No. A program can be part of a proof, but there also needs to be an argument that the program is complete and correct. That part can’t be done in code.
On the other hand, there’s not all that great a difference between computer code and a symbolic formal system of the sort used to write a proof. One could just as well claim that you can’t write a proof in a symbolic formal system, because you need both the formal derivation and an argument that the derivation is complete and correct.
This is a little bit of a hijack, but if you’re dealing with C or most other imperative languages, the difference between proofs and programs is a vast chasm. There are other languages where the difference is a bit smaller, to say the least, but that’s not what almost anyone is thinking about here.
I’m not sure how you’re getting this, although it is a bit hard to parse. But I think drhess’s question could be rephrased as:
“Under the traditional rules where a draw (meaning too many repetitions) is a win for Hare, can the Hare, using best play, always win against the Hounds?”
I do think the answer is “no, the hounds can force a win”, although I’m not as certain as septimus is.
On re-reading what drhess said, and then re-reading it again because I still had the wrong reading stuck in my head, I realize that I was completely mis-parsing the question, and gave an answer that wasn’t asked for. Ignore my post 62.
A listing of all possible Hare moves and winning Hounds’ responses would constitute a rather rigorous proof, I think, at least if English phrases like “if Hare plays … Hounds play …” were inserted. My program can be modified to produce such a listing by adding one print statement.
As my brain power has deteriorated with age, I’ve tried to make my C codings more simple and transparent. I think SCSimmons can attest, however, that my brain needs to deteriorate much more before my code has acceptable readability. :smack:
In the game room thread, the dogs immediately occupied the center position, and it was shown that if after the hare’s second move it goes back to the far right position, the hounds can force a win. There are only three other possibilities for the Hare’s location after its second move, due to symmetry. Those other three possibilities could be examined in the same manner fairly easily using the code.
That’s assuming a win for the Hare isn’t found from that position, so you didn’t have to back up a move.
So I finally found time to take a crack at solving this game. My approach…
The number of game states is small. There are 11 spaces to be occupied; it is someone’s turn; and the hounds have accumulated some number 0 through 9 of vertical moves. In this enumeration, the number of game states is:
11 * 10 * 9 * 8 * 2 * 10 / 6 = 26400
where the 6 in the denominator accounts for the indistinguishable hounds.
Many of these board states are only accessible after passing through a “win” state, so we can cull those. Many others are simply inaccessible, i.e., they have no valid parent state, such as this one:
Not accessible, since it's the hounds turn.
The hare couldn't have come from anywhere...
+ + D
+ + + D R T=D VM=0
+ + D
In the above notation, D=hound(dog), R=hare(rabbit), T=whose turn, VM=number of accumulated vertical hound moves.
After culling post-win and inaccessible states, there are 23742 states left.
Previous to this (to facilitate the culling and the later steps), I set up a multiply-linked list of the available game states. Each node of the network corresponds to a state and carries with it a list of all possible daughter states and all possible parent states.
Step 1:
Simply loop through the list of 23742 states, tagging all win-states.
Step 2:
Loop through again, looking for any state which is tagged as a win for one team but it is the other team’s turn. That is, if Team A wins in this state but it is Team B’s turn, then Team A is able to force this win by moving to this state on the previous turn. So, tag all parents of these states as wins for Team A.
Step 3:
Loop through again, looking for any state which is not yet tagged for either team. If all daughter states for this state are tagged for the same team, then this state is a lock for that team. Tag it as such.
I repeat Steps 2 and 3 until the number of undetermined states no longer decreases. It so happens that when this condition is met, all states have been tagged for one team or the other.
*Result: *there are 861 game states in which hounds can force a win. The starting state is not one of them. That is, hare can force a win.
Of the 861 states from which hounds can force a win, only 95 distinct layouts exist when you remove the vertical-move-count multiplicity. Thus, I can list all 95 layouts from which a hound force is possible. The VM notation used below indicates the range of accumulated vertical moves that are okay if the hounds are to force.
D D R
+ + + + + T=D VM=0-9
+ + D
D D +
+ + + + R T=D VM=0-7
+ + D
D R D
+ D + + + T=D VM=0-9
+ + +
D R D
+ + D + + T=R VM=0-9
+ + +
D + D
+ + D + R T=D VM=0-8
+ + +
D + D
+ + + D R T=D VM=0-7
+ + +
D R D
+ + + + + T=D VM=0-9
D + +
D R D
+ + + + + T=D VM=0-8
+ D +
D + D
+ + + + R T=D VM=0-9
+ D +
D + D
+ + + R + T=D VM=0-8
+ + D
D + D
+ + + + R T=D VM=0-9
+ + D
D + D
+ + + + R T=R VM=0-8
+ + D
D + +
D + + + R T=D VM=0-9
+ + D
D R +
+ D + + + T=D VM=0-9
+ + D
D + R
+ D + + + T=D VM=0-9
+ + D
D R +
+ + D D + T=D VM=0-8
+ + +
D R +
+ + D + + T=R VM=0-9
+ + D
D + R
+ + D + + T=D VM=0-9
+ + D
D + +
+ + D R + T=R VM=0-7
+ + D
D + +
+ + D + R T=D VM=0-7
+ + D
D + +
+ + + D R T=D VM=0-7
+ + D
D + +
+ + + + + T=D VM=0-9
D R D
+ D D
+ + + D R T=D VM=0-7
+ + +
+ D D
+ + + R + T=D VM=0-6
D + +
+ D D
+ + + + + T=D VM=0-6
D R +
+ D D
+ + + + R T=D VM=0-8
+ D +
+ D D
+ + + + + T=D VM=0-6
+ D R
+ D D
+ + + R + T=D VM=0-8
+ + D
+ D D
+ + + + R T=R VM=0-8
+ + D
+ D R
D + + + + T=D VM=0-8
+ + D
+ D +
D + + + R T=D VM=0-8
+ + D
+ D R
+ D + + + T=D VM=0-7
+ + D
+ D +
+ D + + R T=D VM=0-9
+ + D
+ D +
+ + D R + T=D VM=0-9
D + +
+ D +
+ + D + + T=D VM=0-9
D R +
+ D +
+ + D + + T=D VM=0-9
+ D R
+ D R
+ + D + + T=R VM=0-9
+ + D
+ D +
+ + D R + T=D VM=0-9
+ + D
+ D +
+ + D + R T=D VM=0-9
+ + D
+ D +
+ + + D R T=D VM=0-9
+ + D
+ D +
+ + + + R T=D VM=0-9
D + D
+ D +
+ + + + + T=D VM=0-8
D R D
+ D R
+ + + + + T=D VM=0-8
+ D D
+ D +
+ + + + R T=D VM=0-9
+ D D
+ R D
D + D + + T=D VM=0-9
+ + +
+ + D
D + D R + T=D VM=0-9
+ + +
+ + D
D + + + R T=D VM=0-9
+ + D
+ R D
+ D D + + T=D VM=0-8
+ + +
+ + D
+ D D + R T=D VM=0-7
+ + +
+ + D
+ D + D R T=D VM=0-7
+ + +
+ + D
+ D + + R T=D VM=0-7
+ D +
+ + D
+ D + R + T=D VM=0-9
+ + D
+ + D
+ D + + R T=D VM=0-7
+ + D
+ + D
+ D + + R T=R VM=0-9
+ + D
+ + D
+ + D D R T=D VM=0-9
+ + +
+ + D
+ + D R + T=R VM=0-7
D + +
+ + D
+ + D + R T=D VM=0-7
D + +
+ + D
+ + D + + T=R VM=0-7
D R +
+ + D
+ + D + + T=D VM=0-7
D + R
+ + D
+ + D R + T=D VM=0-9
+ D +
+ + D
+ + D + R T=D VM=0-7
+ D +
+ + D
+ + D + + T=R VM=0-7
+ D R
+ + D
+ + D R + T=R VM=0-9
+ + D
+ + D
+ + D + R T=D VM=0-9
+ + D
+ + D
+ + + D R T=D VM=0-8
D + +
+ + D
+ + + D R T=D VM=0-9
+ D +
+ + D
+ + + D R T=R VM=0-0
+ + D
+ + D
+ + + + R T=D VM=0-8
D D +
+ + D
+ + + R + T=D VM=0-9
D + D
+ + D
+ + + + R T=D VM=0-8
D + D
+ + D
+ + + + R T=R VM=0-9
D + D
+ + D
+ + + R + T=D VM=0-8
+ D D
+ + D
+ + + + R T=R VM=0-8
+ D D
+ + R
D + D D + T=D VM=0-8
+ + +
+ + R
D + D + + T=D VM=0-9
+ D +
+ R +
D + D + + T=D VM=0-9
+ + D
+ + R
D + D + + T=D VM=0-9
+ + D
+ + R
D + D + + T=R VM=0-9
+ + D
+ + +
D + D R + T=D VM=0-9
+ + D
+ + +
D + D + R T=R VM=0-9
+ + D
+ + +
D + D + + T=D VM=0-9
+ R D
+ + R
+ D D D + T=D VM=0-4
+ + +
+ R +
+ D D + + T=D VM=0-8
+ + D
+ + R
+ D D + + T=R VM=0-6
+ + D
+ + +
+ D D R + T=D VM=0-6
+ + D
+ + +
+ D D + R T=D VM=0-8
+ + D
+ + +
+ D D + + T=D VM=0-8
+ R D
+ + +
+ D + + + T=D VM=0-9
D R D
+ + +
+ + D D + T=D VM=0-8
D R +
+ + +
+ + D D R T=D VM=0-9
+ + D
+ + +
+ + D + R T=D VM=0-9
D + D
+ + +
+ + D + + T=R VM=0-9
D R D
+ + +
+ + D + R T=D VM=0-9
+ D D
+ + +
+ + + D R T=D VM=0-8
D + D
+ + +
+ + + D R T=D VM=0
+ D D
I haven’t seen anything so far that looks out-of-sorts, but I haven’t read the other thread yet. If anyone wants to give me an unlisted state that they think should be a hound-lock, I can do an analysis of that state (either to show why it isn’t a hound-lock or to uncover a bug in my code 
)
I also haven’t chewed over these results much at all; hopefully someone finds something interesting in them…
So can’t your program play against Septimus’?
Or make up a system of algebraic notation, and print out the moves in algebraic notation. So what are you waiting for? Hop to it!
Yes. I haven’t had a chance to parse the history of this thread, so: is the conclusion still from septimus that hounds can force from the starting configuration? If so, then I’d be happy to play against septimus’s program with mine, if only to find a fault with mine.
I don’t see the position in post 18 shown as a win for the hounds, but we played that one out, and it seemed to be a forced win for the hounds. I’d like to see that one checked. I believed the plays I didn’t make as the hare always led to a loss for the hare, and eventually I could see the hare would lose no matter the move.
ETA: the hounds just moved to reach that position.
ETA2: I reference post 9 as losing for the hare a couple times and you do have that as a win for the hounds.
Beautiful… This is exactly the sort of test I wanted! Upon tracing this state’s tagging sequence, I found a mistake… (misplaced curly brace!). New results coming in next post…
Updated result after bugfix (thanks, ZenBeam!)
There are 4122 states from which hounds can force a win, and the starting configuration is one of them. That is, hounds can force a win.
Eliminating the vertical-move-count multiplicity leaves 438 layouts, which I will attempt to paste into this message if the hamsters let me…
Okay they won’t, but I’m only over by 2000 characters. I’ll break the list in two. Here are 219 of the hound-lock layouts:
D D D
+ + + R + T=D VM=0-6
+ + +
D D R
D + + + + T=D VM=0-9
+ + +
D D +
D R + + + T=D VM=0-6
+ + +
D D +
D + + R + T=D VM=0-9
+ + +
D D +
D + + + R T=D VM=0-9
+ + +
D D +
D + + + R T=R VM=0-8
+ + +
D D +
D + + + + T=D VM=0-6
+ R +
D D +
D + + + + T=D VM=0-8
+ + R
D D R
+ D + + + T=D VM=0-9
+ + +
D D +
+ D + + R T=D VM=0-9
+ + +
D D +
+ D + + + T=D VM=0-7
+ + R
D D R
+ + D + + T=R VM=0-9
+ + +
D D +
+ + D R + T=D VM=0-9
+ + +
D D +
+ + D + R T=D VM=0-9
+ + +
D D R
+ + + D + T=D VM=0-5
+ + +
D D +
+ + + D R T=D VM=0-7
+ + +
D D R
+ + + + + T=D VM=0-9
D + +
D D +
+ + + R + T=D VM=0-8
D + +
D D +
+ + + + R T=R VM=0-8
D + +
D D +
+ + + + + T=D VM=0-8
D R +
D D +
+ + + + + T=D VM=0-9
D + R
D D R
+ + + + + T=D VM=0-8
+ D +
D D +
+ + + + R T=D VM=0-9
+ D +
D D +
+ + + + + T=D VM=0-8
+ D R
D D R
+ + + + + T=D VM=0-9
+ + D
D D +
+ + + R + T=D VM=0-8
+ + D
D D +
+ + + + R T=D VM=0-9
+ + D
D D +
+ + + + R T=R VM=0-8
+ + D
D + D
D + + R + T=D VM=0-9
+ + +
D + D
D + + + R T=D VM=0-9
+ + +
D + D
D + + + R T=R VM=0-9
+ + +
D + D
D + + + + T=D VM=0-9
+ + R
D R D
+ D + + + T=D VM=0-9
+ + +
D + D
+ D + R + T=D VM=0-9
+ + +
D + D
+ D + + R T=R VM=0-9
+ + +
D + D
+ D + + + T=D VM=0-9
+ + R
D R D
+ + D + + T=R VM=0-9
+ + +
D + D
+ + D R + T=R VM=0-7
+ + +
D + D
+ + D + R T=D VM=0-9
+ + +
D + D
+ + D + + T=D VM=0-7
+ + R
D + D
+ + + D R T=D VM=0-8
+ + +
D R D
+ + + + + T=D VM=0-9
D + +
D + D
+ + + R + T=D VM=0-9
D + +
D + D
+ + + + R T=D VM=0-9
D + +
D + D
+ + + + + T=D VM=0-9
D R +
D R D
+ + + + + T=D VM=0-8
+ D +
D + D
+ + + R + T=D VM=0-6
+ D +
D + D
+ + + + R T=D VM=0-9
+ D +
D + D
+ + + + R T=R VM=0-6
+ D +
D + D
+ + + + + T=D VM=0-9
+ D R
D + D
+ + + R + T=D VM=0-9
+ + D
D + D
+ + + + R T=D VM=0-9
+ + D
D + D
+ + + + R T=R VM=0-9
+ + D
D R +
D D + + + T=D VM=0-9
+ + +
D R +
D D + + + T=R VM=0-9
+ + +
D + R
D D + + + T=D VM=0-9
+ + +
D + R
D D + + + T=R VM=0-9
+ + +
D + +
D D R + + T=D VM=0-9
+ + +
D + +
D D R + + T=R VM=0-9
+ + +
D + +
D D + R + T=D VM=0-9
+ + +
D + +
D D + R + T=R VM=0-9
+ + +
D + +
D D + + R T=D VM=0-9
+ + +
D + +
D D + + R T=R VM=0-9
+ + +
D + +
D D + + + T=D VM=0-9
R + +
D + +
D D + + + T=R VM=0-9
R + +
D + +
D D + + + T=D VM=0-9
+ R +
D + +
D D + + + T=R VM=0-9
+ R +
D + +
D D + + + T=D VM=0-9
+ + R
D + +
D D + + + T=R VM=0-9
+ + R
D R +
D + D + + T=D VM=0-9
+ + +
D R +
D + D + + T=R VM=0-9
+ + +
D + R
D + D + + T=D VM=0-9
+ + +
D + R
D + D + + T=R VM=0-9
+ + +
D + +
D R D + + T=R VM=0-7
+ + +
D + +
D + D R + T=D VM=0-9
+ + +
D + +
D + D R + T=R VM=0-9
+ + +
D + +
D + D + R T=D VM=0-9
+ + +
D + +
D + D + R T=R VM=0-9
+ + +
D + +
D + D + + T=D VM=0-7
R + +
D + +
D + D + + T=D VM=0-9
+ R +
D + +
D + D + + T=R VM=0-7
+ R +
D + +
D + D + + T=D VM=0-9
+ + R
D + +
D + D + + T=R VM=0-9
+ + R
D + +
D + + D R T=D VM=0-9
+ + +
D R +
D + + + + T=D VM=0-9
D + +
D R +
D + + + + T=R VM=0-9
D + +
D + R
D + + + + T=D VM=0-9
D + +
D + R
D + + + + T=R VM=0-9
D + +
D + +
D R + + + T=D VM=0-9
D + +
D + +
D R + + + T=R VM=0-9
D + +
D + +
D + R + + T=D VM=0-9
D + +
D + +
D + R + + T=R VM=0-9
D + +
D + +
D + + R + T=D VM=0-9
D + +
D + +
D + + R + T=R VM=0-9
D + +
D + +
D + + + R T=D VM=0-9
D + +
D + +
D + + + R T=R VM=0-9
D + +
D + +
D + + + + T=D VM=0-9
D R +
D + +
D + + + + T=R VM=0-9
D R +
D + +
D + + + + T=D VM=0-9
D + R
D + +
D + + + + T=R VM=0-9
D + R
D R +
D + + + + T=D VM=0-8
+ D +
D + R
D + + + + T=D VM=0-8
+ D +
D + +
D R + + + T=D VM=0-6
+ D +
D + +
D + + R + T=D VM=0-9
+ D +
D + +
D + + + R T=D VM=0-9
+ D +
D + +
D + + + R T=R VM=0-8
+ D +
D + +
D + + + + T=D VM=0-9
+ D R
D + R
D + + + + T=D VM=0-9
+ + D
D + +
D + + R + T=D VM=0-9
+ + D
D + +
D + + + R T=D VM=0-9
+ + D
D + +
D + + + R T=R VM=0-9
+ + D
D R +
+ D D + + T=D VM=0-8
+ + +
D + R
+ D D + + T=R VM=0-8
+ + +
D + +
+ D D R + T=D VM=0-8
+ + +
D + +
+ D D + R T=D VM=0-9
+ + +
D + +
+ D D + + T=D VM=0-8
+ R +
D + +
+ D D + + T=R VM=0-8
+ + R
D + R
+ D + D + T=D VM=0-9
+ + +
D + +
+ D + D R T=D VM=0-9
+ + +
D R +
+ D + + + T=D VM=0-9
D + +
D + R
+ D + + + T=D VM=0-9
D + +
D + +
+ D R + + T=R VM=0-9
D + +
D + +
+ D + R + T=D VM=0-9
D + +
D + +
+ D + + R T=R VM=0-9
D + +
D + +
+ D + + + T=D VM=0-9
D R +
D + +
+ D + + + T=D VM=0-9
D + R
D + R
+ D + + + T=D VM=0-9
+ D +
D + +
+ D + + R T=D VM=0-9
+ D +
D + +
+ D + + + T=D VM=0-9
+ D R
D R +
+ D + + + T=D VM=0-9
+ + D
D + R
+ D + + + T=D VM=0-9
+ + D
D + +
+ D + R + T=D VM=0-9
+ + D
D + +
+ D + + R T=R VM=0-9
+ + D
D R +
+ + D D + T=D VM=0-8
+ + +
D + R
+ + D D + T=R VM=0-6
+ + +
D + +
+ + D D R T=D VM=0-6
+ + +
D R +
+ + D + + T=R VM=0-9
D + +
D + R
+ + D + + T=D VM=0-9
D + +
D + +
+ + D R + T=R VM=0-9
D + +
D + +
+ + D + R T=D VM=0-9
D + +
D + +
+ + D + + T=R VM=0-9
D R +
D + +
+ + D + + T=D VM=0-9
D + R
D R +
+ + D + + T=D VM=0-9
+ D +
D + R
+ + D + + T=R VM=0-9
+ D +
D + +
+ + D R + T=D VM=0-9
+ D +
D + +
+ + D + R T=D VM=0-9
+ D +
D + +
+ + D + + T=R VM=0-9
+ D R
D R +
+ + D + + T=R VM=0-9
+ + D
D + R
+ + D + + T=D VM=0-9
+ + D
D + +
+ + D R + T=R VM=0-9
+ + D
D + +
+ + D + R T=D VM=0-9
+ + D
D + R
+ + + D + T=D VM=0-9
D + +
D + +
+ + + D R T=R VM=0-9
D + +
D + +
+ + + D + T=D VM=0-9
D + R
D + R
+ + + D + T=D VM=0-5
+ D +
D + +
+ + + D R T=D VM=0-5
+ D +
D + +
+ + + D R T=D VM=0-8
+ + D
D R +
+ + + + + T=D VM=0-8
D D +
D + R
+ + + + + T=D VM=0-9
D D +
D + +
+ + + R + T=D VM=0-8
D D +
D + +
+ + + + R T=R VM=0-8
D D +
D + +
+ + + + + T=D VM=0-9
D D R
D R +
+ + + + + T=D VM=0-9
D + D
D + +
+ + + R + T=D VM=0-9
D + D
D + +
+ + + + R T=D VM=0-9
D + D
D + +
+ + + + + T=D VM=0-9
D R D
D R +
+ + + + + T=D VM=0-8
+ D D
D + +
+ + + R + T=D VM=0-8
+ D D
+ D D
D + + R + T=D VM=0-7
+ + +
+ D D
D + + + R T=D VM=0-8
+ + +
+ D D
D + + + R T=R VM=0-7
+ + +
+ D D
D + + + + T=D VM=0-7
+ + R
+ D D
+ D + + + T=D VM=0-7
+ + R
+ D D
+ + D + R T=D VM=0-9
+ + +
+ D D
+ + + D R T=D VM=0-7
+ + +
+ D D
+ + + R + T=D VM=0-8
D + +
+ D D
+ + + + + T=D VM=0-8
D R +
+ D D
+ + + + R T=D VM=0-9
+ D +
+ D D
+ + + + + T=D VM=0-8
+ D R
+ D D
+ + + R + T=D VM=0-8
+ + D
+ D D
+ + + + R T=R VM=0-8
+ + D
R D +
D D + + + T=D VM=0-7
+ + +
+ D R
D D + + + T=D VM=0-9
+ + +
+ D +
D D + R + T=D VM=0-9
+ + +
+ D +
D D + + R T=D VM=0-9
+ + +
+ D +
D D + + R T=R VM=0-7
+ + +
+ D +
D D + + + T=D VM=0-7
R + +
+ D +
D D + + + T=D VM=0-7
+ + R
+ D R
D + D + + T=D VM=0-9
+ + +
+ D R
D + D + + T=R VM=0-9
+ + +
+ D +
D + D R + T=D VM=0-9
+ + +
+ D +
D + D R + T=R VM=0-9
+ + +
+ D +
D + D + R T=D VM=0-9
+ + +
+ D +
D + D + R T=R VM=0-9
+ + +
+ D +
D + D + + T=D VM=0-9
+ + R
+ D +
D + + D R T=D VM=0-8
+ + +
+ D R
D + + + + T=D VM=0-9
D + +
+ D +
D R + + + T=D VM=0-6
D + +
+ D +
D + + R + T=D VM=0-9
D + +
+ D +
D + + + R T=D VM=0-9
D + +
+ D +
D + + + R T=R VM=0-8
D + +
+ D +
D + + + + T=D VM=0-8
D R +
+ D +
D + + + + T=D VM=0-8
D + R
+ D R
D + + + + T=D VM=0-8
+ D +
+ D +
D + + R + T=D VM=0-8
+ D +
+ D +
D + + + R T=D VM=0-9
+ D +
+ D +
D + + + R T=R VM=0-8
+ D +
+ D +
D + + + + T=D VM=0-8
+ D R
+ D R
D + + + + T=D VM=0-7
+ + D
+ D +
D + + R + T=D VM=0-7
+ + D
+ D +
D + + + R T=D VM=0-9
+ + D
+ D +
D + + + R T=R VM=0-7
+ + D
+ D R
+ D D + + T=D VM=0-8
+ + +
+ D +
+ D D + + T=D VM=0-9
+ + R
+ D +
+ D + D R T=D VM=0-6
+ + +
+ D R
+ D + + + T=D VM=0-9
D + +
+ D +
+ D + + R T=D VM=0-9
D + +
+ D +
+ D + + + T=D VM=0-9
D + R
+ D R
+ D + + + T=D VM=0-9
+ + D
And here are the other 219:
+ D +
+ D + + R T=D VM=0-9
+ + D
+ D R
+ + D D + T=D VM=0-8
+ + +
+ D R
+ + D + + T=R VM=0-9
D + +
+ D +
+ + D R + T=D VM=0-9
D + +
+ D +
+ + D + R T=D VM=0-9
D + +
+ D +
+ + D + + T=D VM=0-9
D R +
+ D +
+ + D + + T=R VM=0-9
D + R
+ D R
+ + D + + T=D VM=0-9
+ D +
+ D +
+ + D + + T=D VM=0-9
+ D R
+ D R
+ + D + + T=R VM=0-9
+ + D
+ D +
+ + D R + T=D VM=0-9
+ + D
+ D +
+ + D + R T=D VM=0-9
+ + D
+ D +
+ + + D R T=D VM=0-5
D + +
+ D +
+ + + D + T=D VM=0-5
D + R
+ D +
+ + + D R T=D VM=0-9
+ + D
+ D R
+ + + + + T=D VM=0-8
D D +
+ D +
+ + + + R T=D VM=0-9
D D +
+ D +
+ + + + + T=D VM=0-8
D D R
+ D R
+ + + + + T=D VM=0-9
D + D
+ D +
+ + + R + T=D VM=0-6
D + D
+ D +
+ + + + R T=D VM=0-9
D + D
+ D +
+ + + + R T=R VM=0-6
D + D
+ D +
+ + + + + T=D VM=0-8
D R D
+ D R
+ + + + + T=D VM=0-8
+ D D
+ D +
+ + + + R T=D VM=0-9
+ D D
+ + D
D D + R + T=D VM=0-9
+ + +
+ + D
D D + + R T=D VM=0-9
+ + +
+ + D
D D + + R T=R VM=0-9
+ + +
+ + D
D D + + + T=D VM=0-9
+ + R
+ R D
D + D + + T=D VM=0-9
+ + +
+ + D
D + D R + T=D VM=0-9
+ + +
+ + D
D + D R + T=R VM=0-8
+ + +
+ + D
D + D + R T=D VM=0-8
+ + +
+ + D
D + D + R T=R VM=0-9
+ + +
+ + D
D + D + + T=D VM=0-9
+ R +
+ + D
D + D + + T=D VM=0-9
+ + R
+ + D
D + D + + T=R VM=0-8
+ + R
+ + D
D + + R + T=D VM=0-9
D + +
+ + D
D + + + R T=D VM=0-9
D + +
+ + D
D + + + R T=R VM=0-9
D + +
+ + D
D + + + + T=D VM=0-9
D + R
+ + D
D + + R + T=D VM=0-7
+ D +
+ + D
D + + + R T=D VM=0-9
+ D +
+ + D
D + + + R T=R VM=0-7
+ D +
+ + D
D + + + + T=D VM=0-7
+ D R
+ + D
D + + + R T=D VM=0-9
+ + D
+ R D
+ D D + + T=D VM=0-8
+ + +
+ + D
+ D D R + T=D VM=0-8
+ + +
+ + D
+ D D + R T=D VM=0-9
+ + +
+ + D
+ D D + + T=D VM=0-8
+ R +
+ + D
+ D D + + T=R VM=0-8
+ + R
+ + D
+ D + D R T=D VM=0-8
+ + +
+ + D
+ D + R + T=D VM=0-9
D + +
+ + D
+ D + + R T=R VM=0-9
D + +
+ + D
+ D + + + T=D VM=0-9
D R +
+ + D
+ D + + + T=D VM=0-9
D + R
+ + D
+ D + + R T=D VM=0-9
+ D +
+ + D
+ D + + + T=D VM=0-9
+ D R
+ + D
+ D + R + T=D VM=0-9
+ + D
+ + D
+ D + + R T=D VM=0-8
+ + D
+ + D
+ D + + R T=R VM=0-9
+ + D
+ + D
+ + D D R T=D VM=0-9
+ + +
+ + D
+ + D R + T=R VM=0-9
D + +
+ + D
+ + D + R T=D VM=0-9
D + +
+ + D
+ + D + + T=R VM=0-9
D R +
+ + D
+ + D + + T=D VM=0-9
D + R
+ + D
+ + D R + T=D VM=0-9
+ D +
+ + D
+ + D + R T=D VM=0-9
+ D +
+ + D
+ + D + + T=R VM=0-9
+ D R
+ + D
+ + D R + T=R VM=0-9
+ + D
+ + D
+ + D + R T=D VM=0-9
+ + D
+ + D
+ + + D R T=D VM=0-8
D + +
+ + D
+ + + D R T=D VM=0-9
+ D +
+ + D
+ + + D R T=R VM=0-0
+ + D
+ + D
+ + + R + T=D VM=0-8
D D +
+ + D
+ + + + R T=D VM=0-9
D D +
+ + D
+ + + + R T=R VM=0-8
D D +
+ + D
+ + + + + T=D VM=0-9
D D R
+ + D
+ + + R + T=D VM=0-9
D + D
+ + D
+ + + + R T=D VM=0-9
D + D
+ + D
+ + + + R T=R VM=0-9
D + D
+ + D
+ + + R + T=D VM=0-8
+ D D
+ + D
+ + + + R T=R VM=0-8
+ D D
R + +
D D D + + T=R VM=0-8
+ + +
+ R +
D D D + + T=D VM=0-8
+ + +
+ + R
D D D + + T=D VM=0-9
+ + +
+ + R
D D D + + T=R VM=0-8
+ + +
+ + +
D D D R + T=D VM=0-8
+ + +
+ + +
D D D R + T=R VM=0-9
+ + +
+ + +
D D D + R T=D VM=0-9
+ + +
+ + +
D D D + R T=R VM=0-8
+ + +
+ + +
D D D + + T=R VM=0-8
R + +
+ + +
D D D + + T=D VM=0-8
+ R +
+ + +
D D D + + T=D VM=0-9
+ + R
+ + +
D D D + + T=R VM=0-8
+ + R
+ + +
D D + D R T=D VM=0-9
+ + +
R + +
D D + + + T=D VM=0-9
D + +
R + +
D D + + + T=R VM=0-9
D + +
+ R +
D D + + + T=D VM=0-9
D + +
+ R +
D D + + + T=R VM=0-9
D + +
+ + R
D D + + + T=D VM=0-9
D + +
+ + R
D D + + + T=R VM=0-9
D + +
+ + +
D D R + + T=D VM=0-9
D + +
+ + +
D D R + + T=R VM=0-9
D + +
+ + +
D D + R + T=D VM=0-9
D + +
+ + +
D D + R + T=R VM=0-9
D + +
+ + +
D D + + R T=D VM=0-9
D + +
+ + +
D D + + R T=R VM=0-9
D + +
+ + +
D D + + + T=D VM=0-9
D R +
+ + +
D D + + + T=R VM=0-9
D R +
+ + +
D D + + + T=D VM=0-9
D + R
+ + +
D D + + + T=R VM=0-9
D + R
R + +
D D + + + T=D VM=0-7
+ D +
+ + R
D D + + + T=D VM=0-7
+ D +
+ + +
D D + R + T=D VM=0-9
+ D +
+ + +
D D + + R T=D VM=0-9
+ D +
+ + +
D D + + R T=R VM=0-7
+ D +
+ + +
D D + + + T=D VM=0-7
R D +
+ + +
D D + + + T=D VM=0-9
+ D R
+ + R
D D + + + T=D VM=0-9
+ + D
+ + +
D D + R + T=D VM=0-9
+ + D
+ + +
D D + + R T=D VM=0-9
+ + D
+ + +
D D + + R T=R VM=0-9
+ + D
+ + R
D + D D + T=D VM=0-9
+ + +
+ + +
D + D D R T=D VM=0-9
+ + +
+ + +
D + D D R T=R VM=0-9
+ + +
+ + +
D + D D + T=D VM=0-9
+ + R
R + +
D + D + + T=D VM=0-7
D + +
+ R +
D + D + + T=D VM=0-9
D + +
+ R +
D + D + + T=R VM=0-7
D + +
+ + R
D + D + + T=D VM=0-9
D + +
+ + R
D + D + + T=R VM=0-9
D + +
+ + +
D R D + + T=R VM=0-7
D + +
+ + +
D + D R + T=D VM=0-9
D + +
+ + +
D + D R + T=R VM=0-9
D + +
+ + +
D + D + R T=D VM=0-9
D + +
+ + +
D + D + R T=R VM=0-9
D + +
+ + +
D + D + + T=D VM=0-9
D R +
+ + +
D + D + + T=R VM=0-9
D R +
+ + +
D + D + + T=D VM=0-9
D + R
+ + +
D + D + + T=R VM=0-9
D + R
+ + R
D + D + + T=D VM=0-9
+ D +
+ + +
D + D R + T=D VM=0-9
+ D +
+ + +
D + D R + T=R VM=0-9
+ D +
+ + +
D + D + R T=D VM=0-9
+ D +
+ + +
D + D + R T=R VM=0-9
+ D +
+ + +
D + D + + T=D VM=0-9
+ D R
+ + +
D + D + + T=R VM=0-9
+ D R
+ R +
D + D + + T=D VM=0-9
+ + D
+ + R
D + D + + T=D VM=0-9
+ + D
+ + R
D + D + + T=R VM=0-8
+ + D
+ + +
D + D R + T=D VM=0-9
+ + D
+ + +
D + D R + T=R VM=0-8
+ + D
+ + +
D + D + R T=D VM=0-8
+ + D
+ + +
D + D + R T=R VM=0-9
+ + D
+ + +
D + D + + T=D VM=0-9
+ R D
+ + +
D + + D R T=D VM=0-9
D + +
+ + +
D + + D R T=D VM=0-8
+ D +
+ R +
D + + + + T=D VM=0-6
D D +
+ + R
D + + + + T=D VM=0-8
D D +
+ + +
D R + + + T=D VM=0-6
D D +
+ + +
D + + R + T=D VM=0-9
D D +
+ + +
D + + + R T=D VM=0-9
D D +
+ + +
D + + + R T=R VM=0-8
D D +
+ + +
D + + + + T=D VM=0-9
D D R
+ + R
D + + + + T=D VM=0-9
D + D
+ + +
D + + R + T=D VM=0-9
D + D
+ + +
D + + + R T=D VM=0-9
D + D
+ + +
D + + + R T=R VM=0-9
D + D
+ + R
D + + + + T=D VM=0-7
+ D D
+ + +
D + + R + T=D VM=0-7
+ D D
+ + +
D + + + R T=D VM=0-8
+ D D
+ + +
D + + + R T=R VM=0-7
+ D D
+ + R
+ D D D + T=D VM=0-7
+ + +
+ + +
+ D D D R T=R VM=0-7
+ + +
+ + +
+ D D D + T=D VM=0-7
+ + R
+ R +
+ D D + + T=D VM=0-8
D + +
+ + R
+ D D + + T=R VM=0-8
D + +
+ + +
+ D D R + T=D VM=0-8
D + +
+ + +
+ D D + R T=D VM=0-9
D + +
+ + +
+ D D + + T=D VM=0-8
D R +
+ + +
+ D D + + T=R VM=0-8
D + R
+ + R
+ D D + + T=D VM=0-9
+ D +
+ + +
+ D D + + T=D VM=0-8
+ D R
+ R +
+ D D + + T=D VM=0-8
+ + D
+ + R
+ D D + + T=R VM=0-8
+ + D
+ + +
+ D D R + T=D VM=0-8
+ + D
+ + +
+ D D + R T=D VM=0-9
+ + D
+ + +
+ D D + + T=D VM=0-8
+ R D
+ + +
+ D + D R T=D VM=0-9
D + +
+ + +
+ D + D + T=D VM=0-9
D + R
+ + +
+ D + D R T=D VM=0-6
+ D +
+ + +
+ D + D R T=D VM=0-8
+ + D
+ + R
+ D + + + T=D VM=0-7
D D +
+ + +
+ D + + R T=D VM=0-9
D D +
+ + +
+ D + + + T=D VM=0-9
D D R
+ + R
+ D + + + T=D VM=0-9
D + D
+ + +
+ D + R + T=D VM=0-9
D + D
+ + +
+ D + + R T=R VM=0-9
D + D
+ + +
+ D + + + T=D VM=0-9
D R D
+ + R
+ D + + + T=D VM=0-7
+ D D
+ + +
+ + D D R T=D VM=0-6
D + +
+ + +
+ + D D + T=D VM=0-8
D R +
+ + +
+ + D D + T=R VM=0-6
D + R
+ + +
+ + D D + T=D VM=0-8
+ D R
+ + +
+ + D D R T=D VM=0-9
+ + D
+ + +
+ + D R + T=D VM=0-9
D D +
+ + +
+ + D + R T=D VM=0-9
D D +
+ + +
+ + D + + T=R VM=0-9
D D R
+ + R
+ + D + + T=D VM=0-7
D + D
+ + +
+ + D R + T=R VM=0-7
D + D
+ + +
+ + D + R T=D VM=0-9
D + D
+ + +
+ + D + + T=R VM=0-9
D R D
+ + +
+ + D + R T=D VM=0-9
+ D D
+ + +
+ + + D R T=D VM=0-7
D D +
+ + +
+ + + D + T=D VM=0-5
D D R
+ + +
+ + + D R T=D VM=0-8
D + D
+ + +
+ + + D R T=D VM=0-7
+ D D
+ + +
+ + + R + T=D VM=0-6
D D D
Further reduction (e.g., due to a layout’s symmetry) is probably warranted. Perhaps later tonight…
Out of curiosity, what was the bug?
It was really stupid. I was writing in C++. I had a line like this:
for () {
if (condition)
set_some_flag;
}
A second later I realized that the loop could break, too, if the condition was met, so I added a break:
for () {
if (condition)
set_some_flag;
break;
}
Oops! That should have read:
for () {
if (condition) {
set_some_flag;
break;
}
}
That was the bug. (When I write more formal code, I never use the bracket-less syntax so as to prevent such mistakes. But, when I write code for something like the SDMB, I’m looking to be fast, and that bit me here.)
Ah, that’d do it. Usually when I’m going bracketless, I keep it all on one line, to prevent that. There is one program I wrote, though, where I have a whole slew of ifs one after the other, with no brackets (I could of course rewrite it to a single if with a bunch of logical ands, but this way it’s easier to add or remove conditions one at a time).
[hijack]The coding standard that I have to follow requires the braces to be omitted if possible. I hate it for exactly that reason.[/hijack]
Yeah, I usually do the one-line thing in these cases, too, and it actually might have been all on one line initially, unlike what I wrote above. In that case, I might have put in the hard-return first, got distracted for a split second, and then mindlessly added the ‘break’…