PlayStation Portable

However, due to dedicated users like Fanjita, at the time of writing at least some unsigned software can be run by any firmware version through the use of a special loader program. CBS has run several stories concerning Sudoku, including on the Early Show in Summer 2005, and on the CBS Evening News that autumn, on October 26. Compare to the GP2X handheld by Gamepark, which supports and encourages homebrew software. The stunt was cleverly timed to coincide with a major road expansion, where an imposed 40 mph speed restriction allowed drivers to safely view the puzzle whilst driving. Finally, users who utilize emulation software have been discouraged by firmware versions 1.52 and above, each of which added new blocks to prevent unsigned code from being executed. The puzzle was carved into a hillside in Chipping Sodbury, near Bristol, England, in view of the M4 motorway. The PSP has also been criticized for its high price, more comparable to that of the Playstation 2 console than competing handhelds. A Sky One publicity stunt to promote the programme with the world's largest Sudoku puzzle went awry when the 275 foot (84 m) square puzzle was found to have 1,905 correct solutions.

However, firmware releases since then have added new formats, including Microsoft's WMA, and more may be forthcoming. The audience at home was in a separate interactive competition. At launch, the PSP was criticized for its lack of support for popular file types, following Sony's trend in preferring to use proprietary formats. Conferring was permitted although the lack of acquaintance of the players with each other inhibited an analytical discussion. This trojan downgrader is fairly rare, unless a downgrader is downloaded from an "untrustworthy" site. Each player had a hand-held device for entering numbers corresponding to answers for four cells. This can be caused by two things: the interruption of a program writing to the flash (Upgrader, Downgrader) or a trojan downgrader that purposely deletes all data on the flash. Nine teams of nine players (with one celebrity in each team) representing geographical regions competed to solve a puzzle.

Please note that systems that do not power on correctly (the green power button is on, but it will not boot) are considered "bricked," and all data stored on the internal flash memory has been deleted or corrupted. It was presented by Carol Vorderman. Issues from sticky "square" buttons, to analog nubs that do not work properly, and even systems that simply cannot power on, are also noticed on occasion. As a one-off, the world's first live TV Sudoku show, Sudoku Live, was broadcast on 1 July 2005 on Sky One. However, recent PSPs seem to be free of such defects. On 2 August 2005 the BBC's programme guide Radio Times started to feature a weekly Super Sudoku. The PSP also suffered from a plague of dead pixels straight out of the factory, along with an extremely high defect rate at the time of its initial release. From July 2005 Channel 4 included a daily Sudoku game in their Teletext service (at page 391).

Due to its use of high density optical media, loading times exist on many games, over half a minute long in some. Recognizing the different psychological appeals of easy and difficult puzzles The Times introduced both side by side on 20 June 2005. For example, in Grand Theft Auto: Liberty City Stories, when an explosion occurs near the character, he will exhibit ghosting. A simpler explanation is that the puzzle attracts and retains readers—Sudoku players report an increasing sense of satisfaction as a puzzle approaches completion. Some early models have more "ghosting" than others, meaning that one can see a trail left from moving objects on the screen. Sudoku became particularly prominent in newspapers soon after the 2005 general election leading some commentators to suggest that it was filling the gaps previously occupied by election coverage. A possible rebuttal is that the first year of a new system usually sees a drought in quality software, as seen with the PS2. The rapid rise of Sudoku from relative obscurity in Britain to a front-page feature in national newspapers attracted commentary in the media (see References below) and parody (such as when The Guardian's G2 section advertised itself as the first newspaper supplement with a Sudoku grid on every page [16]).

The PSP is often criticized for a perceived lack of quality games, as many of its titles consist of ports or remakes from console systems. Newspapers competed to promote their Sudoku puzzles, with The Times and the Daily Mail each claiming to have been the first to feature Sudoku. Whilst the PSP does not have input devices (yet)such as a keyboard using a usb cable one can connect to any PC run the portable apps and save Photo,jpeg and other user files in the PHOTO file on the PSP Pro Duo card for viewing later somthing a U3 usb drive is unable to do portable apps can be downloaded from http://portableapps.com/. As the name Sudoku became well-known in Britain, the Daily Mail adopted it in place of its earlier name "Codenumber". Portable application used in this way vastly increase the funtionality of the PSP. By April and May 2005 the puzzle had become popular in these publications and it was rapidly introduced to several other national British newspapers including The Independent, The Guardian, The Sun (where it was labelled Sun Doku), and The Daily Mirror. It is possible to use the PSP Pro duo memory card inside the PSP as a container from which portable applications such as Firefox, Open office, and many other usefull portable apps these run from the memory card in a similar way to U3 usb memory sticks. That newspaper already had plans for taking advantage of their market lead, and a first Sudoku book was already on the stocks before any other national UK papers had realised just how popular Sudoku might be.

. Until then the Times had kept very quiet about the huge daily interest that its daily Sudoku competition had aroused. Letter varies to the version depends on the country. The Telegraph continued to splash the puzzle on its front page, realizing that it was gaining sales simply by its presence. D is 2.00 (unconfirmed). There is no doubt that it was not until the British Daily Telegraph introduced the puzzle on a daily basis on 23 February 2005 with the full front-page treatment advertising the fact, that the other UK national newspapers began to take real interest. C is 1.52. The immense surge in popularity of Sudoku in British newspapers and internationally has led to it being dubbed in the world media in 2005 the "fastest growing puzzle in the world".

B is 1.51. Nationwide News Pty Ltd began publishing the puzzle in The Daily Telegraph of Sydney on 20 May 2005; five puzzles with solutions were printed that day. For the value pack in the U.S., A is 1.5. The Daily Telegraph introduced its first Sudoku by its puzzle compiler Michael Mepham on 19 January 2005 and other Telegraph Group newspapers took it up very quickly. Each letter corresponds to which version it represents. Three days later The Daily Mail began to publish the puzzle under the name "Codenumber". To help buyers be aware of what version they are getting, there is a letter near the bar code on the PSP merchandise box. The puzzles by Pappocom, Gould's software house, have been printed daily in the Times ever since.

This exploit now works on firmware version 2.60 also. Knowing that British newspapers have a long history of publishing crosswords and other puzzles, he promoted Sudoku to The Times in Britain, which launched it on 12 November 2004 (calling it Su Doku). Recently, an exploit, for firmware version 2.5, was found in the game Grand Theft Auto: Liberty City Stories that allows homebrew code to be run from a save game file when loaded into the game. Over 6 years he developed a computer program to produce puzzles quickly. However there are limitations with running homebrew on 2.0 being programs will be run in user mode and not kernel mode. In 1997, retired Hong Kong judge Wayne Gould, 59, a New Zealander, saw a partly completed puzzle in a Japanese bookshop. Using a buffer overflow exploit, it is possible to install 1.50 firmware onto a 2.0 firmware PSP, thus downgrading it and allowing for the execution of unsigned code. Sudoku has been called the "Rubik's cube of the 21st century".

Later exploits have allowed for PSPs using version 1.50 of the firmware to run homebrew software nearly transparently. Within the context of puzzle history, parallels are often cited to Rubik's Cube, another logic puzzle popular in the 1980s. What this meant in practice was that these PSPs could run homebrew software, as the mechanism for checking to make sure that software has been approved by Sony had not yet been activated. It is also often included in puzzle anthologies, such as The Giant 1001 Puzzle Book (under the title Nine Numbers). In May 2005, it was found that PSPs using the 1.00 version of the firmware (meaning original, first launch Japanese-only PSPs) could execute unsigned code. Additionally, Kappa reprints Nikoli Sudoku in GAMES Magazine under the name Squared Away; the New York Post, USA Today, The Boston Globe, Washington Post, and San Francisco Chronicle now also publish the puzzle. UK is the only European country in which Sony has taken any form of legal action against importers of the PSP prior to its European release. Bringing the process full-circle, Dell Magazines, which publishes the original Number Place puzzle, now also publishes two Sudoku magazines: Original Sudoku and Extreme Sudoku.

One such importer, Electricbirdland Ltd., claimed they had sold several PSP consoles to SCEE staff [15]; they were subsequently singled out and taken to court. Yoshimitsu Kanai published his computerized puzzle generator under the name Single Number for the Apple Macintosh [13] in 1995 in Japanese and English, for the Palm (PDA) [14] in 1996, and for the Mac OS-X [15] in 2005. Sony Europe took legal action against small importers [14] in the UK citing trademark infringement. At least one publisher still uses that title. This resulted in PSPs being imported without authorisation, from Japan and the United States into Europe. In 1989, Loadstar/Softdisk Publishing published DigitHunt on the Commodore 64, which was apparently the first home computer version of Sudoku. Sony Computer Entertainment Europe had delayed the launch date originally set for March to meet demand from other regions. Within Japan, Nikoli still holds the trademark for the name Sudoku; other publications in Japan use alternative names.

The European and Oceanian launch took place on 1 September 2005 [13]. It is now published in mainstream Japanese periodicals, such as the Asahi Shimbun. Ten days later this was followed by a joint launch in Singapore, Hong Kong, and Taiwan on May 12, 2005. In 1986, Nikoli introduced two innovations which guaranteed the popularity of the puzzle: the number of givens was restricted to no more than 32 and puzzles became "symmetrical" (meaning the givens were distributed in rotationally symmetric cells). It was later released in North America on March 24, 2005 and in South Korea on May 2, 2005. At a later date, the name was abbreviated to Sudoku (数独, pronounced SUE-dough-coo; sū = number, doku = single); it is a common practice in Japanese to take only the first kanji of compound words to form a shorter version. The PlayStation Portable was first introduced to the public at the Tokyo Game Show 2004 (see: http://www.eurotechnology.com/tokyogameshow2004/ ) and released on December 12, 2004 in Japan. The puzzle was named by Kaji Maki (鍜治 真起), the president of Nikoli.

Similar cases also applied to the game Coded Arms. The puzzle was introduced in Japan by Nikoli in the paper Monthly Nikolist in April 1984 as Suuji wa dokushin ni kagiru (数字は独身に限る), which can be translated as "the numbers must be single" or "the numbers must occur only once" (独身 literally means "single; celibate; unmarried"). For example, a user running the Japanese version of Ridge Racer cannot play (via wireless) with another user running the UK version of Ridge Racer. The puzzle was first published in New York by the specialist puzzle publisher Dell Magazines in its magazine Dell Pencil Puzzles and Word Games, under the title Number Place (which we can only assume Garns named it). A Japanese version of a game cannot be played against an American or European version of the same game. Although likely inspired by the Latin square invention of Leonhard Euler, Garns added a third dimension (the regional restriction) to the mathematical construct and (unlike Euler) presented the creation as a puzzle, providing a partially-completed grid and requiring the solver to fill in the rest. However, multiplayer compatibility across regions is not preserved. The puzzle was designed by Howard Garns, a retired architect and freelance puzzle constructor, and first published in 1979.

Probably there is a difference between the Japanese and European region 2 settings. The inverse problem—the fewest givens that render a solution unique—is unsolved, although the lowest number yet found for the standard variation without a symmetry constraint is 17, a number of which have been found by Japanese puzzle enthusiasts [11] [12], and 18 with the givens in rotationally symmetric cells. Note: however at least some region 1 PSP's with V.1.5 cannot play region 2 (European) movies. Since this applies to Latin squares in general, most variants of Sudoku have the same maximum. It should also be noted that, despite what many websites say, Region 1 PSPs are capable of playing Region 2 and Region 4 UMD movies, and Region 2 PSPs are capable of playing Region 4 UMD movies (except the Region 4 version of Be Cool for an unknown reason). The maximum number of givens that can be provided while still not rendering the solution unique is four short of a full grid; if two instances of two numbers each are missing and the cells they are to occupy form the corners of an orthogonal rectangle, and exactly two of these cells are within one region, there are two ways the numbers can be assigned. There are ways around the region protection through such programs as UMD Emulator (currently this is only possible through firmwares V1.00 and V1.50). The number of valid Sudoku solution grids for the 16×16 derivation is not known.

Movies, on the other hand, are usually region-locked. Russell and Jarvis also showed that when symmetries were taken into account, there were 5,472,730,538 solutions [10] (sequence A109741 in OEIS). This follows the lead that Nintendo started with their Game Boy line, leaving open the "portability" of the handheld, as well as enabling gamers who want to buy a PSP game while visiting another country will still be able to play it on their native PSP's. The derivation of this result was considerably simplified by analysis provided by Frazer Jarvis and the figure has been confirmed independently by Ed Russell. There will be no limitation as to which country's handheld can play which country's version of the game. The result was derived through logic and brute force computation. Games for the PSP are currently being encoded as region-free, and an official Sony statement [12] states that this will continue indefinitely. This number is equal to 9! × 72² × 2⁷ × 27,704,267,971, the last factor of which is prime.

Sony has recently stated that PSP games will be region free while UMD Movies are region locked. Nonetheless, the number of valid Sudoku solution grids for the standard 9×9 grid was calculated by Bertram Felgenhauer in 2005 to be 6,670,903,752,021,072,936,960 [9] (sequence A107739 in OEIS). However, support for regional lockout does not necessarily mean it will be used for all software. There are significantly fewer valid Sudoku solution grids than Latin squares because Sudoku imposes the additional regional constraint. This scheme is based on the DVD CCA's DVD regional lockout scheme; Japanese PSP hardware already has a R2 logo on its box. A valid Sudoku solution grid is also a Latin square. The PSP supports region locking for games and movies, which limits which software may be played on each region's hardware. The puzzle is then completed by assigning an integer between 1 and 9 to each vertex, in such a way that vertices that are joined by an edge do not have the same integer assigned to them.

(Some European PSPs had version 2.0 on the demo disc, but came preinstalled with version 1.5.) *See External Links for Firmware Release ChangeLogs. In this case, two distinct vertices labelled by and are joined by an edge if and only if:. Version 2.0 of the firmware was supplied on the demo disk inside the box of European PSPs, with version 1.52 preinstalled on the unit. The vertices can be labelled with the ordered pairs , where x and y are integers between 1 and 9. Various updates have included WPA-PSK encryption; a built-in web browser; the ability to stream audio using RSS; Location Free player (the PlayStation 3 will have this function built into it), keyboard input mode for Web input; AVC video playback from memory stick; audio switch function and 4:3 mode for memory stick video; GIF, BMP, PNG, and TIFF image viewing; AAC, ATRAC3plus, WAV and WMA audio playback from memory stick; wallpaper function; an image sharing feature; region-free streaming television and higher security for a recently discovered exploit in the Photo menu. The graph in question has 81 vertices, one vertex for each cell of the grid. The current firmware version is 2.60. The aim of the puzzle in its standard form is to construct a proper 9-colouring of a particular graph, given a partial 9-colouring.

While firmware updates can be used with PSPs from any region, Sony recommends only downloading firmware updates released for the corresponding region. Solving Sudoku puzzles (as well as any other NP-hard problem) can be expressed as a graph colouring problem. The PSP's firmware is updatable via Wi-Fi infrastructure connection to a Sony server, by downloading the update application with a PC and transferring to the PSP via USB, or from a UMD disk (allowing games to update the firmware automatically). This gives some indication of why Sudoku is difficult to solve, although on boards of finite size the problem is finite and can be solved by a deterministic finite automaton that knows the entire game tree. User skins can also be made available through downloads or by game publishers within their game discs. The general problem of solving Sudoku puzzles on n² x n² boards of n x n blocks is known to be NP-complete [8]. For older versions of firmware there exist homebrew programs, such as PSPSet or PSPPersonalise, which allow changing the PSP's background. Here are some of the more notable single-instance variations:.

Firmware 2.0 and greater allows manual choice of color theme, or specify a wallpaper from any photos that the user has stored to the PSP memory card. Top Notch claim this as a feature designed to defeat solving programs. Upon release, the default background color changed depending on the current month of the year, as follows:. It is debatable whether these are true Sudoku puzzles: although they purportedly have a single linguistically valid solution, they cannot necessarily be solved entirely by logic, requiring the solver to determine the embedded words. The OS may be accessed at any time in a game by pressing the "Home" button on the console. The Code Doku [6] devised by Steve Schaefer has an entire sentence embedded into the puzzle; the Super Wordoku [7] from Top Notch embeds two 9-letter words, one on each diagonal. The main menu system allows the user to, amongst other things, adjust settings such as date, time, and the PSP's nickname for wireless networking, play video or audio files from the memory stick, load games or movie UMDs, check on estimated battery life, and set the PSP into a "link mode" which makes the inserted memory stick available to a PC via USB. Recent variants have just that, often in the form of a word reading along a main diagonal once solved; determining the word in advance can be viewed as a solving aid.

It consists of a horizontal sequence of icons (Settings, Photo, Music, Video, Games, Network (added in 2.0; for now only features the tab-supported web browser and the LocationFree Player; 2.60 brought "RSS Reader" to the Network tab, which allows users to stream RSS 2.0 (audio) feeds through the Internet.)) which when highlighted show a vertical sequence of sub-icons (for example, selecting Games allows the memory stick or a UMD to be selected). Alphabetical variations have also emerged; there is no functional difference in the puzzle unless the letters spell something. The PSP's main menu interface is the "Cross Media Bar (XMB)" used by recent Sony TVs and the PSX hardware. Sequential grids, as opposed to overlapping, are also published, with values in specific locations in grids needing to be transferred to others. These are similar in concept to the cheap battery life extenders available for mobile telephones. Often, no givens are to be found in overlapping regions. These are typically either USB charging cables that allow the PSP to charge from any PC with a USB port or are simply a series of AA batteries with a voltage regulator. [5] Puzzles with twenty or more overlapping grids are not uncommon in some Japanese publications.

A number of companies are now offering other chargers for the device. In The Times and The Sydney Morning Herald this form of puzzle is known as Samurai SuDoku. The PSU itself is about the same size as a deck of cards. Five 9×9 grids which overlap at the corner regions in the shape of a quincunx is known in Japan as Gattai 5 (five merged) Sudoku. This multivoltage power supply is internally and externally similar to but not compatible with similar ones used with Sony's CLIÉ PDAs, and the power lead is a standard figure-of-eight cable similar to the power cable used with the PlayStation and PlayStation 2. Puzzles constructed from multiple Sudoku grids are common. The system ships with a multivoltage power supply for recharging the battery, allowing it to be charged in any country with the appropriate power lead. Some such variants forsake standard givens entirely.

It is available in Japan, the U.S., and Europe. Other kinds of extra restrictions can be mathematical in nature, such as requiring the numbers in delineated segments of the grid to have specific sums or products (an example of the former being Killer Su Doku in The Times), demarcating all places arithmetically adjacent digits appear orthogonally adjacent in the grid, providing the parity of all cells, requiring the Lo Shu Square to appear in the solution, and so on. Additionally, in late 2005, Sony released a battery that has a 20% higher charge capacity. [3] [4] In this variant, all the numbers must appear in all the concentric rings as well as in all pairs of adjacent wedges. There is also a variety of third-party batteries that have more than twice the battery life compared to the standard Sony battery. Also found is the Circular Sudoku, also known as Target Sudoku, invented by Essex mathematician Peter Higgins. A Sony high-speed charger is available as an optional accessory. Another dimension in use is digits with the same relative location within their respective regions; such puzzles are usually printed in colour, with each disjoint group sharing one colour for clarity.

One is thus able to purchase extra batteries as an accessory; at the Japanese launch, they cost ¥5,040 including tax (around US$47, €37, £26, AU$62). The Daily Mail also features Super Sudoku X in its Weekend magazine: an 8×8 grid in which rows, columns, main diagonals, 2×4 blocks and 4×2 blocks contain each number once. The PSP's battery is removable for replacement by the end-user. The aforementioned Number Place Challenger puzzles are all of this variant, as are the Sudoku X puzzles in the Daily Mail, which use 6×6 grids. While full-length movie UMDs were not available for this test, a repeating loop of the demo UMD bundled in the Value Pack provided a little over four hours of playback on a full charge. Often the restriction takes the form of an extra "dimension"; the most common is for the numbers in the main diagonals of the grid to also be required to be unique. The system is capable of approximately ten hours of MP3 playback from memory stick on a full charge and around half this for AVC playback. Another common variant is for additional restrictions to be enforced on the placement of numbers beyond the usual row, column, and region requirements.

In one test[11], this dropped to approximately two and three quarter hours when using Wi-Fi multiplayer continuously. Larger grids are also possible, with Daily SuDoku's 12×12-grid Monster SuDoku [2], the Times likewise offers a 12×12-grid Dodeka sudoku with 12 regions each being 4×3, Dell regularly publishing 16×16 Number Place Challenger puzzles (the 16×16 variant often uses 1 through G rather than the 0 through F used in hexadecimal), and Nikoli proffering 25×25 Sudoku the Giant behemoths. In practice, tests using Ridge Racer have given between three and a half and slightly less than six hours of continuous gameplay, depending on screen brightness and volume. Puzzle Championship had a Sudoku with parallelogram regions that wrapped around the outer border of the puzzle, as if the grid were toroidal. Currently the PSP's CPU is fabricated using a 90-nm process, but eventually Sony will shift to 65-nm and 45-nm when the technology becomes available. [1] Even the 9×9 grid is not always standard, with Ebb regularly publishing some of those with nonomino regions (also known as a jigsaw variation); the 2005 U.S. Ken Kutaragi, president of Sony Computer Entertainment, has compared the system to the Walkman, in that battery life will be improved with each product revision, and has outlined some steps (switching to a different fabrication process, for example) which will be used to improve the system's endurance. Although the 9×9 grid with 3×3 regions is by far the most common, numerous variations abound: sample puzzles can be 4×4 grids with 2×2 regions; 5×5 grids with pentomino regions have been published under the name Logi-5; the World Puzzle Championship has previously featured a 6×6 grid with 2×3 regions and a 7×7 grid with six heptomino regions and a disjoint region; Daily SuDoku features new 4×4, 6×6, and simpler 9×9 grids every day as Daily SuDoku for Kids.

Battery life is heavily dependent on the game chosen; technically simpler games such as Lumines tend to extend the battery life of the system, with graphically advanced games (or games that frequently access the UMD drive) such as Grand Theft Auto: Liberty City Stories tending toward shorter battery life. The challenge to Sudoku programmers is teaching a program how to build clever puzzles, such that they may be indistinguishable from those constructed by humans; Wayne Gould required six years of tweaking his popular program before he believed he achieved that level. The system's manual states that the PSP is capable of three to six hours of gameplay, depending on the screen brightness or volume level selected. The Guardian famously claimed that because they were hand-constructed, their puzzles would contain "imperceptible witticisms" that would be very unlikely in computer-generated Sudoku. The PSP uses a rechargeable lithium-ion battery for power (an AC adaptor is included for charging and running from the mains). The Sudoku puzzles printed in most UK newspapers are apparently computer-generated but employ symmetrical givens; The Guardian licenses and publishes Nikoli-constructed Sudoku puzzles, though it does not include credits. The PSP was preceded in this regard by Nokia's N-Gage in 2003, the Nintendo DS, and the Tapwave Zodiac in 2004. Dell Number Place Challenger (see Variants below) puzzles also list authors .

Nonetheless, the implementation of a GPU in the PSP is still a significant technological advance, in that it implements robust hardware-rendering for 3D graphics in the handheld market. Nikoli Sudoku are hand-constructed, with the author being credited; the givens are always found in a symmetrical pattern. Unlike Sony's PlayStation 2 console, the GPU (PS2 Vector Unit equivalent) is not programmable, meaning that many effects that the PS2 can resolve in hardware must be implemented in software on the PSP. The puzzle generator was written with Visual C++, and although it had options to generate a more Japanese-style puzzle, with symmetry constraints and fewer numbers, Dell opted not to use those features, at least not until their recent publication of Sudoku-only magazines. Specifications state that the PSP is capable of rendering 33 million flat-shaded polygons per second, with a 664 million pixel per second fill rate [10]. Wei-Hwa Huang claims that he was commissioned by Dell to write a Number Place puzzle generator in the winter of 2000; prior to that, he was told, the puzzles were hand-made. The independent 166 MHz 90 nm graphics chip sports 2 MiB embedded memory and through its 512 bit interface it provides hardware polygon and NURBS rendering, hardware directional lighting, clipping, environment projection and texture mapping, texture compression and tessellation, fogging, alpha blending, depth and stencil tests, vertex blending for morphing effects, and dithering, all in 16 or 32 bit colour, along with handling image output. They also have no authoring credits — that is, the name of the constructor is not printed with any puzzle.

It doesn't have integrated memory. It is commonly believed that Dell Number Place puzzles are computer-generated; they typically have over 30 givens placed in an apparently random scatter, some of which can possibly be deduced from other givens. The Coprocessor 0 that normally manages the TLB-based MMU seems to be a custom effort by Sony. Building a Sudoku with symmetrical givens is a simple matter of placing the undefined givens in a symmetrical pattern to begin with. No evidence of a TLB has been found to date. (This technique is adaptable to composing puzzles other than Sudoku as well.) Great caution is required, however, as failing to recognize where a number can be logically deduced at any point in construction—regardless of how tortuous that logic may be—can result in an unsolvable puzzle when defining a future given contradicts what has already been built. There is no memory management unit for the CPU. This technique gives the constructor greater control over the flow of puzzle solving, leading the solver along the same path the compiler used in building the puzzle.

The system has 32 MiB of main RAM and 4 MiB of embedded DRAM. Such an undefined given can be assumed to not hold any particular value as long as it is given a different value before construction is completed; the solver will be able to make the same deductions stemming from such assumptions, as at that point the given is very much defined as something else. The primary CPU core is responsible for traditional game processor functions; the secondary core, dubbed the "Virtual Media Engine," is responsible for decoding multimedia, for example the H.264 decoder. Building a Sudoku puzzle by hand can be performed efficiently by pre-determining the locations of the givens and assigning them values only as needed to make deductive progress. Exploits could, on previous firmware versions, unlock 333 MHz operation to seemingly no ill effect (except a slight decrease in battery life), but changes to the power management in firmware 2.60's kernel have since made this impossible. It is possible to set starting grids with more than one solution and to set grids with no solution, but such are not considered proper Sudoku puzzles; as in most other pure-logic puzzles, a unique solution is expected. Overheating concerns have also been cited as a possible reason for the cap, and gaming site Gamesradar has said this is the "most logical reason for the processor capping." The cap was previously set at the level of add-on software, not through the firmware (though the crossbar runs at 222 MHz). Some online versions offer several difficulty levels.

During the GDC, Sony revealed that it has currently capped the PSP's CPU clock at 222 MHz; apparently in an attempt to lengthen battery life. This estimation allows publishers to tailor their Sudoku puzzles to audiences of varied solving experience. The PlayStation Portable's CPU is a dual-core MIPS32 R4000-based CPU, each core being globally clocked between 1 and 333 MHz. Computer solvers can estimate the difficulty for a human to find the solution, based on the complexity of the solving techniques required. The most noticeable element of the PSP is its 110 mm/4.3" (diagonal) 16:9 ratio TFT LCD screen sporting a 480 x 272 pixel resolution capable of 16.77 million colours. It is based on the relevance and the positioning of the numbers rather than the quantity of the numbers. The unit measures 170 mm (6.7 in) in length, 74 mm (2.9 in) in width, and 23 mm (0.9 in) in depth, and weighs 280g / .62 lbs (including battery). A puzzle with a minimum number of givens may be very easy to solve, and a puzzle with more than the average number of givens can still be extremely difficult to solve.

The PlayStation Portable (PSP) was designed by Shi Ogasawara [小笠原氏] for the Sony Computer Entertainment company. Perhaps surprisingly, the number of givens has little or no bearing on a puzzle's difficulty.
. Published puzzles often are ranked in terms of difficulty. However, there are homebrew applications which use PSP as a TV remote controller, such as PSP IR Remote. A very fast solver is usually required for most trial-and-error puzzle-creation algorithms. The PSP features an IrDA port located on the top left of the device; however this is not currently used by any games. This is the method now preferred by many Sudoku programmers, mainly by virtue of its speed.

South Korean PSPs will ship with software providing web browsing and multimedia streaming features, but only through company-owned Wi-Fi hotspots, and with a monthly fee[9]. This method can be directly applied to solving Sudoku problems, counting all possible solutions for most puzzles rapidly. launch, supporting online play. A highly efficient way of solving such constraint problems is Donald Knuth's Dancing Links Algorithm. Use of infrastructure networks in PSP software began with a small number of titles at the U.S. Backtracking may be applied when alternate values cannot otherwise be excluded. Packet tunneling systems are in development by third-parties which allow any Wi-Fi game to operate across the Internet (see External links). A constraint program specifies the constraints of the puzzle (the fact that every number in each row, each column, and each 3×3 region must be unique, and the provided "givens"); a finite domain solver applies the constraints successively to narrow down the solution space until a solution is found.

Navy Seals) and an as-of-yet untitled MMORPG, have been announced which use this wireless network functionality. Another alternative uses finite domain constraint programming. launch games (Including the multi-million selling game, SOCOM: U.S. A more efficient program could keep track of potential values for cells, eliminating impossible values until only one value remains for a cell, then filling that cell in and using that information for more eliminations, and so on until the puzzle is solved. A handful of titles, including sixteen U.S. Although far from computationally efficient, this "brute force" method will find a solution, given sufficient computation time (even a fairly naive implementation will typically not take a noticeable amount of time). The PSP's menu can recognize protected and non-protected wireless networks within its range, and attempt to request a firmware update from Sony's servers. If a cell cannot be filled, the program backs up one level (from that cell) and tries the next value at the higher level (hence the name backtracking).