in the puzzle or comments], [earnest assertion of his belief that someone can solve the puzzle]" Mar 21, 2016 at 18:46

Oh my!!! I figured it out and sheesh this was a real wicked question. Very sly.

It's the place of all of the "e"s in the question.

That was a good one.

Everyone was overthinking it including me.

The hint would result in:
3 5 11 ...

• Did I give it away when I said it can be solved with e's? Mar 21, 2016 at 21:09
• Nope. Picked up on that afterward. Hahaha. Mar 21, 2016 at 21:10

# Design Notes - Not an Answer

This part is really only for people who are interested in designing puzzles. I haven't been at it long - just over a month - but I have learned a little and I have a few theories about what makes a good puzzle. Even for a puzzle with a simple idea like this one, there are things that I did that, I hope, made it better. Doubtless there are more things I should have done to make it great and if anyone has ideas in that direction I would love to hear them.

For me, this puzzle was about expectations.

The tricky part was deciding exactly what to say in the preamble. I wanted the first few numbers to be prime, then continue with odd numbers hitting some primes as I went (not hard since they are pretty dense in that range), and finally mostly letting them fall where they may. The mind is quick to see patterns and I wanted to suggest a few trails to run down. The letter "e" appears with a fair degree of regularity so the spacing tended to have a fairly natural appearance. I engineered it to have a few clumps and a few bigger gaps but I decided against using any words with two "e"'s in a row in the perhaps mistaken belief that the eye would be drawn to them and might give away the pattern. Someone actually commented that they wished they could randomize the numbers when they looked at the page. I thought this was very acute.
One of the earliest comments asked if the arrangement of the numbers had any significance. I think, even though I truthfully answered that it didn't, that seeing the numbers arranged in a perfect square with one extra number nags at the back of the reader's mind. Why the extra number? We want things to follow a pattern. We want them to square up. The fact that it is one more than a perfect square must mean something. That's my theory anyway.

The next problem in composition was how much to say.

I needed to have enough numbers for the pattern to be unique. I couldn't have it match anything else and people here are absolutely amazing at finding number patterns. On the other hand I didn't want to appear to be droning on for the sake of droning on. I wanted to mention the count early on to suggest that it was something I knew before I began writing instead of something I generated near the end of the process. The title was something I wanted to say in the preamble but couldn't find a way to insert naturally.

I added a hint after a few days of inactivity on the puzzle. I assumed people had given up on it. Comments appearing afterwards indicate I was probably mistaken.

The point of the hint was, of course, the pun on "ease" and "e"'s. This dictated the wording "true to say" and "in a sense". I threw in some information given in comments as filler to make the nature of the hint less obvious. Ideally, I like a hint to be a sort of mini-puzzle in itself.

Creating a puzzle should make you happy.

Self-reference is kind of an obsession with me and part of the charm for me was that the seemingly inconsequential introduction to the problem of finding the pattern is the pattern. I like that the words about how my puzzles can be hard or easy were deliberately chosen to make it harder to solve. They were also quite true. When I typed in the puzzle, the "e"'s seemed to leap from the screen shouting their positions. Particularly the first two. I had no idea whether the puzzle would take 5 minutes or 5 days to solve. I love the complex problems that appear on this site and the care that goes into them but I also love the way simple, low-tech ideas can provide an entertaining challenge as well. Hopefully we will continue to see great examples of both.

• Whilst I saw this question and answer back when it was posted, I just (belatedly) stumbled across this behind the scenes post... Thanks for including it, it was an interesting read. I've often wondered if there'd be any interest in a "making of" type post on one of my puzzles, as I (personally) feel like the evolution of the puzzle itself, can be a fascinating journey. May 23, 2016 at 4:15
• @Alconja I would certainly be interested in a "making of" post. I find your puzzles fascinating. May 23, 2016 at 11:39

All these numbers are...

...in this question and there are no more numbers with this property :)

This answer will still be valid if you update the number list.

• You got me! Write it out and get your tick. Mar 21, 2016 at 19:26
• oh for cryin out Mar 21, 2016 at 19:29
• What about the special equipment? Mar 21, 2016 at 19:29
• Wait. Maybe he doesn't have it. And the name is suspicious. Who is this really? Mar 21, 2016 at 19:37
• So... Free hint. There is a way to interpret this answer as a really sly hint at the real answer. Mar 21, 2016 at 19:41