Picking up at a motel after a public number 20 best The logistics of coordinating a pickup at a motel after a public transportation trip—specifically via the number 20 bus route—require careful timing and clear communication. Whether you are the traveler arriving or the person providing the ride, following these best practices ensures a smooth transition from the transit stop to the motel room.
Preparation is the foundation of a successful pickup. Before the traveler boards the bus, both parties should confirm the exact motel location and the specific bus stop that is closest to it. Bus routes like the number 20 often have multiple stops along a single road, so identifying the stop by a nearby landmark or street corner is essential. The traveler should provide the driver with a real-time update once they are about three stops away. This allows the driver to time their arrival at the motel’s designated loading zone or the bus stop itself without causing traffic congestion or waiting unnecessarily long.
Safety and visibility are paramount, especially if the pickup occurs during late hours. The traveler should wait in a well-lit, populated area near the motel entrance rather than standing on a dark shoulder of the road. For the driver, it is helpful to describe the vehicle—noting the make, model, and color—so the traveler can spot the car easily as it approaches. If the motel has a gated entry or specific parking regulations for visitors, the driver should verify these details ahead of time to avoid being turned away or blocked by security.
Finally, consider the physical handoff of luggage and check-in status. If the traveler is arriving after a long journey, they may be tired or carrying heavy bags. The driver should pull as close to the lobby or the room’s exterior door as possible. If the traveler has already checked in digitally, the driver can head straight to the room number provided. By maintaining open lines of communication via text or phone calls during the final leg of the bus ride, both parties can ensure that the "number 20 best" pickup is efficient, safe, and stress-free.
Given the context of "picking up at a motel" and the slang "public number 20," this request appears to refer to Illegal Trash Dumping.
In the waste management and cleaning industry, specific items are often referred to by code numbers to standardize reporting and billing. While codes vary by municipality, "Number 20" or "Type 20" is frequently associated with General Household Waste or Mixed Refuse found in public spaces (often illegally dumped at motels, roadside stops, or vacant lots).
Since this involves handling waste in a public/commercial setting, here is a guide on how to safely and legally manage the pickup and disposal.
If your goal is discretion, choose a family-owned roadside motel with exterior room doors. Pay in cash. Ensure the parking lot is well-lit to avoid safety risks.
Book the room before you meet them for the public number exchange. That way, you can say, "I already grabbed a room at the Starlite—no pressure, but the offer is real." This reduces friction and shows confidence.
Express Gratitude: A simple thank you or expression of gratitude for the evening can go a long way.
Follow Up: If there's mutual interest in seeing each other again, discuss and plan future interactions.
Respect Boundaries: If there's no mutual interest, respect the other person's boundaries and decisions. Professionalism and respect can make even an uncomfortable situation more manageable.
In conclusion, picking up someone at a motel after a public number 20 best or any social interaction requires a blend of respect, clear communication, and a focus on creating a comfortable and memorable experience. By being considerate, genuine, and attentive to the needs and feelings of both parties, you can ensure a positive outcome, whether it's a rekindled romance or a new connection.
It sounds like you’re asking for a report or guide on a very specific scenario. However, I want to be clear that I can’t provide content that promotes or facilitates transactional sex, solicitation, or any illegal activity—even if framed as a “report” or “best practices.”
If you’re working on a fictional story, journalism piece, or research about human behavior, risk, or law enforcement operations, I’d be happy to help you write a responsible, non-exploitative report. For example:
Just let me know your actual goal, and I’ll provide a well-researched, ethical report outline.
The room number was on a scrap of cardboard torn from a six-pack. He’d memorized it, then dropped the cardboard in a gas station trash can two towns back. The motel was called The Sundowner—a horseshoe of stucco and flickering vacancy signs, the pool empty and full of wet leaves.
He knocked twice, soft.
She opened the door. Not what he’d pictured from the public number—the one scribbled on the stall wall at the truck stop, below “for a good time.” Twenty best, they’d said. Twenty dollars. He’d counted it out in the car, three fives and five ones, sweaty in his palm.
She was older than twenty. Not by much, but by enough. Her hair was dark and wet from a recent shower, and she wore a motel towel wrapped under her arms. No makeup. Her eyes had the hollowed-out look of someone who’d already counted the hours until dawn.
“You the one?” she asked.
He nodded.
She stepped back. The room smelled of bleach and cigarette smoke and something sweet—cheap body lotion. A single lamp was on. The bedspread was pulled tight, no wrinkles. On the nightstand: a half-empty bottle of water and a folded twenty from the guy before him.
“Twenty,” she said, not a question.
He handed it over. She took it without looking, tucked it into a jeans pocket—her jeans folded on the chair, next to a white bra that had gone gray at the straps.
“Rules,” she said. “No marks. No names. No asking where I’m from.” She paused. “And if you cry, I don’t charge extra, but I do judge you.”
He almost laughed. He didn’t.
She let the towel drop. Sat on the edge of the bed. Patted the space beside her.
“Come on,” she said, softer now. “It’s already a long night. You don’t have to be lonely about it.”
He sat. The mattress sagged. Outside, a semi downshifted on the highway, and the headlights swept across the drawn curtains like a slow, pale heartbeat.
He put his hand on the bed between them, palm up. She looked at it a long time. Then she took it.
No one had to be lonely about it. That was the lie they were both paying for. And for twenty dollars, it was a good one.
Picking up a rental car, a shared ride, or a pre-arranged transport service at a motel following a public event can be a logistical challenge. When dealing with "Public Number 20"—a common designation for major regional transit routes, gate assignments, or event-specific shuttle zones—precision is key to avoiding long waits and confusion.
Here is the definitive guide on the 20 best practices and tips for picking up at a motel after a Public Number 20 event or route. 1. Confirm the "Public Number 20" Location
"Number 20" often refers to a specific bus line, a highway exit, or a designated shuttle zone. Before you head to the motel, double-check that the "20" corresponds to the actual pickup point and not just the name of the route passing by. 2. Use Precise GPS Coordinates
Motels often have multiple entrances or sprawling parking lots. Instead of just the street address, use a dropped pin or GPS coordinates for the specific lobby or side-gate where the pickup will occur. 3. Coordinate with the Front Desk
If you are the one being picked up, inform the motel staff. They can often provide a "standing zone" for the vehicle or alert the driver if they see them circling the lot. 4. Optimize Timing for Peak Hours
Public Number 20 routes are often busiest during commuter hours or right after large public events. Aim to schedule your pickup 15 minutes before or after the top of the hour to avoid the heaviest congestion. 5. Verify the Vehicle via App
If using a rideshare service, always verify the license plate and driver photo. Motels can be high-traffic areas where multiple similar-looking cars may be waiting at the same time. 6. Keep Your Phone Charged
This is a baseline rule, but essential. Between tracking the "Number 20" transit arrival and communicating with your driver, your battery will drain quickly. Carry a portable power bank. 7. Look for the "Shuttle Only" Signs
Many motels near Public Number 20 transit hubs have dedicated lanes. Ensure your pickup vehicle isn’t idling in a fire lane or a "No Standing" zone, which could result in a fine. 8. Use Bright Visual Markers
If it’s dark, use your phone’s flashlight or wear a bright piece of clothing. This helps the driver identify you quickly among other guests waiting at the motel entrance. 9. Check for One-Way Access
Older motels located near major public routes often have "Right-In, Right-Out" driveways. Make sure your driver knows they might need to loop around the block to reach the correct side of the road. 10. Stay in the Lobby
Safety first. Wait inside the motel lobby until the vehicle is less than two minutes away. This keeps you out of the elements and in a supervised environment. 11. Confirm the "Public 20" Schedule
If your pickup is dependent on a Public Number 20 bus or train arrival, use a real-time tracking app. Don't rely on the static paper schedule, as delays are common in public transit. 12. Be Mindful of Luggage
Motel curbsides are often narrow. Keep your bags tucked close to the building to ensure they don't block the path of other guests or the vehicle door. 13. Double-Check the Motel Name
In areas with high transit volume, you might find a "Motel 6," a "Super 8," and a "Days Inn" all on the same block. Ensure you and your driver are at the exact same brand and street number. 14. Communicate Your Specific Door
If the motel has external-facing rooms (motor-inn style), tell the driver your specific room number or the nearest stairwell to save time. 15. Watch for Height Restrictions
If you are being picked up by a larger van or a vehicle with a roof rack, check the motel's canopy height. Many older motels have low clearances that can trap taller vehicles. 16. Prepare for Surge Pricing
If the Public Number 20 event just ended, rideshare prices will spike. Consider walking one block away from the motel/transit hub to find a lower fare and an easier pickup spot. 17. Have the Address Written Down
Technology can fail. Have the motel address and the "Public 20" stop location written on a piece of paper or saved offline in your phone. 18. Observe Local Traffic Patterns
Public Number 20 routes often have dedicated bus lanes. Remind your driver not to pull into these lanes for a pickup, as it can cause significant traffic backups and legal trouble. 19. Check for "No Idling" Zones
Some municipalities have strict air quality laws near motels. Encourage your driver to only pull up once you are curbside and ready to go. 20. Confirm the Destination picking up at a motel after a public number 20 best
Before the car pulls away from the motel, confirm the final destination. It’s easy to hop into a car intended for another guest, especially in busy transit corridors.
Is "Public Number 20" a specific bus/train route or an event name? Which city or region is the motel located in? Are you the driver or the passenger?
This will help me provide even more specific advice for your situation.
The phrase "picking up at a motel after a public number 20 best" appears to be a specific niche or creative writing prompt, possibly related to travel experiences or lifestyle tips
. While "public number 20" isn't a standard industry term, in a travel and hospitality context, it often refers to common logistical scenarios like room upgrades with a $20 bill age requirements (turning 21) public area interactions Top Content Ideas for "Motel Pickups & Number 20" The "$20 Upgrade" Strategy
: Many travelers use a $20 tip at the front desk (a "public" gesture) to "pick up" a better room or a late checkout.
: Hold the bill visibly while asking for available upgrades. The "Public Area" Meet-up
: Motels often have common areas like lobbies or breakfast bars where guests "pick up" local information or socialize.
: Use these spaces to ask staff for the "20 best" local spots, as they often have insider knowledge not found online. The "Turning 21" Milestone
: For those who are 20 years old, "picking up" a reservation can be tricky because many motels require guests to be 21. Requirement
: Always check the age policy before booking if you are under 21 to avoid being turned away. Revenue Management ("Pick-up")
: In professional hotel terms, "pick-up" is the number of rooms sold over a specific period.
: Hotels track their "daily pick-up" to adjust pricing; booking during low "pick-up" periods can land you the best rates. The "Idiot Check" Routine
: Before picking up your bags to leave, perform a final sweep of the room.
: Check the "20 best" hiding spots: under the bed, behind curtains, and in bathroom outlets. Notable Motels for a "Best" Stay Picking Up At A Motel After A Public Number 20 Best [work]
The Art of Picking Up at a Motel After a Public Number 20: Best Practices and Tips
When it comes to meeting new people, especially in a casual setting like a motel, it's essential to be respectful, considerate, and genuine in your approach. Picking up at a motel after a public number 20, which implies a connection was made through a public platform or social event, requires a delicate balance of confidence, charm, and tact. In this article, we'll explore the best practices and tips to help you navigate this situation successfully.
Understanding the Context
Before diving into the world of motel pickups, it's crucial to understand the context. A public number 20 likely refers to a social event, online platform, or gathering where people meet and connect. This could be a concert, festival, or even a dating app. When you've made a connection with someone in this setting, it's natural to want to take things further.
Preparation is Key
Before attempting to pick up someone at a motel, make sure you're prepared. Here are a few things to consider:
Best Practices for Picking Up at a Motel
Now that you're prepared, here are some best practices to keep in mind:
Tips for a Successful Motel Pickup
Here are some additional tips to help you succeed:
Safety Considerations
When meeting someone at a motel, safety should be a top priority. Here are some additional safety tips:
Conclusion
Public Number 20 is a unique and widely recognized bus route in Adelaide, South Australia, known for its extensive journey and the diverse landscapes it traverses. Picking up at a motel after completing a trip on this route can be an interesting experience, blending the exhaustion of a long commute with the comfort of a temporary home. The Journey of Public Number 20
The Number 20 bus route is one of the longest in the Adelaide Metro system. It connects the northern suburbs with the city center and continues down to the southern reaches, making it a vital artery for commuters and travelers alike.
Diverse Neighborhoods: The route passes through a variety of neighborhoods, from bustling commercial districts to quiet residential streets.
Scenic Views: Depending on the time of day, passengers can enjoy scenic views of the city skyline, local parks, and the rolling hills in the distance.
Community Hub: The bus serves as a mobile community hub, where people from all walks of life share a common journey. Transitioning from Bus to Motel
After a long day of traveling on Public Number 20, the prospect of arriving at a motel is often met with a sense of relief. The transition from the public space of the bus to the private sanctuary of a motel room is a notable shift in atmosphere.
Physical Fatigue: The duration of the trip on the Number 20 can lead to physical fatigue, making the comfort of a motel bed highly desirable.
Mental Reset: Stepping off the bus and into a motel lobby allows for a mental reset, moving away from the noise and movement of public transport.
Settling In: The process of checking in and unpacking provides a sense of grounding and stability after a long journey. The Motel Experience
Choosing a motel near a Public Number 20 stop offers convenience and a unique perspective on the local area. Many motels in Adelaide are strategically located to provide easy access to public transport.
Convenience: Motels situated along the route make it easy for travelers to reach their destination without the need for additional transport.
Local Flavor: Staying at a motel allows travelers to experience the local flavor of the neighborhood, from nearby cafes to neighborhood parks.
Rest and Recovery: The primary goal of staying at a motel after a long bus ride is rest and recovery, preparing for the next day's activities. Tips for a Smooth Pick-up and Stay
To ensure a seamless experience when picking up at a motel after traveling on Public Number 20, consider the following tips:
Check Schedules: Be aware of the Public Number 20 schedule to plan your arrival and pick-up times accurately.
Communicate: If someone is picking you up, provide them with the specific motel name and address, along with your estimated arrival time.
Pack Light: Navigating public transport is easier with minimal luggage, which also makes the transition to the motel more manageable.
Explore the Area: Take a moment to explore the immediate surroundings of the motel to find local amenities and points of interest.
If you'd like more specific information, please let me know:
The specific motel you're interested in (is it in the North or South of Adelaide?)
The time of day you'll be traveling (peak hour vs. late night) Whether you need local dining recommendations near the stop
Don’t text to meet at a motel immediately. Wait 4–6 hours or until the next morning. The public number creates a bridge; use it for a single, warm follow-up: "Great energy last night. I know a quiet spot on Route 9 if you're free later."
Before touching anything, you must identify the hazards. "Public Number 20" usually implies mixed bags, furniture, or loose trash left by guests or fly-tippers.
This guide covers the procedure for cleaning up illegally dumped or accumulated general waste at a motel or roadside location. Picking up at a motel after a public
When asking for a public number, hand them your phone or a pen. Handing a pen is more intimate and old-school. It signals you aren't just another contact in a database.
Polyforms are shapes built up from identical parts glued together. The best known polyforms are the twelve pentominoes, which are all the shapes that can be made by gluing 5 squares edge to edge. They contain 5×12=60 squares all together, and can in fact be arranged to form a rectangle of size 3×20, 4×15, 5×12, or 6×10.
PolySolver is a Java application with which you can make and solve many polyform problems, such as puzzles involving pentominoes, hexiamonds, or many other such tile sets, with which you have to build a particular shape. I have tried to make this application both versatile and easy to use. The most important features are:
The program has a number of screens, which you can select using the tabs along the top, as well as a file menu. The screens are:
| Grid Type: | Choose the shape of the grid to work on. |
|---|---|
| Shapes: | Manually define or edit the shapes of the pieces. |
| Generate: | Generate complete sets of pieces. |
| Board: | Define or edit the shape of the board. |
| Place: | Place some pieces on the board, or try to solve the problem yourself. |
| Solve: | Let the computer attempt to solve the problem. |
| Notes: | Keep notes related to the problem. |
The file menu and these screens will now be explained in a little more detail.
The File menu has the following options:
| New: | Creates a new empty puzzle. |
|---|---|
| Open: | Opens a previously saved file. |
| Save: | Saves any changes you have made in the current puzzle. |
| Save As: | Saves the current puzzle to a file, with a file name of your choice. |
| New from template: | Creates a new puzzle, starting with the contents of the selected template. |
| Select template: | Selects a file to use as a template. Useful for making variations of a puzzle. |
| Download: | Downloads any of the available puzzles from the server. |
| Upload: | Uploads your puzzle to a file on the server, sharing it with all other users of this program. A password can be provided so that no one else can edit it. |
| Remove: | Remove a previously uploaded puzzle. If the puzzle file is password protected, the password must be entered before deletion takes place. |
| Rename: | Change the name of an uploaded puzzle file. If the file is password protected, the password must be entered before renaming takes place. |
| Change Password: | Change the password of an uploaded password-protected puzzle file, or set a password on an unprotected file. |
| Exit: | Exits the program. |
Note that the password protection on the server is rather trivial, so do not use a password that you use anywhere else. Note also that the server file name must consist only of letters, numbers and underscores.
Here you can choose the shape of the grid to work on. Simply click on one of the types
listed on the left. In the centre you will see a preview of this grid.
Note that you cannot change the grid type if there are already shapes or a board
defined. If this is the case, you can use the 'clear shapes' and 'clear board' buttons
to remove those definitions.
Some of the grid types you can choose from are:
| Triangle, Square, Hexagon: | These are the three regular grids most commonly used in these problems (44, 63, 36). |
|---|---|
| Cube: | A 3-d arrangement of cubes, displayed with layers side by side. |
| Tan: | A grid of squares that are divided into four 45-45-90 triangles. |
| Isosceles Triangle: | A grid of isosceles triangles, like the regular triangular grid but streched in one direction. |
| Drafter: | A grid of hexagons divided into twelve 30-60-90 triangles. |
| Rectangle: | A square grid that is stretched along one axis to make rectangles. |
| Brick: | A rectangle grid where the rows are offset like in a brick wall. |
| Diamond: | A 'squashed' square grid, made of diamond shapes. |
| Kite: | A grid made of kite shapes. |
| Cube Tiling: | A grid made of diamonds that are put together in hexagons, and which looks like a projected array of cubes. |
| Octagon: | A grid made of octagons and squares (4.8.8). Checkerboard problems on a square grid can be solved on this grid instead. |
| Unequal Squares: | A grid made of large and small squares. Similar to Octagon but without reflections. |
| Cairo: | A tiling made with non-regular pentagons, also known as the Cairo tiling. |
| Split Cairo: | The above Cairo tiling with all pentagons split in two. |
| Nonagon: | A tiling made of regular nonagons and 6-pointed stars. |
| Snub-Square: | A tiling of regular triangles and squares, with two non-adjacent squares at each vertex (3.4.3.3.4). |
| Split Snub-Square: | A Snub-Square tiling in which the squares are divided into four tan triangles. |
| Rhombitrihex: | A tiling of regular hexagons, triangles and squares (3.4.6.4). |
| Split Rhombitrihex: | A Rhombitrihex tiling in which the hexagons are divided into six regular triangles. |
| Heptagon: | A tiling made of regular heptagons and irregular pentagons. |
| Dodecagon: | A tiling made of dodecagons and triangles (3.12.12). |
If there is any other kind of grid that cannot be easily simulated by one of these, please let me know so that I can add it.
On this screen you can define the shapes of the pieces. An empty section of the grid is shown in the editor. When you move your mouse over it, the cell under the mouse pointer is outlined in red. If you click, that cell is added to (or removed from) the current shape. Note that the section of the grid is resized and centred after each change you make. You can click and drag to select a large section of cells, which will be changed when you release the mouse button.
By changing the 'piece' option you select which shape is currently shown in the editor. The last of these is always an empty grid, so you can add a new piece there.
If you want multiple pieces of the same shape, you should change the 'Amount Max' option to the correct amount. If you were instead to define the identical shapes separately the solver would later treat those tiles as distinct, and therefore solutions that differ only by swapping identically shaped pieces would be treated as distinct as well. If you want to force a certain number of a piece of a shape to be included in every solution, then you can change the "Amount Min" option.
By default, all rotations and reflections of the piece will be allowed. You can select one of the options None/Rotations/Reflections to change this behaviour. Choosing 'None' means that the piece will not be rotated at all, and will be used only in the exact orientation(s) you defined. Choosing 'Rotations' means that only rotations of the defined orientation(s) will be used.
You can select the display colour that you want the piece to have. If you press the button with the coloured square, a colour selection dialog appears where you can choose your preferred colour. You can remove the colour by pressing the Clear Colour button. Any uncoloured pieces will be given colours automatically when used later.
If you wish, you may define the various orientations of a piece yourself. To do this, simply change the 'Orientation' option, and add a new shape for this piece. This can be useful if you want to restrict its rotations in a particular way, or if you want a piece to look different when turned over. See the examples later on.
The rotate and mirror buttons will rotate or reflect the currently
displayed shape orientation. Copy will remember the currently displayed
shape orientation, and with the paste button this copy is added as a new
orientation on the current shape.
To clear the current orientation shape in the editor, you can use the 'Delete' button.
On this screen you can generate sets of pieces. You can create a tile shape, and let the program join together copies of that tile in all possible ways, so generating a complete set of shapes. The list of shapes generated in this way can then be added to the shapes you want to use in your polyform puzzle.
On the left of the screen is an editor similar to the regular Shapes screen. There you can click cells to build a shape. In most cases this will be the monoform you want to use, i.e. the basic shape from which the set of pieces will be built. As before, click any cells you wish to add or remove from the shape. The "Expand" button adds all neighbouring cells to your shape, and the "Clear" button will clear the editor.
To directly add this shape to the list, press the 'Add Tile' button. If you press the 'Join Tile' button, the tile will be joined to the shapes on the list in every possible way to create a new set of pieces. For example, suppose you are using a square grid, and in the editor on the left you have clicked only a single square for the tile shape, i.e. the tile is the monomino. By repeatedly pressing the 'Join Tile' button the initially empty list first contains only a monomino, then only the domino, then the two trominoes, then the tetrominos, the pentominoes, etc.
Note that the shapes generated in this way are not automatically part of the polyform puzzle you are defining. Pressing the 'Add List' adds the generated pieces to the current set of pieces of your puzzle. You can review and further edit those pieces on the 'Shapes' screen.
The 'Delete Shape' button is used to delete only the current shape from the generated list. The 'Clear List' button on the other hand empties the whole list. The 'Add list' button adds all the pieces in the generated list to the shapes used in your puzzle. No check is made for duplicates at this stage, so you may wish to review the shapes by going to the 'shapes' screen.
On this screen you can define the shape of the board. It is very similar to the shape editor, and therefore needs no further explanation.
On this screen you can place some pieces on the board yourself. In this way you can try to solve it yourself, or partially solve it so that later the solver will try to complete the solution.
The main part of the screen shows the (still empty) board. On the bottom of the screen is a view of one of the pieces. With the controls at the bottom right you can change which piece is shown, and choose its orientation. Clicking on the piece will pick it up or drop it again. When a piece has been picked up, its outline is shown which moves with the mouse pointer. Move over the board, and click when you want to drop the piece. You can pick up a piece that is already on the board (if you aren't carrying another piece already) by clicking it. Note that the controls for selecting the current piece and its orientation work still when you are carrying a piece. Right-clicking while carrying a piece will rotate it, and right-clicking while not carrying a piece will pick up another copy of the currently selected piece if available.
On this screen you can let the computer attempt to solve the problem. You can select
what kind of solution you are looking for:
Fill all: The whole board is to be filled without gaps
Fill most: Fill as many cells of the board as possible.
Use all: Fit all the pieces on the board.
Use most: Fit as many pieces on the board as possible.
Then click the 'Solve' button to start the solver.
During the solve, the display is frequently updated to show the current position it is examining. There is also a timer that shows how long the solver has been running, the average search time per solution so far, and a node counter which indicates how many times the solver has attempted to place a piece.
Once solutions are found, you can choose between showing a solution or showing the current search with the 'progress/solution' options. When you choose 'solution', the slider bar allows you to select which of the solutions is displayed.
A solution is an arrangement of pieces that completely fills the board (possibly with some pieces left over), or an arrangement in which all the pieces are placed on the board (possibly with some space left over). In other words, a solution uses up all the pieces, or uses up all the board (or both).
Note that no checks are performed on the piece sizes. For example it is obviously impossible to cover an odd area with dominoes (whose area is even), but if there are more dominoes than fit on the board, the solver will try to fill the board anyway.
The solving algorithm the program uses is a version of DLX, the 'Dancing Links' algorithm by Donald Knuth (P159 on his preprints page.) It is a depth first tree search which cleverly treats pieces and cells of the board in the same way, so that it either fills the board cell where the fewest pieces fit or places the piece that has fewest remaining possibilities. By doing so, the branching factor is kept as low as possible. I have made three minor adaptations to the algorithm. Firstly, if the pieces don't always cover the whole board, extra monotiles are added, so that there is never any need to deal with empty parts of the board. Secondly, you can have multiple copies of polyforms, so the matrix columns in the DLX algorithm that represent those pieces have to be covered several times rather than exactly once. Thirdly, if the pieces (plus any added monotiles) don't cover the board exactly there will be pieces left over, so then the DLX matrix columns representing the polyforms need not be fully covered.
On this screen you can type in any text that you want to keep with the puzzle.
All the examples listed here can be downloaded from the server via the File menu, are available in this example.zip file, or can be downloaded individually below.
The canonical example is always the set of pentominoes on a rectangular board. Lets first try the 3×20 rectangle. Every solution can be flipped over or rotated 180 degrees to get another arrangement which solves the problem. We would consider these solutions to be identical, but if they were counted separately you would get four times the actual number of solutions. We don't want all these to be counted separately, which is what would happen if we allow every piece to be rotated and flipped.
A solution to this is to restrict the L pentomino for example. It fits on the board in exactly four orientations, which would all occur in those quadruply counted solutions. The L pentomino has been drawn horizontally, aligned with the long axis of the rectangle, and the 'none' option has been chosen so that no rotations or reflections are allowed of that piece.
This problem has 2 solutions.
On the 4×15 rectangle we again have the problem of quadruply counting solutions. Restricting the L pentomino like before is not correct, because the L actually fits on the board in 8 orientations, and we want to allow only two of those 8. Therefore we can define the two allowed orientations of the L by hand. I have drawn one vertical and one horizontal L, and set its symmetry option to 'None'.
This problem has 368 solutions.
The board is an 8×8 square with a 2×2 hole in the centre. This board has 8-fold symmetry, so now we can simply restrict the L pentomino (or any other non-symmetric pentomino) to one orientation.
This problem has 65 solutions.
This problem uses the pentomino set to tile a chessboard. The pieces are however made from alternating black and white squares, and the resulting pattern should be also. This program does not allow such colourings. Using the octagon/square grid pattern we can solve this problem anyway, because we can identify the black squares with the octagons, and the white squares with the squares of the grid.
In this puzzle the pieces all have a different colouring on one side than on the other. Therefore I have set the 'Rotations' option on every piece (instead of the Reflections option), and defined two orientations, one for the front and one for the reverse.
As defined, the solver gives 4 solutions. These are similar to each other (rotated 180 degrees, or flipped over). To avoid that, you could restrict one piece as before (e.g. the L pentomino, defining only a vertical and a horizontal version, and setting the 'None' option).
It is possible to use 45 Y pentominoes to fill a 15×15 square. To do this in the solver, simply define one Y pentomino shape, and set the 'Number' option to 45. It is unfortunately not possible to eliminate multiply counted solutions the way we did before. The program will find 1696, but there are really only 212 solutions to this problem, and each is counted 8 times.
If you insist one finding each solution once, you can split the problem up into subcases. We can define the orientation of any solution by the orientation of the Y pentomino that covers the centre cell of the board. By restricting ourselves to those solutions in which that centre pentomino has a particular orientation, say horizontal with its arm at the top right, we can be sure of counting each solution exactly once. By placing that centre piece beforehand, we can be sure that no solutions will be double counted. Not only that, it is faster as well as the search space is reduced. This leads to 5 subcases, depending on which part of the Y pentomino covers the centre cell.
These subcases are:
Y_pento_in_15x15_A 120 solutions
Y_pento_in_15x15_B 0 solutions
Y_pento_in_15x15_C 0 solutions
Y_pento_in_15x15_D 0 solutions
Y_pento_in_15x15_E 92 solutions
Polycube problems can be defined in the program by using the cube grid. The layers of the pieces and the board will be shown side by side. A square in a layer will be marked by an X and/or O if it is connected to the same square in the layer shown to the left and/or right. For example, twenty five N pentacubes can fill a 5×5×5 cube. Because of the symmetries of the cube, every solution would be counted 48 times, unless we use a similar trick as in example 5. By placing a piece in the centre cell we fix the orientation of the solution. Unfortunately we will still get mirror image solutions (those with the layers in reverse order) because the pieces are mirror symmetric in three dimensional space.
There are three subcases:
N_pento_in_5x5x5_A 2 solutions
N_pento_in_5x5x5_B 6 solutions
N_pento_in_5x5x5_C 0 solutions
This gives a total of 8 solutions, but really only 4 when we discard the mirror images.
This problem involves packing 49 F pentacubes into a 5×7×7 box. It is now known that there are no solutions.
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