bonanova

I'm cool.

With a nod to the maximally meticulous we ask: What is the greatest number of equilateral triangles that can be defined by choosing groups of three points from a set of 16 distinct fixed points in the plane?

What are we trying to learn? Their identity (which is which in some sense)? Or the hand, for each person, that means Yes?

Looks like that's the answer then. Nice. I'm wondering whether that's the optimal configuration for 16 points to generate ETs. I'm also wondering whether the number of ETs increases proportionately faster then the number of points. It's easy to see that adding a 17th point at 6,4 increases the ratio from 2.5625 to 2.70588 (46 ETs.)

Wondering whether a solution has been found.

Thanks, never earned a gold star before. System keeps track of it? box. The star is just my own thing. Nothing to do with the site. I have unabashedly called it the "coveted bonanova gold star" with tongue in cheek, of course. Yes, it's surprising that everything is + and -; also surprising that the solution flowed from the 7-1 box. I'll give it another try. Again, great solve.

Ah, but of course my decision tree is incorrect. kudos to witzar (first solver) and DeGe for their clear thinking.

I have to say your approach looks right, and no doubt the programs agree on the answer that follows from it. I have two comments. One is it would be interesting to simulate the flips. I haven't simulated it, as the computer than has my favorite programming language on it is being repaired. The second comment is that I have a fairly clear analysis that gives a larger number of flips. Simulation would probably verify one of our approaches.

Very nice. I could not make any substantial progress without guessing, but even so I could not sort out the options in rows 3 and 4. I never found the 5-2-5 answer in the first two columns. Two stars for no trial and error.

Several of us logic-puzzle types got our feet wet playing Asylum Mafia last month. There's a new Sign-ups [Mafia] game that has four openings. I'd encourage some more of us to cross over to this genre of puzzle. It's different, you get to lie, cheat, pretend, lynch and kill. Add your name to the roster .

Yes Yes No (3 or more implies addition or multiplication)

Nice approach. Your answer is smaller than what I get.

I hope you weren't counting on any ... sympathy ... for having to pack ... for Paris.

As I noted Rookie is willing to email recent Mafia players to invite them back. I'll forward to him any suggestions you all may have. So far I've forwarded to him these names: Aaryan Brainiac100 curr3nt dyalDragon Hirkala Magic_luver101 mboon MikeD MissKitten Molly Mae Panther ShadowAngel7 Thalia TheCube tolecnal TwoaDay Yodell

KenKen is like sudoku. The numbers 1 - n fill the columns and rows of an n x n grid. Numbers are further constrained, to obey certain mathematical operations. Two numbers inside a box marked 3- would have to differ by 3. e.g., 5 and 8 in some order. Three numbers in a box marked 15x would have a product of 15. 1, 3 and 5 in some order. Here is an 8x8 KenKen puzzle where the boxes are just marked with a number, like 3 or 15. The mathematical operation is not specified. You have to figure that out as part of the puzzle. One hint is that a boxes that contains more than 2 numbers must be either add or multiply. Boxes that are marked 1 must be subtract: the other operators would require identical numbers or zero. Each box should be solved as completely as possible before solving rows or columns. A box with 1 number contains the marked number. A box with 2 numbers marked 15 could be either 3x5 or 7+8. Nothing else. A box with 2 numbers marked 12 could be 2x6, 3x4, 4+8 or 5+7. Only the number 1 would be excluded. A box with 3 numbers marked 12 permits all eight numbers. And so forth. This KenKen puzzle is one that I have not been able to solve. A gold star to anyone who solves it. Good luck

I imagined 10 green balls. I misread the problem.

You toss a fair coin repeatedly, hoping to see an odd number of T sandwiched between two H. e.g. H T T H H T T T T H T H ... ( 12 tosses. ) On average, how many tosses does this take?

Site admin is cool with emailing invites to this game. In addition to the names in the previous post, who else should we lure back in the clutches of Mafia addiction? I'll send the list to Admin later today.

Lengths of absences: Of the sign-ups, Hirkala and mboon last posted in 2012. Brainiac and Cube last posted in 2013. All the others, including MM, DDragon, TwoaDay, Magic and Panther posted during 2014. I've asked Site Admin if email can be used to invite recent players back. We need at least 4 replacements, maybe 6. Candidates: (all posted this year.) Aaryan (Feb 2) Curr3nt (last post marked private) MissKitten (March 24) GMaster (August 9) Thalia (June 25)

1. Flamebirde - 2014 2. MikeD - 2013 3. DyalDragon - 2012 4. Kikacat123 - 2013 5. Marksmanjay - 2013 6. bonanova - 2014 7. Barcallica - 2013 8. Brainiac100 - 2012 9. The Cube - 2013 10. araver - 2014 11. onetruth - 2014 12. dee_tot - 2013 13. TwoaDay - 2012 14. Aura - so long ago they dropped me from the roster 15. Magic - 2014 16. Hirkala - 2012 17. Panther - 2014 18. Bmad - 2013 19. mboon - 2012 Make it a full house.