I assume that ( 1 ) as the number of flags is bounded (between 100 and 1000), we can require enough memory to store a record for each found flag, and can declare how long a record is ( 2 ) a memory cell has finite precision, and that the dimensions of the maze could be arbitrarily greater than the largest value of a cell. So, although we could store some information about each found flag, we could NOT store coordinates. In fact we cannot even store coordinates of one spot (after all, we may have walked a googolplex number of steps in a straight line). ( 3 ) we are NOT permitted to leave anything in a square except a flag, and are not permitted to distinguish the orientation of the flag. Are these all true assumptions about the rules?
BMAD, I'm also having difficulty interpreting the words "...d has to decrease by two to keep the same median". The only median mentioned so far is the median of a and b. As Rob and Araver have said, the value of d has no effect on the median of a and b. So, should we interpret the fragment above as: "...d has to decrease by two to keep the same median of (a,b,c,d)"?
Araver, I'm assuming that the shortest path is what counts, and that a stakes assignment with two or three equal numbers counts as zero. I think the coin-flipping is window dressing...Of course, Bonanova's opinion is more reliable :-) Here's my answer at 8 steps:
I think I misunderstood; I guess in your description, a "turn" is the same as a "round", and the "two active players" are the two who flipped the same side of the coin. So, if they had 1,1,3 and the 3 was the odd man out, then the game is over. Have I got it this time?