Mister
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About Tar Mothers: they can exist \"nude\" (that is, without any tar surrounding them), but can they \"spawn\" nude? If not, a mother can not be adjacent to a pit, for example (unless tar can exist on pits).

Considering only non-? on the table, and that Mother can spawn alone:

1010^4 = 1040604010000 combinations without Tar nor Serpents (Tar mothers counted, too);
205040000 combinations with Serpents;
and 1936 with Tar;
add 1 for the \"special\" case;

and my grand total is: 1 040 809 051 937


[Edited by Mister on 04-06-2003 at 06:22 AM GMT]

agaricus5
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Ooh...That\'s a good answer. It\'s bigger than my lower bound, but smaller than my upper (Yes, the speculation zone is around 418,967,597,049 if you wanted to know) but, I\'m not including checkpoints into this solution yet, so your estimate is a little large for the working out you have done (Save it for part 3 though... that is, if you don\'t mind a further complication to the puzzle...).

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agaricus5
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mister wrote:

Total combinations for a single square (without considering questions marks nor serpents): 1016!!!

[Edited by Mister on 04-06-2003 at 03:46 AM GMT]

Actually, even that doesn\'t appear correct. Even with checkpoints, I count only 1001 different square combinations (on your list):

(23 * 43) + 1 + 2 + 2 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 989 + 12 = 1001

And without checkpoints, as in the solution, there would be 958 in your list, which is still near to one of my correct answers though.

[Edited by agaricus5 on 04-06-2003 at 11:19 AM GMT]

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krammer
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Can tar mothers exist in a 2x2 room? They always appear to be within a 4x3 block of tar or larger. Therefore, they should not be considered for this puzzle.

Also, arrows can be found on pits when Beethro collapses a trap beneath an arrow.

[Edited by krammer on 04-06-2003 at 05:47 PM GMT]

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agaricus5
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Tar mothers are included because I did say that every legal combination can be part of the solution, even if you do not find them at the start of a room. Go to Level 14 1E to experiment with the tar mother - you can cut the tar around her to a 2*2 blob with her as a part of it, and if you are good, can get her lone without any tar surrounding her at all.

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Mister
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agaricus5 wrote:
Tar mothers are included because I did say that every legal combination can be part of the solution, even if you do not find them at the start of a room.

But all Tar mothers start surrounded by Tar, and that can\'t exists on a 2x2 room, hence my doubts...

agaricus5 wrote:
Go to Level 14 1E to experiment with the tar mother

I\'ve got it down to a single square

[Edited by Mister on 04-06-2003 at 09:08 PM GMT]

Mister
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This is the updated table, considering only the combinations we are SURE can exist:

              Rch RQn Wrt Eye Gbl Spd Brn Tar Mot Bby Non Srp
Floor          8   8   8   8   8   1   1   1   1   1   1   Y  |  46
Checkpoint     8   8   8   8   8   1       1       1   1   Y  |  44
Scroll         8   8   8   8   8   1               1   1      |  43
Scroll/Trap    8   8   8   8   8   1               1   1      |  43
Trapdoor       8   8   8   8   8   1       1       1   1   Y  |  44
Arrow         64  64  64  64  64   8               8   8      | 344
Arrow/Trap    64  64  64  64  64   8               8   8      | 344
Yellow Open    8   8   8   8   8   1       1       1   1   Y  |  44
Yellow Closed  8   8   8   8   8   1       1       1   1   Y  |  44
Wall                                       1       1   1      |   3
Pit                    8                               1      |   9
Arrow/Pit             64                               8      |  72
Crumbly Wall                                           1      |   1
Red door                                               1      |   1
Green door                                             1      |   1
Blue door                                              1      |   1
Orbs                                                   1      |   1
Mimic potion                                           1      |   1
Invis potion                                           1      |   1
===================================================================
             184 184 256 184 184  23   1   6   1  24  40       1087
                                                  w/o Tar/Srp: 1081

With Checkpoints:

w/o Tar/Srp:  1081^4                         = 1365534810721
w/Serpents:   16*5^4 + 8*5^3*1081 + 8*5^2*1081^2 = 234803200
w/Tar:        6^4*1^0 + 6^3*1^1 + 6^2*1^2 + 6^1*1^3   = 1554
Special:                                                   1
TOTAL:                                         1365769615476

Without Checkpoints:

w/o tar/Srp:  1038^4                         = 1160885573136
w/Serpents:   16*4^4 + 8*4^3*1038 + 8*4^2*1038^2 = 138448384
w/Tar:        5^4*1^0 + 5^3*1^1 + 5^2*1^2 + 5^1*1^3    = 780
Special:                                                   1
TOTAL:                                         1161024022301

agaricus5
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That\'s great! It\'s not what I calculated exactly, but the method is correct. I shall now go to Erik and find out what exactly is possible, so that I can provide a final solution, so we\'ll see if you did it correctly.

Four problems though:

1. How did you find the tar value? The working out looks suspicious.

2. Do you actually know what the \'special\' arrangement actually is, or did you just include it?

3. Everybody, and that means everybody, has left out a vital part of the solution out. It\'s really obvious too, once you know what it is, so see if you can guess at what it is.

4. Has anyone considered tar mothers yet?

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Mister
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1. I\'ll explain the \"with checkpoints\" case, the other is similar.
If some tar is present, it has to cover all the room. However, it can be 4 squares of tar, or 3 tar and 1 mother, 2 tar & 2 mothers, and 1 tar & 3 mothers. Tar can exist over 6 kind of squares, while mothers only on plain squares (unless someone states otherwise)
So, the equation is 6^4*1^0 + 6^3*1^1 + 6^2*1^2 + 6^1*1^3.

2. The statue/pyramid/whatever, right?

3. I haven\'t considered the surroundings of the 2x2 room, if that\'s what you meant (it can change the shape of doors). I haven\'t considered stairs either.
Right now I\'m working to add Beethro, Mimics and the \'Neather to the equation.

4. The above result considered mothers. The first number considers everything in the table except Tar and Serpent. Mothers included.

agaricus5
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mister wrote:
1. I\'ll explain the \"with checkpoints\" case, the other is similar.
If some tar is present, it has to cover all the room. However, it can be 4 squares of tar, or 3 tar and 1 mother, 2 tar & 2 mothers, and 1 tar & 3 mothers. Tar can exist over 6 kind of squares, while mothers only on plain squares (unless someone states otherwise)
So, the equation is 6^4*1^0 + 6^3*1^1 + 6^2*1^2 + 6^1*1^3.

Oh dear... the method is very seriously flawed, just as I suspected. Watch how you arrange Tar Mothers...It\'s not as simple as you think. Oh, and go to level 16, where you will find a tar mother on something other than a normal floor tile.

2. The statue/pyramid/whatever, right?

Yay!

3. I haven\'t considered the surroundings of the 2x2 room, if that\'s what you meant (it can change the shape of doors).

No. Only solutions just in the confines of a 2*2 room, not as part of an external, so that means no lone tar corners or something like that.

I haven\'t considered stairs either.
Right now I\'m working to add Beethro, Mimics and the \'Neather to the equation.

Ok... it\'s a good idea, but once you get a result, wait until part 3 to post. But it\'s still not what has been missed!
I\'ll disclose it in my next post.

4. The above result considered mothers. The first number considers everything in the table except Tar and Serpent. Mothers included.

I think that it then is wrong - again, watch how tar mothers are incorporated into the equation...

[Edited by agaricus5 on 04-07-2003 at 06:48 AM GMT]

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Mister
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Oh dear... the method is very seriously flawed, just as I suspected. Watch how you arrange Tar Mothers...It\'s not as simple as you think
...
watch how tar mothers are incorporated into the equation...

In the main equation, I considered Tar Mothers among all other things except Tar and Serpents. I allowed Mothers to be vertically adjacent to each other, and can be adjacent to any thing (which may be impossible, since we only see them spawn on 4x3 tar, but this would make them impossible to appear on a 2x2 square).
Next I consider Tar, which can exist with or without mothers (up to 3; the four mothers case was considered before).
Maybe I should also consider mothers with her eyes closed?

Oh, and go to level 16, where you will find a tar mother on something other than a normal floor tile.

I\'ll check.

it\'s still not what has been missed!
I\'ll disclose it in my next post.

I got it! Roach eggs, right?


[Edited by Mister on 04-07-2003 at 01:38 PM GMT]

zex20913
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I thought it might be that (at least) blue doors can\'t go around corners...that\'ll change the answer by a very small amount relatively.



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krammer
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zex20913 wrote:
I thought it might be that (at least) blue doors can\'t go around corners...that\'ll change the answer by a very small amount relatively.

How do you know? Yellow, red and green doors can, so why not blue ones?


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agaricus5
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The missing parts were roach eggs, all three stages of them.

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Mister
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Yay! I was right.

But if multiple eggs are present, all of them must be at the same stage; this makes things more complicated... Or the problem considers eggs in multiple stages?
Should we consider Queens and Tar Mothers with 30 stages? (hope not) Or maybe just Mothers with closed/open eyes.

New calculation coming soon!

agaricus5
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mister wrote:

Should we consider Queens and Tar Mothers with 30 stages? (hope not) Or maybe just Mothers with closed/open eyes.

No. Only mothers with open eyes.

I\'m expecting some confirmation from Erik on what\'s possible or not in DROD, so that I can make a final answer to this puzzle, so be patient.

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Mister
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Now I see my silly mistake in the tar calculation. Shame on me!

              Rch RQn REg Wrt Eye Gbl Spd Brn Tar Mot Bby Non Srp
Floor          8   8   3   8   8   8   1   1   1   1   1   1   Y  |  49
Checkpoint     8   8   3   8   8   8   1       1       1   1   Y  |  47
Scroll         8   8       8   8   8   1               1   1      |  43
Scroll/Trap    8   8       8   8   8   1               1   1      |  43
Trapdoor       8   8       8   8   8   1       1   1   1   1   Y  |  45
Arrow         64  64      64  64  64   8               8   8      | 344
Arrow/Trap    64  64      64  64  64   8               8   8      | 344
Yellow Open    8   8       8   8   8   1       1       1   1   Y  |  44
Yellow Closed  8   8       8   8   8   1       1       1   1   Y  |  44
Wall                                           1       1   1      |   3
Pit                        8                               1      |   9
Arrow/Pit                 64                               8      |  72
Crumbly Wall                                               1      |   1
Red door                                                   1      |   1
Green door                                                 1      |   1
Blue door                                                  1      |   1
Orbs                                                       1      |   1
Mimic potion                                               1      |   1
Invis potion                                               1      |   1
=======================================================================
             184 184   6 256 184 184  23   1   6   2  24  40       1094
                                                      w/o Tar/Srp: 1088


With Checkpoints:

w/o Tar/Srp:  1088^4                             = 1401249857536
w/Serpents:   16*5^4 + 8*5^3*1088 + 8*5^2*1088^2     = 237846800
w/Tar:        6^4*2^0 + 4*6^3*2^1 + 6*6^2*2^2 + 4*6^1*2^3 = 4080
Special:                                                     = 1
TOTAL:                                             1401487708417


Without Checkpoints:

w/o Tar/Srp:  1042^4                             = 1178883463696
w/Serpents:   16*4^4 + 8*4^3*1042 + 8*4^2*1042^2     = 139515392
w/Tar:        5^4*2^0 + 4*5^3*2^1 + 6*5^2*2^2 + 4*5^1*2^3 = 2385
Special:                                                     = 1
TOTAL:                                             1179022981474

I\'ve allowed Roach Eggs stages to coexist. Is this alright? If not, then:

With Checkpoints:

w/o Egg/Tar/Srp: 1082^4                                     = 1370594684176
w/Egg:           3*(4*2^1*1082^3+6*2^2*1082^2+4*2^3*1082+2^4) = 30485756880
w/Serpents:      16*5^4 + 8*5^3*1082 + 8*5^2*1082^2             = 235236800
w/Egg/Srp:       8*5^3*6+16*5^2*6*1082+8*5^2*2^2*3                = 2605200
w/Tar:           6^4*2^0 + 4*6^3*2^1 + 6*6^2*2^2 + 4*6^1*2^3         = 4080
Special:                                                                = 1
TOTAL:                                                        1401318287137

Without Checkpoints:

w/o Egg/Tar/Srp: 1039^4                                     = 1165365589441
w/Egg:           3*(4*1^1*1039^3+6*1^2*1039^2+4*1^3*1039+1^4) = 13478911677
w/Serpents:      16*4^4 + 8*4^3*1039 + 8*4^2*1039^2             = 138714752
w/Egg/Srp:       8*4^3*3+16*4^2*3*1039+8*4^2*1^2*3                 = 799872
w/Tar:           5^4*2^0 + 4*5^3*2^1 + 6*5^2*2^2 + 4*5^1*2^3         = 2385
Special:                                                                = 1
TOTAL:                                                        1178984018128

Edited: Roach Eggs can NOT exist on trapdoors. Silly me!


[Edited by Mister on 04-09-2003 at 10:55 PM GMT]

agaricus5
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At last!

After long extended discussions between Beethro (Me) and the project manager (Erik) in a cabin on the field (That is, via E-mail), they managed to sort out the many problems and questions raised by the workers (All of you) and finally made a revised combinations list .

This is a finalised version, made on the assumption that only what actually happens in the game is countable (but each piece is metonimic - where one stands for the whole, so if one force arrow does it, they all do it) with the exception of force arrows on trapdoors: it is assumed that all monsters capable of stepping on force arrows will also be able to step on force arrows on trapdoors (which is logical).

Anyway, after my extra long sentence, here s the list:

All elements/monsters can all exist by themselves (Obviously)

Element/Element Combinations:

Force Arrows can exist on Pits and Trapdoors.

Scrolls can exist on Trapdoors, but not Pits anymore.

Potions cannot exist on anything but normal floor tiles.

Monster/Element Combinations:

Roaches, Queens, Evil Eyes and Goblins can all exist on Force Arrows, Trapdoors, Open and Closed Yellow Gates and Scrolls, and also the double combination of Force Arrows on Trapdoors

Tar Babies can exist on Force Arrows, Trapdoors, Open and Closed Yellow Gates and Scrolls, the double combination of Force Arrows on Trapdoors, and also Walls.

Wraithwings are airborne so they can go on Pits as well as Force Arrows, Trapdoors, Open and Closed Yellow Gates and the double combination of Force Arrows on Trapdoors, but an instance of Wraithwings on scrolls can not be found in the game, so it is not counted.

Roach Eggs and Brains cannot exist on anything but normal floor tiles.

Spiders can exist on Force Arrows, Trapdoors, Open Yellow Gates and the double combination of Force Arrows on Trapdoors, but not scrolls or Closed Yellow Gates - those combinations cannot be found in the game.

Serpents can exist on Trapdoors, and Open and Closed Yellow Gates.

Specifically Tar:

Tar exists on Trapdoors, Open and Closed Yellow Gates and Walls, but not Crumbly ones.

Tar Mothers, apart from normal floor tiles, can only exist on Trapdoors. However, they can exist as single eyes or a pair as part of a 2x2 tar mass, or by themselves.

If anyone cannot understand this, then reply and I\'ll do it properly (I have to go to bed in 10 minutes!). Even better would be a table like the previous ones by mister, though I don\'t expect that of anyone.

And finally...Anyone who wants to can have a guess. Look at previous posts to get an idea as to what to do, and have a go, because I will wait for a while for all guesses to be posted before disclosing the answer.

Good Luck!

Wesley Chua

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mrimer
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I can\'t remember: is a monster facing different directions counted more than once? For example, is a goblin facing north different than a goblin facing south? Or is an evil eye facing north different than one facing south?

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agaricus5
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All monster rotations are separately counted, so a goblin facing North is different from one facing South.

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Mister
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There are three stages of Roach eggs. Can two or more of them coexists? (it is more complicated if not, see my last post).

What about Tar Mothers by themselves? That is, without tar surrounding it. Considering that all Mothers are spawned surrounded by tar, in the game it\'s impossible to have a Tar Mother adyacent to a Crumbly Wall. Must we count these combinations?
And a pair of eyes vertically or diagonally adjacent? Is it allowed?

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Not that I really know a lot about this stuff, but I think it would be pretty obvious that stages of roach eggs cannot coexist; it\'s impossible, because all queens use the same counter and there is no possible event that could offset one or more of them.

Tar mothers by themselves are perfectly plausible, because it is possible (albeit very difficult) in the game to cut away all the tar from a mother so there\'s nothing left but the eyes. By the same token, you could then chop off one of the eyes and have only one left. Or you could have two mothers right next to each other and chop off various parts of them; in short, all combinations of eyes should be possible. That\'s basically what Beethro (agaricus) just said... extended version.

BTW, why don\'t mothers with eyes closed count? It\'s perfectly reasonable, so long as all of the eyes in this 2x2 square are either closed or open.

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You also mentioned how long it would take if each setup took 2 minutes. Assuming that 2 minutes includes setup and take-down time (which seems logical), the current calculations say that those poor people (and their descendants) will be at that field for a good 4,489,305 years! (with a rough approximation of extra days due to leap years) That\'ll be enough to take the wind out of Dugan\'s sails.

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Mister
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Sokko wrote:
Tar mothers by themselves are perfectly plausible, because it is possible (albeit very difficult) in the game to cut away all the tar from a mother so there\'s nothing left but the eyes.

Yes, I know that. But nobody seems to understand what I\'m trying to say...

If we have this:

+-------+--------+
| Floor | Orb    |
+-------+--------+
| Floor | Mother |
+-------+--------+

The mother alone is perfectly feasible. However, Mothers start surrounded by tar, so for this position to be reachable, Tar did exist over the Orb, which is not possible. So I\'m asking for positions like these; posible, but unreachable.

Also:

+--------+--------+
| Mother | Floor  |
+--------+--------+
| Floor  | Mother |
+--------+--------+

Is this allowed?

agaricus5
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It is strange, but I have actually seen it in Caravel DROD. Especially when the queen is moving, different stages of eggs can appear simultaneously, for some unknown reason. Anyway, we just assume that in Beethro\'s world, Roach eggs do not take a particular length of time to develop - like natural insects, some eggs hatch faster than others.

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agaricus5
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mister wrote:

Sokko wrote:
Tar mothers by themselves are perfectly plausible, because it is possible (albeit very difficult) in the game to cut away all the tar from a mother so there\'s nothing left but the eyes.

Yes, I know that. But nobody seems to understand what I\'m trying to say...

If we have this:

+-------+--------+
| Floor | Orb    |
+-------+--------+
| Floor | Mother |
+-------+--------+

The mother alone is perfectly feasible. However, Mothers start surrounded by tar, so for this position to be reachable, Tar did exist over the Orb, which is not possible. So I\'m asking for positions like these; possible, but unreachable.

Oh no!!!

That was an excellent flaw in my method...
Thanks, Mister, for bringing it to light!

It appears that if tar cannot sit on it, then an element tile that cannot move; such as orbs, force arrows, pits and so on cannot be part of a combination in conjunction with a mother as she starts completely surrounded by tar.

I have to re-calculate!

Boo hoo!

Also:

+--------+--------+
| Mother | Floor  |
+--------+--------+
| Floor  | Mother |
+--------+--------+

Is this allowed?
No.

Erik said that tar mothers cannot be found next to each other so only single tar mothers in the combinations please.

I\'ve decided that I shall reply to all questions about the puzzle solution\'s integrity, but as for answers, please post them to the thread as separate messages (So don\'t mix questions and solutions) so that I can find them easily and then use them in the final announcement.

I shall wait for a few weeks to collect answers, so anyone who has even an inkling as to what it could be, please don\'t get put off by answers already here; it is likely that they could be wrong and yours right, so post a guess!

Finally don\'t forget, as Sokko reminded, to send an answer for how long the workers would take to set up each combination individually, supposing that it takes two minutes to set each up and that the workers never stop.

Happy puzzling!

Edited Because I put \"Schik\" instead of \"Sokko\". Sorry!

[Edited by agaricus5 on 04-22-2003 at 10:07 PM GMT]

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              Rch RQn REg Wrt Eye Gbl Spd Brn Bby Non Srp Tar Mot
Floor          8   8   3   8   8   8   1   1   1   1   Y   Y   Y  |  47
Scroll         8   8           8   8           1   1              |  34
Scroll/Trap    8   8           8   8           1   1              |  34
Trapdoor       8   8       8   8   8   1       1   1   Y   Y   Y  |  43
Arrow         64  64      64  64  64   8       8   8              | 344
Arrow/Trap    64  64      64  64  64   8       8   8              | 344
Yellow Open    8   8       8   8   8   1       1   1   Y   Y      |  43
Yellow Closed  8   8       8   8   8           1   1   Y   Y      |  42
Other door                                         3              |   3
Wall                                           1   1       Y      |   2
Pit                        8                       1              |   9
Arrow/Pit                 64                       8              |  72
Crumbly Wall                                       1              |   1
Orbs                                               1              |   1
Potion                                             2              |   2
=======================================================================
             176 176   3 232 176 176  19   1  23  39               1021

agaricus5
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mister wrote:

              Rch RQn REg Wrt Eye Gbl Spd Brn Bby Non Srp Tar Mot
Floor          8   8   3   8   8   8   1   1   1   1   Y   Y   Y  |  47
Scroll         8   8           8   8           1   1              |  34
Scroll/Trap    8   8           8   8           1   1              |  34
Trapdoor       8   8       8   8   8   1       1   1   Y   Y   Y  |  43
Arrow         64  64      64  64  64   8       8   8              | 344
Arrow/Trap    64  64      64  64  64   8       8   8              | 344
Yellow Open    8   8       8   8   8   1       1   1   Y   Y      |  43
Yellow Closed  8   8       8   8   8           1   1   Y   Y      |  42
Other door                                         3              |   3
Wall                                           1   1       Y      |   2
Pit                        8                       1              |   9
Arrow/Pit                 64                       8              |  72
Crumbly Wall                                       1              |   1
Orbs                                               1              |   1
Potion                                             2              |   2
=======================================================================
             176 176   3 232 176 176  19   1  23  39               1021

Thanks, mister, but there are a few mistakes...I\'m sorry - I\'ll correct them.

     Rch RQn REg Wrt Eye Gbl Spd Brn Bby Non Srp Tar Mot
Floor          8   8   3   8   8   8   1   1   1   1   Y   Y   Y  |  47
Scroll         8   8           8   8           1   1              |  34
Scroll/Trap    0   0           0   0           0   1              |   1
Trapdoor       8   8       8   8   8   1       1   1   Y   Y   Y  |  43
Arrow         64  64      64  64  64   8       8   8              | 344
Arrow/Trap    64  64      64  64  64   8       8   8              | 344
Yellow Open    8   8       8   8   8   1       1   1   Y   Y      |  43
Yellow Closed  8   8       8   8   8           1   1   Y   Y      |  42
Other door                                         3              |   3
Wall                                           1   1       Y      |   2
Pit                        8                       1              |   9
Arrow/Pit                  0                       8              |   8
Crumbly Wall                                       1              |   1
Orbs                                               1              |   1
Potion                                             2              |   2
=======================================================================
           168 168   3 168 168 168  19   1  22  39                  924

But anyway, thanks!

When you get the final answer, post it here!

____________________________
Resident Medic/Mycologist

Mister
Level: Master Delver
Rank Points: 104
Registered: 02-27-2003
IP: Logged

I see... some may be feasible, but as they aren\'t found in the game, aren\'t considered (e.g. Wraiths on Arrow/Pits)

I\'ll add a new useful datum:
Number of \"Tar may have existed\" tiles: 186

My grand total is:


[Edited by Mister on 04-23-2003 at 11:01 PM GMT]

agaricus5
Level: Smitemaster
Rank Points: 1838
Registered: 02-04-2003
IP: Logged

agaricus5 wrote:
Thanks, mister, but there are a few mistakes...I\'m sorry - I\'ll correct them.

     Rch RQn REg Wrt Eye Gbl Spd Brn Bby Non Srp Tar Mot
Floor          8   8   3   8   8   8   1   1   1   1   Y   Y   Y  |  47
Scroll         8   8           8   8           1   1              |  34
Scroll/Trap    0   0           0   0           0   1              |   1
Trapdoor       8   8       8   8   8   1       1   1   Y   Y   Y  |  43
Arrow         64  64      64  64  64   8       8   8              | 344
Arrow/Trap    64  64      64  64  64   8       8   8              | 344
Yellow Open    8   8       8   8   8   1       1   1   N   Y      |  43
Yellow Closed  8   8       8   8   8           1   1   N   Y      |  42
Other door                                         3              |   3
Wall                                           1   1       Y      |   2
Pit                        8                       1              |   9
Arrow/Pit                  0                       8              |   8
Crumbly Wall                                       1              |   1
Orbs                                               1              |   1
Potion                                             2              |   2
=======================================================================
           168 168   3 168 168 168  19   1  22  39                  924

But anyway, thanks!

When you get the final answer, post it here!

Oh no!, there was something I missed - I\'m really sorry!

Tar mothers do not go on yellow doors. I\'ve re-corrected the chart.

Please re-calculate and re-send.

Thanks


____________________________
Resident Medic/Mycologist