# New Riddles/ Brain Teasers Needed! **URL:** \ **Category:** The Game Room\ **Created:** [August 31, 2015, 9:31pm UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546 "2015-08-31T21:31:57Z")\ **Posts on this page:** 20\ **Page:** 12
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 27, 2015, 6:55pm UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/221 "2015-09-27T18:55:36Z")
I’ll note that my coloring game doesn’t really depend on using a hexagonal tiling; I just wanted a a tiling with at most three tiles meeting at any point, and that was the simplest example. You could just as well play the same game on something more complex like [this](https://upload.wikimedia.org/wikipedia/commons/3/31/1-uniform_n3.svg), with the same rules (+$1 for points with clockwise RGB; -$1 for points clockwise RBG). I can tell you immediately on sight that the provided coloring breaks precisely even, and that you can do a lot better; given a minute to count, I can tell you that you can earn a maximum of $31 on that board. You can even play the game on a tetrahedron or a cube instead (coloring the faces and gaining/losing dollars from vertices by the same rules as ever). Or a soccer ball! Indeed, you may find playing around with such figures particularly enlightening. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 27, 2015, 7:05pm UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/222 "2015-09-27T19:05:49Z")
> [@Indistinguishable](#): > > you can earn a maximum of $31 on that board. Er, unfortunate time for a typo: I meant to write $21. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 27, 2015, 7:27pm UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/223 "2015-09-27T19:27:50Z")
OK, even seeing the answer, I still don’t get the stite-nyet one. A little help? ---
**Author:** ![jimbuff314](https://avatars.discourse-cdn.com/v4/letter/j/c57346/32.png) [@jimbuff314](https://boards.straightdope.com/u/jimbuff314)\ **Post date:** [September 27, 2015, 8:07pm UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/224 "2015-09-27T20:07:52Z")
I didn’t get it either but looking at it and knowing the answer, I see it’s a simple letter substitution. ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [September 27, 2015, 9:38pm UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/225 "2015-09-27T21:38:32Z")
I’ve always wondered if [SPOILER]a cryptogram existed which decodes into TWO different valid sentences. For some reason the _Nevermore_ line popped into my head as one to try. I couldn’t construct a twin sentence, obviously, but the five components (bayou etc.) are all in a dictionary! It was only later that I realized Nevermore was especially appropriate: Poe popularized cryptograms in his short story _The Gold Bug_.[/SPOILER] ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 27, 2015, 11:37pm UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/226 "2015-09-27T23:37:29Z")
Certainly such cryptograms exist. Z xq. That can decode to either “I am.”, or “I do.”. The real question is, what’s the longest cryptogram which can be decoded in at least two valid ways? ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [September 28, 2015, 2:07am UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/227 "2015-09-28T02:07:08Z")
Here’s a familiar type of puzzle (though this particular one has never been solved AFAIK until today.) Billy did his long division problem properly, but his sister, now part of a religious cult, needed to smudge out all the digits in the homework exercise except the single 2. Can you reconstruct the problem and its solution? ```auto xxx xx)xxxx x2 xxx xxx xxx xx x ``` ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [September 28, 2015, 2:40am UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/228 "2015-09-28T02:40:20Z")
When you say “single 2”, are you implying that there was only a single 2 in the unsmudged problem? ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [September 28, 2015, 2:44am UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/229 "2015-09-28T02:44:06Z")
> [@Dr.Strangelove](#): > > When you say “single 2”, are you implying that there was only a single 2 in the unsmudged problem? Yes. ---
**Author:** ![Biotop](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/biotop/32/321_2.png) [@Biotop](https://boards.straightdope.com/u/Biotop)\ **Post date:** [September 28, 2015, 3:15am UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/230 "2015-09-28T03:15:44Z")
6340÷13 ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [September 28, 2015, 3:51am UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/231 "2015-09-28T03:51:46Z")
Sorry if it was too easy. 🙂 I’ll try to make a harder one but … it’s my bedtime. If you want another easyish one; sister has changed cults and now must leave the 7’s intact, smudging every other digit. ```auto x7x xx)xxxxx xx xx xx xxx xx xx ``` ---
**Author:** ![Biotop](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/biotop/32/321_2.png) [@Biotop](https://boards.straightdope.com/u/Biotop)\ **Post date:** [September 28, 2015, 3:59am UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/232 "2015-09-28T03:59:14Z")
Which word does not belong: BUTTERCUP, DANCER, EVERGREEN, PINAFORE, RAINBOW, RENAISSANCE, SNOWBANK, TEMPO ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 28, 2015, 6:26am UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/233 "2015-09-28T06:26:31Z")
The word that does not belong is BUTTERCUP, as Janna Ryan has not yet served as First Lady ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 28, 2015, 7:04am UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/234 "2015-09-28T07:04:23Z")
I should perhaps give a hint for my coloring puzzle, since I worry people must be giving up on it. My hint is this: go, pick a nice symmetric board, color it however you like, and calculate your profit. Then, Change the color of the centermost tile any which way, and recalculate your profit Repeat this process several times, if desired. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 28, 2015, 2:17pm UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/235 "2015-09-28T14:17:25Z")
> [@](#): > > Which word does not belong: > > BUTTERCUP, DANCER, EVERGREEN, PINAFORE, RAINBOW, RENAISSANCE, SNOWBANK, TEMPO I guessed the basic premise on my own, but even if I hadn’t, a Google of those terms turns up the relevant Wiki page as the second hit (after this very thread). **Indistinguishable** , I’m curious about your puzzle, but just haven’t had a chance to play around with it yet. I’m guessing, though, that you could start with an arbitrary initial state and allow it to evolve towards optimal by running something like the [Demon cellular automaton](https://en.wikipedia.org/wiki/Cyclic_cellular_automaton). ---
**Author:** ![Biotop](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/biotop/32/321_2.png) [@Biotop](https://boards.straightdope.com/u/Biotop)\ **Post date:** [September 28, 2015, 2:43pm UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/236 "2015-09-28T14:43:53Z")
Which word does not belong: WINTER, AUTUMN, SUMMER, SPRING, JOY, HOPE, GREED, FEAR, DEATH, LUXURY ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [September 28, 2015, 9:53pm UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/237 "2015-09-28T21:53:43Z")
I’ll summarize my conclusions about **Indistinguishable** ’s puzzle, though I’m embarassed not to be anywhere remotely near a formal proof. Especially embarrassing is that I noticed what became his Hint while I was playing around, but didn’t consciously proceed to an Aha! :o [SPOILER] Paint Red-Green-Blue-Red-Green-Blue-… around the edges, easily taking $1 profit for every three edge tiles. For simplicity, completely avoid Red in the interior so you needn’t worry about any scoring there. For the hexagon grids, this is easy. For the more complicated grid, there are 64 edge tiles (not counting two useless tits in the bottom corners) for a score of 64/3 = $21. When I colored that grid the details got complicated: some of the edge tiles are adjacent to 4 (or more) other edge tiles instead of just two. In some of those cases I scored an extra $1 on the edge, but had to pay back $1 to lock out a Red which was protruding into the interior. This gave me enough satisfaction that I can quit this puzzle and move on with the rest of my life, though it’s a minisculely tiny sliver of satisfaction compared with **Indistinguishable** ’s, who presumably has proof outlines for this result.[/SPOILER] ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 28, 2015, 10:19pm UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/238 "2015-09-28T22:19:01Z")
Good work, **septimus**! Your conclusions are correct. On a flat board with no holes, the only thing that matters is how the outermost tiles are colored: run around the outside border in clockwise order calculating each red-\>green, green-\>blue, or blue-\>red transition as +$1/3, and each red-\>blue, blue-\>green, or green-\>blue transition as -$1/3. The result will be your total profit, _no matter how the inner tiles are colored_. Thus, your profit is maximized by painting red-\>green-\>blue-\>red-\>green-\>blue-… clockwise along the outside border, netting you floor(perimeter/3) dollars. There is a simple reason why things work out this way (nothing high-falutin’). In case anyone would enjoy figuring it out, I’ll leave that mystery open for now (as well as the implications for playing on a closed surface like a tetrahedron, cube, or soccer ball); if not, I’ll post the punchline this evening. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [September 28, 2015, 10:43pm UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/239 "2015-09-28T22:43:11Z")
Oh, one other technical point which **septimus** already saw: On some boards, there may be tiles which hang onto the border but never actually touch two other tiles (for example, the two red squares at the bottom corners [here](https://upload.wikimedia.org/wikipedia/commons/3/31/1-uniform_n3.svg)); these are, as **septimus** put it, “useless tits”, since they touch no points at which dollars may be gained or lost. Just ignore these when painting red-\>green-\>blue-\>… along the outside border. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 28, 2015, 10:48pm UTC](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546/240 "2015-09-28T22:48:55Z")
Ooh, is this related to the generalized Gauss’s Law? Oh, and **Biotop** , we do of course expect that you’ll pass along the puzzles you get from your family, too (if you’re not already doing so). [Previous page](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546.md?page=11) [Next page](https://boards.straightdope.com/t/new-riddles-brain-teasers-needed/729546.md?page=13)