A calculator only has 3 buttons. The first multiplies the current value by 3, the second adds 2 and the third subtracts 2. The calculator always starts with 0. What is the smallest positive even number that requires at least 10 button presses to make?
Here is the first version of the puzzle: Thr...
$(A)72$
$(B)18$
$(C)9$
$(D)19$
The question asks you identify the pattern and find the missing character.
I have been trying to solve this problem from a long time but I have not found any pattern till now. Please help!!
@jafe Sooo.. the answer is correct! The explanation of the definition is not. It's seems that something I thought was relatively well known may be slightly more obscure than I thought. This is probably what has foxed people. I'm willing to consider this solved as it has gone on for long enough.
It is well known that two knights and a king alone cannot force a checkmate. But that it on a 64-sqaure board.
According to Edward Winter’s C.N. 5449, William Shinkman found a way to give mate in a KNN-K endgame by adding an extra square below e1 (see the diagram on the left.)
The problem ca...
@GarethMcCaughan Yes that's exactly what I was going for. On the clarity grading scale (en.wikipedia.org/wiki/Diamond_clarity) anything which isn't Flawless or Internally Flawless is deemed "included", so my intention here was to reverse that and refer to those which are not included as flawless.
I have heard about the "four Cs" quite often because it's a thing people tend to talk about when referring to diamonds and engagement rings and all the rest but I guess it's a more obscure reference than I originally thought.
@GarethMcCaughan It's interesting what you say about OED. I'm struggling to find a dictionary reference even though I know the standard nomenclature is to refer to a diamond with inclusions as being "included".
Not sure. I would normally give it to the person who completes it (with the definition, for example) but perhaps my definition part was unfair, so that would make me inclined to give it to jafe. Do either of you have a good one lined up?
A few years ago, when I was a child, I really liked that one logic puzzle.
I tried to google it but couldn't found a puzzle or name of the puzzle.
It uses a grid similar to a crossword grid, in which you have to fill in words. These words are given and sortes by the length of the world. The goal...
A calculator has only 2 buttons. The first multiplies the current value by 2, the second divides it by 3 without a remainder (so 8 becomes 2). Starting with 1 what is the least number of presses you need to reach 9?
Here is a similar question: Three button calculator
This is very much inspired by this question.
Take the first 26 primes and relate each one to a letter of the alphabet.
On this occasion, you may choose how each number is mapped to each letter (so, for example we may have A=67, B=31, etc) but each letter must be mapped to a distinct prime. ...
A calculator only has 2 buttons. The buttons are, however, very powerful: they are programmable buttons, i.e. you can pre-set them to be any function (meaning any map from $\mathbb{Z}$ to $\mathbb{Z}$).
The calculator always starts with $1$. After you pre-set the buttons, a target number will be...
A robot sits in the central square on top of a 3x3 platform. The robot can move up, down, left or right, but if it steps off the platform it will crash and die. You can preprogram the robot to make a sequence of moves, each in one of the four allowed directions. An evil captor can choose to execu...
@WhatsUp (re: our discussion on the "two button calculator" post:) I've got meta posts partially written up with my thoughts on the puzzle / game distinction. It may be worth cleaning them up and posting them?
Yes, but I also think here it's not a puzzle / game distinction, rather a puzzle / mathematical problem distinction.
For example, if one posts a mathematical puzzle, which (s)he doesn't know an optimal answer. Would you then downvote it, because any answer could end up being not provably optimal?
Yes, that's one that's important too. The way you phrased your question made it clear that it was a game, though, and that's the most salient thing I was concerned about. (I do dislike mathematical problems that are not known to be solvable as puzzles, and I downvote many of them.)
Not necessarily. I still think it could be a bad puzzle, even if it's technically possible to find a solution. (Just like "what's the word in the Scrabble dictionary that has the biggest MD5 hash" is a bad puzzle, even though it's technically provably optimal.)
There is a difference between "technically provably optimal" and "found a smart way of proving optimality", though. If the smart guy really found a smart way, then why is the puzzle bad?
That's why I said it could be a bad one. If there does happen to be a clever solution, then I think it could be a good puzzle.
In my opinion: Whether something is a puzzle at all depends on whether it has a solution, something that definitely puts it to rest. (This is a necessary criterion, but maybe not a sufficient one.) This is the reason we don't allow questions where answers are speculative -- because there's no way to tell whether something is an answer.
However a solution (let's say a solution always mean a clevel one) may not exist at the time when the problem is posted, but may be found after people do some research on it. This comes to the dilemma: the question itself doesn't change, but finding a solution changes it from a bad question to a good question?
Whether something is a good puzzle depends on the intended path to the solution. There should be an "aha" moment that gets you to the solution, and the aha moment should be reasonable for people to arrive at, and likely 'hinted' in some way as part of the setup (though often with more mathematical puzzles, this hinting is less necessary). (This criterion is much fuzzier than the last.)
Well, yeah, I think it's definitely possible that finding a solution changes something from a bad question to a good one. If I randomly generated sentences and they happened to form a nice riddle with a single clever solution, but I posted it without knowing that they did, I think it would probably not be a good question. If I instead realized that some cosmic coincidence had happened and my riddle was perfectly solvable, and shared it with the answer in mind, it would be much better.
So then how should people vote for such a question? Before the smart solution is posted, it's a bad question and all downvotes; after the smart solution comes out, it becomes a good question, but still downvotes?
"There is an optimal solution and a proof of optimality; find it" is a puzzle. (If that proof is clever, it is a good puzzle.) "Do as well as you can" is not a puzzle, except maybe by coincidence that it fits one of the other categories.
Well, the question does change, no? It changes from "do as well as you can" to "find the optimal solution and show it's optimal".
In a previous discussion, I gave these two categories (plus a few more, for other relevant types of questions): (a) "What's the definitely optimal way to accomplish this task?" (b) "What's the optimal way to accomplish this task *that the PSE community can come up with?*"
(a) is potentially a puzzle, though an answer should have a proof (and not just be "eh here's the best I can do"). (b) is not a puzzle: it's a game.
I'd offer that whatever the solution ends up being, for it to really be a puzzle, it needed to have intentionally had an interesting (path to a) solution to begin with (what we here generally call the "aha" moment). Otherwise it's just an open-ended question (or problem) for which some solution can be found, but for sure, not all problems are puzzles.
I think the (b) could also be a good question to ask, if it stimulates people thinking/researching on the problem. It may eventually come to a real solution.
Of course one argument is that this could be posted on math.stackexchange. But I think I see people posting many of this kind of questions on this site!
Yes, people do that often (especially a few people in particular, who I've frequently downvoted). That's one reason I've been writing a meta post to argue that these should not be allowed, because they are not puzzles.
We have meta posts covering both the optimization type puzzle (that they must be type (a), not type (b), questions) and the distinction between a puzzle and a mechanical math problem.
OK, I think that should conclude our discussion: there is somehow a standard (and related discussions) in the meta posts (which I of course didn't know).
What is the least amount of chess pieces you can use to cover the board with their possible moves and what is their placement? You can only use the pieces that are found on the chessboard at any given time (for example, you only have one queen, two knights, two rooks, etc.). Similar to this, but ...
@Deusovi As an example, I don't know how to vote for this: puzzling.stackexchange.com/questions/91128/… I can't tell whether there is a provably optimal solution, but I'm almost certain that the author couldn't tell either.
Yet it seems others do like this puzzle (hence all the upvotes).
I dislike it, and don't think it should have been posted. (But I don't think a lot of questions of that sort should have been posted, and I made that clear in several comments.)
(Many of the questions by that author have been non-provably-optimal, or at least not provable in a nice way. A lot seem intended for computer search, which makes them at the very least bad puzzles.)
@Deusovi And here is another example with chess: puzzling.stackexchange.com/questions/91131/fewest-chess-pieces Actually my intention is not to pick out all these posts and ask you to downvote them, but to point out the fact that they are indeed not rare. Anyway I got the point and will try avoid this kind of posts myself.
The included screenshot shows an attempted Sudoku move. The computer is marking it incorrect. There is no other 7 in the row, column, or 3x3 cell. What gives?
Yeah different people may have different tastes (and definitions) for "puzzles"... I guess there must already have been numerous discussions on this in the meta site.
$(A)72$
$(B)18$
$(C)9$
$(D)19$
The question asks you identify the pattern and find the missing character.
I have been trying to solve this problem from a long time but I have not found any pattern till now. Please help!!
It is well known that two knights and a king alone cannot force a checkmate. But that it on a 64-sqaure board.
According to Edward Winter’s C.N. 5449, William Shinkman found a way to give mate in a KNN-K endgame by adding an extra square below e1 (see the diagram on the left.)
The problem ca...
This is very much inspired by this question.
Take the first 26 primes and relate each one to a letter of the alphabet.
On this occasion, you may choose how each number is mapped to each letter (so, for example we may have A=67, B=31, etc) but each letter must be mapped to a distinct prime. ...
The included screenshot shows an attempted Sudoku move. The computer is marking it incorrect. There is no other 7 in the row, column, or 3x3 cell. What gives?
