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So how many possible Commander decks are there? Let's find out!

I got bored last night, so I decided to try to figure out exactly how many different Commander decks there are. The first gut response most players would have is that there are infinitely many. That isn't so. There are a LOT of possible decks, but there are three things that firmly state that there are a finite number of EDH decks:
  1. The finite number of EDH legal cards (@scryfall f:edh lists over 19,000 cards that are legal in Commander, and if you're not using Firefox and a custom Scryfall search engine, you really ought to try it, as it's a massive quality of life improvement).
  2. The firm upper bound on the number of cards in a deck. There are infinitely many Standard decks because Standard has no maximum deck size. I can always add a basic land to those decks to produce a new decklist.
So how many Commander lists are there?
Let's start by getting some statistics.
Color Identity Commanders Partner Pairs* Singleton Cards Unlimited Cards Can Run [[Seven Dwarves]]
C 8 0 1829 1 N
W 101 1* 4883 3 N
U 88 0 4847 4 N
B 103 0 4895 6 N
R 90 0 4867 3 Y
G 84 0 4826 3 N
WU 35 0 8181 6 N
UB 33 0 8199 9 N
BR 37 0 8219 8 Y
RG 33 0 8127 5 Y
GW 36 0 8161 5 N
WB 23 2 8149 8 N
UR 21 3 8078 6 Y
BG 28 2 8095 8 N
RW 27 2 8115 5 Y
GU 22 2 8036 6 N
Bant 15 5 11661 8 N
Esper 17 5 11782 11 N
Grixis 18 5 11775 11 Y
Jund 17 5 11746 10 Y
Naya 18 5 11724 7 Y
Abzan 10 9 11661 10 N
Jeskai 12 9 11641 8 Y
Sultai 13 9 11626 11 N
Mardu 14 9 11704 10 Y
Temur 10 9 11571 8 N
UBRG 1 8 15014 12 Y
WBRG 1 9 15050 11 Y
WURG 1 8 15002 9 Y
WUBG 1 8 15030 12 N
WUBR 1 9 15071 12 Y
5 color 25 0 19897 15 Y
So why did I break out [[Seven Dwarves]] specifically? It's simple. Seven Dwarves is mechanically unique in that it specifies a fixed number of copies of that card a deck can run. Most cards that sidestep the singleton rule are unlimited (Basics, cards like [[Persistent Petitioners]]). Seven Dwarves is different in that it allows for 7 cards. Thus, all decks where red is an element of the color identity must take the possibility of running any number from 0 to 7 copies of Seven Dwarves.
I am not taking Companions into account for the following reasons:
  1. It makes the math much harder. I'd have to take into account the decks that could run each of the Companions and then list them with and without the partner.
  2. Meeting the requirements of the EDH-legal companions is difficult to do and end up with a functioning deck.
  3. I absolutely hate the Companion mechanic, to the extent that I refuse to purchase any card from a product that uses it. (It doesn't help that it is patently obvious that Wizards mad no effort at all to playtest Ikoria for any constructed format.)
So what do we do with these numbers?
First, a note on notation: when you see two numbers above each other, that's a standard notation for a Combination of the top number of things taken the bottom number of times without replacement. Read the Wikipedia article. Unfortunately, this subreddit does not contain TeX-style formatting. However, we're going to be taking the sum of four series:
  1. The series of all decks with single commanders and not running Seven Dwarves
  2. The series of all decks with single commanders that do run Seven Dwarves (so Red must be an element of the color identity)
  3. The series of all decks with two commanders that do not run Seven Dwarves
  4. The series of all decks with two commanders that do run Seven Dwarves.
The formula will thus look like this.
Alternately, for those that aren't comfortable with that level of mathematical notation, here's a little bit of rectally-extracted Python (it's ugly, and I'm sure if I cared more about it I could make it better):
#!/usbin/env python3 import operator, functools #This function performs a combination of n things taken r at a time def ncr(n, r): r = min(r, n-r) numerator = functools.reduce(operator.mul, range(n, n-r, -1), 1) denominator = functools.reduce(operator.mul, range(1, r+1), 1) return numerator // denominator #This computes the number of decks with one commander and no copies of Seven Dwarves def oneCommanderNoDwarves(commanders, singletons, unlimiteds): sum = 0 for i in range(0, 100): sum += commanders * ncr(others - 1, i) * unlimiteds ** (99-i) return sum #This computes the number of decks with one commander and some number of Seven Dwarves def oneCommanderWithDwarves(commanders, singletons, unlimiteds): sum = 0 for s in range(1, 8): #range goes to one less the top number in Python for i in range(0, 100): sum += commanders * ncr(others - 1, max(i-s, 0)) * unlimiteds ** (99-s-i) return sum #This computes the number of Partner decks that do not use Seven Dwarves def partnerWithoutDwarves(partners, singletons, unlimiteds): sum = 0 for i in range(0, 99): sum += partners * ncr(others - 2, i) * unlimiteds ** (98-i) return sum #This computes the number of Partner decks that use Seven Dwarves def partnersWithDwarves(partners, singletons, unlimiteds): sum = 0 for s in range(1, 8): for i in range(0, 99): sum += partners * ncr(others - 2, max(i-s, 0)) * unlimiteds ** (98-s-i) return sum #This combines the above def allDecks(colorIdentity, commanders, partners, singletons, unlimiteds): decks = oneCommanderNoDwarves(commanders, singletons, unlimiteds) if partners > 0: decks += partnerWithoutDwarves(partners, singletons, unlimiteds) if "R" in colorIdentity: decks += oneCommanderWithDwarves(commanders, singletons, unlimiteds) if "R" in colorIdentity and partners > 0: decks += partnersWithDwarves(partners, singletons, unlimiteds) return decks #Let's just pseudocode this for right now. if __name__ == "__main__": table = #open the table above with csv.DictReader decks = 0 for row in table: decks += allDecks(row["Color Identity"], row["Commanders"], row["Partner Pairs"], row["Singleton Cards"], row["Unlimited Cards"]) print(decks) 
The number is big. Very big. Just as a case study, let's take the Colorless decks. Doing the math on just them leads to a number around 5.254 * 10166. For comparison, the age of the universe in seconds is somewhere around 4.35 * 1017 seconds.
So are you ready for this? The number of possible decklists excluding companions is 8.583 * 10 270 as of 2020-07-10. New sets will definitely increase this number considerably. The problem of enumerating these decks is intractable, but the process will eventually halt.
Now here's one other thing I should note: the vast majority of these decks are unplayable or at least functionally unplayable, despite being legal lists. Why? Because any deck, without respect to color identity, has a lot of cases where it isn't running enough mana sources to make its colors reliably. In fact, it may wind up that the only mana sources in the deck are basic Wastes (which can go in any number in any deck), if it has that many. But this question wasn't about playability. It was about how many possible valid lists there are.
* I am including the pairing of [[Gisela, the Broken Blade]] and [[Bruna, the Fading Light]], as allowing these two to work as though they had Partner With is sensible, flavorful, intuitive, a common house rule, and why the hell doesn't Commander have the rule, "If two legendary creatures can meld together, they may both be your commander as though they had Partner with each other." It's the single rule change I'd make to the format.
submitted by thephotoman to EDH

[Let's Build] d100 Unique Home Base Ideas for an Adventuring Party

A lot of campaigns tend to involve the party getting some home for them to return to. Some groups may teleport around the continent, while others spend all their time working through one city or locale, but many like to have a base to return to (even if they're not there most of the time). While regular castles and mansions are cool, let's put together some ideas for homes for players which have something unique, a physical or historical feature that makes them noteworthy.

d100 Unique Home Bases

  1. The Stormhold - a fortress built on and into a shard of mountain that floats through the air, above the clouds. If the party can find a way in and take control of it they can also find a method to pilot it.
  2. Deserted Island - a small tropical Island off the coast which is for some reason, uninhabited. Perhaps there is an old, dilapidated manor, or empty tribal village that provides a quest hook leading to eventually claiming this island, or perhaps just some hidden treasure.
  3. Infernal War Machine - Effectively a building on treads, akin to the Jawa Sandcrawler or Elephant from Halo, this war machine is large enough for a party to adopt quarters within. Outfitted with hellish weapon stations this battlewagon will never quite feel comfortable, but what it lacks in amenities it makes up for in intimidation and power.
  4. Castle on the Lake - maybe you like the idea of being on an Island but not so far from shore? A castle on an island in the middle of lake would be cool, like Bled Castle or Mcdermott's Castle. Maybe the players can speak a command word that causes a bridge to rise or sink from the bottom of the lake. Or maybe the whole Island and castle submerge in a pocket of air and rise on command. Alternatively could be like Mont Saint-Michel where the tide's rising and falling isolates and connects it to/from the shore.
  5. "Haunted" Mansion - Word around the area is that this was the headquarters of a necromancer who went missing years ago, and now lies somewhere out in the woods, too dangerous for any common folk to dare look for trouble and go there. But upon arrival the players meet a pristine estate, sitting on beautiful, well cultivated grounds. An apparently friendly/good-hearted necromancer lived here and his undead servants watch the grounds, landscape, prepare food, keep watch, etc. In particular I like the idea of an "unseen servant"-like ghost who can do things like fetch items or mix drinks for players.
  6. Ma Meagle's Bakery: A quaint little bakery resting at the corner of one of the plazas of the party's home town. Baked confectioneries and bread lines the counter with four squat little tables within for diners. The back rooms of Ma Meagle's are where the polite, sweet old woman bakes her goods... but if one were to wander down to the basement they would find a well-lit base of operations for local explorers, burglars, adventurers and other such folk. Of course, any such uninvited guests will find Ma Meagle's double-reinforced repeating crossbow pointed at their skulls. [sageking14]
  7. Hølmenaa - The largest island in a montane lake, roughly 400 yards upstream of a thunderous falls. The island was used in ancient times as a dueling ground for barbarian chieftains to settle their competing territorial claims. It contains little more than a small stone hut with a hearth and space for six to sleep; a seemingly ageless piste made of slick granite; and three standing stones, with some trees dotting the shoreline. The controller of the island can use the stones to cast heroism as a second level spell, calm emotions, and hold person each twice a day. To gain control of the island a player must successfully get two quarreling parties to meet on the island and agree to a settlement without violence.[Norwejew]
  8. The Flotsam: A group of three masted sailing ships lashed together with heavy ropes. Every time the party captures another vessel, they add it's resources to their hideout. If anyone comes looking for trouble, the exterior ships are all fitted with cannons. Ships can be docked nearby and small ships boats can be rowed in. [Muffinman594]
  9. The Cask: A legendary barrel with the most potent special magics known to mortal minds woven into it. The interior is three hundred feet in diameter at the widest and 500 feet from top to bottom, with gravity local to whichever surface you are nearest. The exterior is roughly 3 feet at the widest and 5 feet tall. It can be exited from the top, the bottom, or the bunghole but only entered from the top or bottom. If it is in it’s side, then simply walking along the circumference of the interior will cause it to roll in that direction with similar speed and force. [Mor_Drakka]
  10. The Blue Manor: The local lord has been revealed to be a traitor, and fled to the mountains to continue their vile work with their dragon ally. The party has been invited by the new governor general to stay in spare rooms at the estate in thanks for uncovering the plots, as the lord's former home functions as the headquarters for the various paladin and guard brigades to discuss planning how to take him for judgement. The estate is quite large, with a large apple orchard and a separate home for the maids that live on the property. The personal library of the lord is massive, with thousands of books gathered over the years on any number of subjects. Several doors in the manor are locked, with no keys to enter them, and very high DC's to lockpick them open. Meanwhile, in the far corners an ancient animist monument exists, its form cracked and eroded by time, though leaving offerings of milk and honey on a regular basis still gets one minor gemstones as thanks from an unknown source. [Shadowhogzilla]
  11. Brigand's Den - A large sea cave once used by smugglers and pirates to avoid the authorities. The area is easily accessible by boat or on land if you know where to look. There are docks large enough to support several boats. [Brand_News_Detritus]
  12. The Coral Villa - An underwater mansion in a secluded bay that legends say was built when a wizard fell in love with a merfolk woman. The mansion is closed off to anyone not wearing specific enchanted rings that also grant Water Breathing (but only in this particular bay). Half of its rooms are filled with water with the other half are within magically maintained bubbles of air. [Brand_News_Detritus]
  13. Under the Mountain - A mountain stronghold re-purposed from mining tunnels from an abandoned dwarven expedition. The living areas have all the creature comforts of home while the various tunnels provide lots of traps, dead-ends and choke points for repelling invaders. [Brand_News_Detritus]
  14. Yggdrasil - A base carved out of a massive Ash tree. [FolkMinotaur]
  15. Obisdian keep - A shining black castle growing out of the side of a dormant volcano. [FolkMinotaur]
  16. Summers Court - A beautiful manor and standing gardens that once slipped into the feywild and has never been the same since. [FolkMinotaur]
  17. Fortress of Time - An ancient fortress built in a bygone era. A failed ritual has ripped open time here, resulting in the laws of time breaking and rewriting themselves in an infinite loop. This causes the different parts of the building to enter different points along its timeline. For example, maybe the living room is an ancient dusty wreck one day, but the next it’s lined with oil paintings from 200 years ago and exquisite antique furniture. [quill-of-doom]
  18. The Dwarves’ Gulch- A valley, in which perfectly-chiseled geyser holes are carved out of the ground and valley sides. When water is released out of the geysers, the water splashes at precise angles to create the shape of a palace made of pressurized water. The water is heated and pressurized from a nearby volcano. Searching underground in the geyser holes leads to giant subterranean lakes with obsidian lining the walls. [waluwyatt]
  19. The Oubliette: a monolith in a wasteland. Anyone with a "key" can open the Oubliette, sucking them into a mansion carved into the center of a planet-sized meteor in the plane of Limbo. The mansion incorporates geometry that would be impossible to construct, much like an M.C. Escher painting. [givemedrawingideas]
  20. A quaint brick house that previously belonged to a talented gnome packed full with helpful gadgets and gizmos that do chores, from polishing armor to cooking dinner. The gadgets don't always work flawlessy (it IS an old house), but residents of the abode often stumble upon new, rarely-used mechanics. The whole house is powered by a huge gear pilfered from the plane of Mechanus which turns on its own endlessly in the basement. [MildlyConcernedGhost]
  21. Baba Yaga's Dancing Hut - An old house standing on giant chicken legs. It is actually able to walk around and function as a travelling base. Previously owned by a hag, it comes fully equipped for practicing alchemy and making potions. [Martinus_XIV]
  22. Sahuagin Bluff - A rock protrsion on a cliffside, named so because it has the shape of a shark's head, complete with a gaping mouth with serrated stone "teeth". There's a hidden cave in the mouth of the shark, which can be accessed through a secret entrance at a stone pillar on top that resembles a dorsal fin. [Martinus_XIV]
  23. Old Clock Tower - From this base, you always have a great view of the town and surrounding area, so you'll spot trouble from miles away. It's a bit noisy when the bell tolls, but at least you'll be the most punctual adventurers to ever grace this realm... Just beware of falling moons... [Martinus_XIV]
  24. Abandoned Roc's Nest - Sure, it's a bit drafty, but the view is maginificent, and you'll never sleep more soundly than on a bed of Roc feathers... [Martinus_XIV]
  25. Mushroom Tower - Embrace your inner Gnome and make your home in this giant hollow mushroom! [Martinus_XIV]
  26. Fallen Arm - The curled fingers of the chopped-off arm of an ancient titan provide shelter from the elements. The palm of the hand is large enough to build a respectable base... [Martinus_XIV]
  27. Crashed Planeship - This absolutely alien-looking structure used to be a ship that could travel the planes and even beyond. While it doesn't work anymore, it still has fully equipped living quarters. With some effort, you might also be able to make use of other systems. It appears to house a holodeck, a clone bay, advanced point-defence systems and who knows what else! Now if only you could get the food replicators to work again... [Martinus_XIV]
  28. Giant Shell - This giant snail's shell has long since been abandoned by its owner, making it free real estate. The body whorl makes for a roomy hall, while the more narrow whorls are the perfect size for living quarters. The warm sunlight filtering through the translucent calcium carbonate walls makes for a cozy and relaxing atmosphere. [Martinus_XIV]
  29. Under-Cliff Monastery - This eastern-looking monastery was built upside-down from an overhanging cliffside, making it extremely hard to reach. At least, let's hope your enemies find it so. [Martinus_XIV]
  30. Wonderous Wagon - A wagon which from the outside appears like any other one but is essentially a TARDIS with plenty of room on the inside for any medium sized party. The wagon weighs the same as a normal one and so the party can take their base on the go with them. [TheTryhardApple]
  31. Terrific Toilet- An outdoor toilet which has a lever allowing you to jump through the bowl and slide into your base, just always make sure to flush first ;) [TheTryhardApple]
  32. Sorry Stables- Who says your party has to live a lavish life. This row of renovated stables each has a small simple living quarters inside. [TheTryhardApple]
  33. The Lofted Greenery - A massive treehouse hidden within the canopy of a dense jungle of massive trees. [A_Heckin_Goblin]
  34. Campus Martius - a group of high-quality but not luxurious tents grouped around a campfire. Build a castle in the clouds, you lose your edge. This keeps the party focused. [felagund]
  35. The Burrow - An unassuming cave entrance leads to a huge interconnecting system of caves and tunnels. No one is quite sure who the original owners were. [Viscumin]
  36. Outpost 35 - A former guard and watch post, it's served as a training facility, firewatch station, local landmark and serviceable trading place for generations. The original owners are long dead and the conflict which required it forgotten. Down in the lower basement is a remarkably well-provisioned food pantry of canned and salted meats, some of them almost as old as the original building. [LordsOfJoop]
  37. The Colony - Built on an island in the middle of a lake, this former artists' colony was repurposed as a leper colony within the previous twenty years or so. The walls are well-built, easy to maintain and have some of the most beautiful artwork in the form of murals, portraits and still life's that the PCs have ever seen. The roof has a built-in garden and there's a statue collection gathered around a deep, narrow grave-like hole in the once-abandoned church marked as 'the last adventure': at the bottom of it lay a tame, well-fed ooze that numbs and kills quickly, singing as it consumes its meal. It uses the voice of its last victim. [LordsOfJoop]
  38. Madhouse - A refurbished asylum, built close to a small town, populated by the former inmates who, while mostly recovered, needed a place to live and raise families. They serve as free assistance and guards, taking care of the place in exchange for no rent being collected and the right to be private and isolated from the civilization that scorned their ancestors. The cells have been bricked shut, locking away the bad memories of the old days.. except for Cell Thirteen, home to an angry, wise spirit of an old woman who was captive for a hundred years by the cruel master of the asylum. Cultivating a relationship with the spirit could prove useful for the group. [LordsOfJoop]
  39. On top of a dragon turtle. [inkwell13]
  40. A River Delta, bunch of silt islands that a small trading town has sprung up on that the players can interact with. [Rancerle]
  41. The Skeleton House - The bones of a truly giant creature lie partially buried in a hill. A previous occupant has run leather walls around the rib cage and built a two decked platform inside. A couple of hollowed out rooms in the hill provide storage and a ladder up the spine into the skull provides a lookout point. There is comfortable room for five or so adventurers, although little privacy. The body lies in a slight coil around a firepit with with a small clay oven near by. One of the rooms carved into the hill has a shaft that leads to fresh water. [Kiyohara]
  42. Wizard's Tower - Built using magic, the tower seems to defy reason. A large tower of perfectly worked stone, it rises over eight stories and is never more than twenty feet around. It is perched atop a craggy stone hill, with a narrow switchback trail leading to the summit. A few storage sheds around the base of the tower supply additional storage. Inside each floor is dedicated to different purposes, with a store room, kitchen, comfortable living space, library, laboratory, and a bed room. Two other floors could easily be made into bedrooms (at least two rooms to a floor) and with minor renovations could house a few more rooms. The Roof is wide circular space used for summoning and astrological viewing. The basement has a well that produces perfectly clear, clean and icy cold water year round regardless of the weather or water table conditions. [Kiyohara]
  43. The Old Mill - A sizable Mill, now abandoned when the local town built one closer to town. It stands a staggering three stories tall, with a massive wheel still slowly turning in the mill pond (now home to a large population of trout), a small stream flows away back towards the river that passes by the town. Inside the main floor is taken up by the stone grinding wheel and gears for the mechanisms; they are sadly out of repair and do not currently work. Behind the main room is a large storehouse, used in the past for grain and flour, now currently empty. The upper floors are where the Miller and his family used to live (along with several apprentices); a large kitchen dominates the second floor with a hearth and oven that seem to sit atop the stone counter balance for the mill stone below. A small family room sits facing the south and the warm rays of the sun. A tiny library and office show the Miller was both literate and dutiful in keeping his records straight. A large master bedroom still retains a giant bed, with heavy oaken pillars and well sewn, if pedestrian looking curtains keep the bed warm in the night and the bugs away. The top floor is all bedrooms, closets, and a large bathroom dominated by a massive wooden tub. A gnomish brass work construction seems to draw water from the mill pond to fill the tub and a pan for oil and a burner seems to indicate that it could warm the water so pulled. [Kiyohara]
  44. The Walking Statue Treehouse - A wizard in years past had created a protector of stone to guard their abode. This walking statue still stands today even though it's locomotion enchantments are long gone. Over the years, many families have built architecture off of the sturdy structure in the center. Paths turned to passageways, open stairways and ladders on the statue itself turned to proper companionways for residents to reach the upper levels with ease and security. One of the premier houses built on the statue extends beyond it's offered left palm. The almost horizontal arm created an ideal place for living that only slightly slopes upwards. The penthouse rests at the statue's upraised right hand as it reaches for the clouds above. The fingers of the statue surrounding and cradling the construction there. It was created by and occupied over the years only by creatures with the capability of flight. [ghenddxx]
  45. Scarred Battleground - Legend tells of a fortress whose garrison made their last stand, laying their lives down to a man and inflicting terrible damage on the encroaching force. The army who cleared them out returned to a camp but a squad of soldiers were dispatched later to burn or bury the bodies of their own soldiers who had fallen in the assault. They came back the next morning terrified and white as bone, telling that the base was crawling with [spirits, fiends, etc. pick your flavor] and since no one has dared go near it, or at least done so and lived to tell the tale. A party who clears it out (may involve consecrating or blessing) are rewarded with an empty, unowned, perhaps well stocked, strategically valuable and defend-able building. [DMDelving]
  46. Seelie Retreat - otherwise just a large manor, but it stands out due to the volume of plant growth. Manifesting in was such as an overgrown yard not just in weeds but in vines, flowers, and perhaps even carnivorous plants. Or vines of ivy which curl around the corners of the structure itself. Perhaps the basement, or a large tree on the property, contains a portal to the feywild. [DMDelving]
  47. []
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submitted by DMDelving to d100

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