Mark S.
Reputation
30/100 score
 Mar 14 revised B & W balls in box. If any time we draw out a ball, the current count of white is always more than black, how many possible cases? as this is a one-player-game with hidden information, it's not really a cgt problem Mar 14 answered Factorization game, can we find winning strategy? Mar 13 comment Factorization game, can we find winning strategy? Is 270000 the only case you are interested in, or do you care about general facts about this game? Also, what is the source of this problem (presumably a contest)? There's a lot to be said about the general case, but I want to make sure that there's not, say, already a paper on this game. Mar 12 comment Determine optimal strategy in board game @RossMillikan, it is, but as they were just asking for hints I didn't think it prudent to reveal what game it was . Mar 12 revised Determine optimal strategy in board game added 68 characters in body Mar 12 answered Determine optimal strategy in board game Mar 12 comment Determine optimal strategy in board game Hetajr, does the pawn only move one space at a time? Are you allowed to write a program? What is the source of this problem and what games/ideas have been covered recently in the class/book? The answer to this is known, but the way you approach it would depend a lot on the relevant context/what you know. Mar 11 comment What does $\ln(\ln(x))$ simplify to? I like $f^{\circ2}$ as a notation for iterated composition that is unlikely to conflict with other notation. Mar 10 revised Game, stealing edges in a graph. added tags Mar 10 answered Finding p positions with 2 subtraction sets in the take-away game Mar 10 comment Finding p positions with 2 subtraction sets in the take-away game @JMoravitz "Subtraction games" (sometimes called "takeaway games") with their "subtraction sets" are well-known things in combinatorial game theory. For one source of background, see cs.cmu.edu/afs/cs/academic/class/15859-f01/www/notes/comb.pdf $P$-positions (and $N$-positions) are probably even more well known (and are also covered in that PDF): An $N$-position is a position where the Next player to move wins, and a $P$-position is a position where the next player to move loses (so that the player who moved just Previously can win). This question was pretty clear, IMO. Mar 9 revised Completing ordered Fields added surreal numbers tag Mar 9 revised How to find periodicity of a nim sequence? added cgt tag Mar 8 comment Are all nimbers included in the surreals? The surreals are the maximal collection of option-closed (a move in a surreal is to another surreal) games that are comparable (in the usual favorability-to-left ordering) to their options. $\star$ is not comparable to its option $0$, and as @EricWofsey pointed out, $\uparrow$ is not comparable to its option $\star$. Mar 7 comment What is a good notation for an “even falling factorial”? Mathworld has a notation for the generalized falling factorial at mathworld.wolfram.com/FallingFactorial.html But I can't say I'm a big fan of the notation there. Mar 6 awarded Yearling Mar 4 revised Placing circles inside of a regular polygon. added cgt tag Mar 4 comment Factorization game, can we find winning strategy? I hope to post an answer with my findings in the next few days, but I think your conjecture at the end is false. I believe $(3,3,3)$ is actually a win for the second player. Mar 2 comment How can we plot four dimensional planes and how the planes intersect? Just for clarification, are you asking "how can we determine (with some algebra) whether their intersection is a line or plane or whatever?" or "how can we use pictures to visualize the intersection?"? Those two questions have very different answers. Mar 2 comment Game-winning strategy @Stefan4024 The relevant use of the word "heap" is in scare quotes. A "heap" in the octal game 0.007 corresponds to a collection of points in the same component in your game. In addition to the 8 or so resources I mentioned that explain the correspondence between positions and heaps of Nim, and one way to compute the Nim values, I also just added a couple sentences on the subject. For example, a component with 6 points in your game happens to act like a Nim heap of size 2 in combinations since you can move to 3 pts (Nim 1), 1pt and 2 pts (Nim 0).