Use the plus shaped pipe on the space to the left of the statue’s rigth hand. Use the upside-down T-shaped pipe on the space to right of the statue’s left hand. Use the pipe without prongs on the space to the far left. Use the H-shaped pipe on the space to the far right. Use the pipe with two prongs on the space below the statue’s right hand. [+]
Use the pipe with three prongs on the space immediately to the left of the statue’s head. Use the pipe with three ends on the space to the far left. Use the pipe without prongs on the top space to the right of the statue’s head. Use the pipe with one prong on the space immediatly to the right of the statue’s head. Use the pipe with two prong on the lower right space. [+] Take the cat sitting next to the chair. Move the chair. Inspect the letter. Go to the next page. Leave the letter. Inspect the broken bolt. Leave the bolt. Inspect the blue bead. Leave the bead. Take the cat from the crates to the left. Use the paw prints on the paint. Inspect the paint. Use the key on the drawers. Inspect the drawers. Use the hammer near the statue at the far end of the room on the nails. Inspect the clipboard. Leave the clipboard. Put the wooden boards on the table saw. Turn on the table saw. Use the hammer and nails on the boards. Pull the lever. Put the ramp on the hook. Pull the lever. Complete the bonus round. Inspect the magazine on the chair. Leave the magazine. Inspect the letter in the lockers. Leave the letter. Inspect the note on the mirror. Leave the note. Inspect the notice in front of the costume references at the back of the room. Use the whip on the left head on the top shelf. Use the whip on the middle head on the top shelf. Use the whip on the right head on the top shelf. Use the leather scabbard on the NIK locker. Use the leather hanging over the front chair on the NIK locker. Use the head with the leather hat on the NIK locker. Use the shoulder jewelry hanging over the chair on the scratched locker. Use the tiara on the head with the long hair. Use the head with the long hair and tiara on the scratched locker. Use the bead skirt on the MT locker. Use the head with the braided hair on the MT locker. Use the broom. Inspect the blue bead. Leave the bead. Use the screwdriver on the scratched name plate. Leave the screwdriver. Leave the name plate. 3–4–2–2–1 Finish the smoothie minigame. 3–1–5–2 Inspect the hat. Use the key on the cabinet. Inspect the cabinet drawer. Open the green bag. Use the brush on the chalk outline. Inspect the box. Leave the box. Use the brush with chalk on the box. Push the buttons from the one with the most chalk to the one with the least chalk. Inspect the box. Inspect the book in the rightmost bookcase. Use the screwdriver from the desk on the floorboards. Inspect the floorboards. Complete the decoder translation of letters. Note that the ruler of the Nile is meant to say PHARAOH. Go to the next note. Note that the famous Nile princess is meant to say NEFERTITI. Go to the next note. Note that who sat on a throne is meant to say LOIS. Go to the next note.[+] 4–4–3 Complete the bonus round. Inspect the article on the table. Leave the magazine. Inspect the registry. Match the name “Kelly M. Common” with “Molly McKenna”. Inspect the key board. Leave the key board. Inspect the Pharaoh movie poster. Decipher the text FIND THE NAJAHAJE. Use the fallen candy on the rug on the candy jar on the counter. Inspect the note in the candy jar. Leave the note. Use the cane on the clock. Fill the watering can near the cane with the fountain. Empty the full watering can on the plant below the clock. Use the glass eye in the plant on the fish trophy behind the counter. Inspect the fish trophy. Use the key on the trophy cabinet. Inspect the coach cushions. Use the keycard on the elevator keypad. Use the hat on the coat. Use the keycard on the elevator keypad. Use the lockpicking set on the lock. Complete the lockpicking game. Inspect the laptop. Leave the laptop. Fill the iron with the bottled water from the nightstand. Turn on the iron. Use the iron on the letter. Inspect the letter. Leave the letter. Inspect the boots. Inspect the card next to the boots. Leave the note. Open the toothbrush. Put the batteries in the remote on the bed. Use the remote on the television. Inspect the television. Leave the television. Inspect the pen on the floor. Use the tweezers on the bathroom towel on the pen cap. Inspect the note from pen cap. Leave the note. Turn on the hot faucet in the bathroom. Combine the bathroom mirror with the television. Use the “Rolodex” password on the laptop. Leave the laptop. 2–2 Inspect the emergency box. Inspect the paint bucket. Leave the paint bucket. Flip the light switch. Inspect the writing on the door. Leave the door. Flip the light switch. Use the hammer on the emergency box on the base of the statue. Use the key on the door. Use the broom on the glass. Inspect the box inside the door. Go left. Open the broken camera. Leave the chip. Open the door. Use the staff prop from the left shelves on the staff prop from the right shelves. Use the ankh prop on top of the left shelves on the ankh prop to the right of the right shelves. Fill the empty vase spot at the back of the room with the decorative urn lying in the aisle. Use the bird statue in the aisle on the bird box at the top of the left shelves. Use the spear in the back of the room on the snake on top of the shelves. Put the snake in the snake prop box. Inspect the snake box. Leave the scepter. Use the mummy lying in front of the sarcophagus on the sarcophagus. Use the staff from the snake box on the sarcophagus. Leave the urn. Use the scoop in the right shelves just over the crate on the packing peanuts. Use the full scoop on the crate of packing peanuts. Inspect the packing crate. Leave the crate. Use the crowbar in the packing crate on the crocodile. Inspect the urn inside the sarcophagus. Use the packing manifest from the crocodile’s mouth on the packing manifest in the sarcophagus urn. Use the crowbar on the flash boom crate. Inspect the flash boom crate. 3–4–2–4 Complete the bonus round. Inspect the handheld device. Use the digital decrypter on the security camera chip. Complete the hacking minigame. Inspect the magazine on the chair. Leave the article. Use the dust from the make-up table on the safe. Open the box on the make-up table. Use the screwdriver on the mirror in the box. Use the mirror from the box on the laser beams. Inspect the note on the safe. Leave the note. Take a dark lightbulb. Inspect the empty socket. Take a dark lightbulb. Inspect the empty socket. Take a dark lightbulb. Inspect the empty socket. Take a dark lightbulb. Inspect the empty socket. Use the B1 note on the blue button. Use the Y2 note on the yellow button. Use the R3 note on the red button. Use the G4 note on the green button. Move the necklace. Inspect the locket. Leave the locket. Move the lipstick. Move the flower. Inspect the biography of Lois Manson. Leave the biography. Inspect the book. Leave the book. Inspect the obituary of Lois Manson. Leave the obituary. Move the glove. Inspect the book. Leave the book. Inspect the picture of Lois Manson. Leave the picture. 4–1–4 Use the battery on the flashlight. Use the snake wrangling cane on a snake. Use the snake wrangling cane on a snake. Use the snake wrangling cane on a snake. Use the snake wrangling cane on a snake. Use the snake wrangling cane on a snake. Use the snake wrangling cane on a snake. Use the snake wrangling cane on a lizard. Use the snake wrangling cane on a lizard. Use the snake wrangling cane on a lizard. Inspect the empty terrarium near the top left. Leave the terrarium. Inspect the rattlesnake swizzle stick on the floor near the spray bottles. Leave the swizzle stick. Inspect the note on the floor near the spill. Leave the note. Inspect the refrigerator to the right. Leave the refrigerator. Complete the bonus round. Inspect the poster. Inspect the snake picture. Decode the text DECDFA. Leave the message. 4–2–1–5–3–3 Inspect the letter. Leave the letter. Use the telephone. Inspect the fountain. Use the cane on the clock. Inspect the fountain. Use the employee card on the telephone. Move the rug. Use the metal N on the sculpture. Push the button inside the sculpture. Use the security panel. Open the camera. Use the digital decrypter on the camera chip. Complete the hacking minigame. Flip the light switch. Use the remote on the television. Leave the television. Inspect the shoes. Leave the credit card. Use the credit card from the shoes on the television. Leave the television. Open the fridge. Use the batteries on the camera. Use the pomegranate syrup from the floor on the coffee filter over the fridge. Use the red coffee filter on the bulb in the lamp of the far cabinet. Use the red bulb on the burnt out bulb in the bathroom. Inspect the notes on the far wall. Leave the notes. Use the telescopic lens from the table on the enlarger near the door. Use the wrench from the table on the sink faucet. Use the film on the leftmost black bin. Use the film on the full sink. Use the film on the rightmost white bin. Use the film on the enlarger. Use the prints on the leftmost black bin. Use the prints on the full sink. Use the prints on the rightmost white bin. Use the prints on the clothesline. Use the hair dryer on the prints. Inspect the prints. Leave the prints. 3–1 Complete the smoothies minigame. Use the blender top on the blender base. Put the apple from the back behind the counter on the blender. Turn on the blender. Use the blender on the juicer behind the counter. Use the screwdriver from the open toolbox on the stage light. Use the dolly on the box. Open the box with the lightbulb. Use the lightbulb on the burnt out light bulb on the stage. Inspect the stage light. Leave the light. Use the audio cable on the microphone. Flip the switch on the microphone. Use the sound panel. Use the cloth from the bar stool on the broken bottle. Use the key on the note behind the glass. Leave the note. Move the picture on the back wall. Use the matchbook from the rightmost table on the unlit candle from the table at the front. Use the tape on the sheet music. Use the sheet music on the stand. Use the seat cushion lying on the floor on the empty spot of the booth. Use the lucky penny from the booth on the wishing fountain at the back. Inspect the wishing fountain. Use the key on the piano lock. Use the sheet music on the piano keys. Play DECDFA. Leave the sheet music. Complete the bonus round. Inspect the poster. Use the poster on the break in the left wall. Inspect the panel on the wall. Push the fake wall. Start the car. Use the lockpick set on the car lock. Complete the lockpicking minigame. Inspect the trunk of the car. Use the wrench on the car. Start the car. Inspect the fountain water. Use the token on the token slot. Inspect the sign. Use the digital decrypter on the phone lines. Complete the hacking minigame. Pull the rope lying on the pier. Use the binoculars lying on the crate on the ship. Leave the ship. Use the binoculars on the streetlight at the far end of the pier. Leave the streetlight. Use the pawprints from the dock on the leftmost nets. Use the fish heads from the leftmost nets on the catapult in the rightmost net. Use the loaded catapult on the street light at the end of the pier. Use the empty bucket halfway across the pier on the water. Use the filled bucket on the hot key beneath the street light. Use the cooled down key on the luggage. Inspect the luggage. Use the hook from the luggage on the pulley. Open the top crate from the stack to the right. Use the wrench on the hook. Pull the rope. Pull the rope. Open the box. Inspect the plans. Leave the plans. Use the battery on the flashlight. Pick one of the crows. The crow either has red eyes, a colored tag, or is entirely black. Based on this color, pick one of the objects with matching colors. Black: Cat to the left of the cellar door. Red: Magazine in the grass in front of the fountain, apple in the middle of the fountain, ladybug on the vines between the windows, and the scoop at the base of the gazebo. White: Wrench in the grass to the left, fish heads in the grass to the right, tweezers in the grass to the right, and duct tape to the right of the base of the fountain. Green: Clover in the grass just below the cellar door, and watering can near the bottom of the screen. Blue: Cup at the left of the base of the fountain, and bead in the grass to the right of the fountain. Gold: Coin to the left of the cellar door, scarab on the statue head right of the cellar door, and goldfish on the lower level of the fountain. Keep matching crows to objects until all crows are gone. [+] Use the lockpick set on the lock of the cellar door. Complete the lockpicking minigame. Use the matchbook at the bottom of the screen on each of the 10 candles.[+] Inspect the lock on the chest. Leave the lock. Inspect the Flash Boom crate. Leave the crate. 5–3–2–2 Inspect the letter. Raise the blinde on the rightmost window. Inspect the note on the window. Leave the note. Move the plane on the rightmost cabinet. Inspect the secret panel. Leave the panel. Inspect the calendar. Leave the calendar. Inspect the book in the rightmost bookcase. Leave the book. Inspect the coat collar. Leave the coat. Use the 21 from the calendar on the safe. Use the 9 from the book on the safe. Use the 37 from the coat on the safe. Open the safe. Inspect the safe. Leave the safe. Use the phone. Turn on the screen. Use the screen on the storyboard. Inspect crate 73 on top of the stack. Open the crate. Leave the blueprints. Move the prop below the pyramids. Use the shovel at the right end of the screen on the sand just below the temple on the top left of the screen. Inspect the ark. Use the hieroglyphs to spell out EGYPTIAN COBRA. 5–2–3–3 Complete the bonus round. Use the matchbook at the bottom of the screen on each of the 10 candles.[+] Use the scarab key on the sacrophagus. Complete the lockpicking minigame. Go down. Finish the excavation minigame. Use the battery on the flashlight. Move the reflective surface near the lightbeam. Repeat until the room is lit.[+] Go left. Inspect the note. Move the pillars with the bird symbol in the order L, O, I, S. Move the pillars with the rain symbol in the order L, O, I, S. Move the pillars with the scorpion symbol in the order L, O, I, S. Move the pillars with the pyramid symbol in the order L, O, I, S. Note that the beams have been removed.[+] Note that in some versions of the game, failing this puzzle once yields a higher score. Inspect the dark room at the top of the stairs. 356660 Inspect the film reel. Leave the reel. Move to the next page. Leave the note. 2 Finish the excavation minigame.
All models are wrong, but some are useful
Agent-based models have the potential to inform policy decisions, for example in response to an outbreak of a unknown contagion. Rather than experimenting with different policies, policy-makers can predict the effects of different scenarios and interventions through agent-based simulation. Of course, the usefulness of such predictions relies on the accuracy of the model and the estimations of its parameter. Agent-based models need to carefully select a level of detail. Too little detail, and the model is unable to reliably predict the effect of policies. Too much detail, and accurately estimating all necessary parameters in reasonable time become prohibitively difficult.
On this page, we take a look at the SIR model, one of the simplest models of the spread of contagion, and consider different ways of increasing the level of detail (and thereby the complexity) of this model. The result is a simplified model of the spread of COVID-19, shown in the script below (open script in a new tab), which extends the SIR model with small-world networks and contagion modelling.
The scripts on this page make use of HTML5.
The SIR model (Kermack & McKendrick, 1927) provides a convenient starting point for constructing an agent-based model of the spread of contagion. This model separates the population into three classes: susceptible individuals who can be infected, infected individuals who spread the contagion to susceptible individuals, and recovered individuals who have become immune to the contagion.
The model is controlled by up to three parameters. The advantage of having very few parameters is that the model is more easy to evaluate and understand, and that it is relatively easy to find suitable values for these parameters. The downside is that the conclusions of the model for the purpose of formulating policy decisions are rather limited. To slow down or even stop the spread of the contagion, the SIR model suggests that policies should aim to reduce the infection rate or increase the recovery rate. However, how policies can achieve these effects is beyond the scope of the SIR model.
Small world network
To draw more fine-grained conclusions, the SIR model needs to be extended. For example, one of the more restrictive assumptions in the SIR model is that the population is well-mixed. This means that every interaction between agents is equally likely. While this may be a reasonable assumption for a small community, it is difficult to defend that people that live in the same street are equally likely to interact as people that live at opposite ends of the country.
In real life, social networks are highly clustered. For example, many people have friends in common with their friends. In addition, social networks tend to have the small world property, so that it takes relatively few steps to move from one individual to another in the network (cf. six degrees of separation.) While it’s not entirely certain that physical interactions can also be modelled as such a small-world network as well, it seems more reasonable than assuming the population is well-mixed.
In the script above, interactions are modelled through a small-world network, where agents are arranged on a circle. When the clustering coefficient is maximal, agents are only connected to neighbours on this circle. The lower the clustering coefficient, the more random the connections between agents become.
In addition to the small world network, the daily infection rate has been separated into the infection probability per interaction and the average number of interactions per agent per day. By making these two changes, the conclusions drawn from the model can be more fine-grained than for the SIR model. This extended model suggests that to slow down or even stop the spread of the contagion, policies should aim to limit the connectivity of people, reduce the number of interactions per person per day, reduce the infection rate per interaction, or increase the recovery rate.
Until now, the contagion has been rather abstract. The progression from susceptible to infected to recovered assumes that individuals are contagious directly after exposure to the contagion. Also, the contagion model ignores any symptoms altogether. In particular, individuals may behave differently depending on symptoms, and policy may be based on these observable symptoms.
We extend the model by representing the contagion as a Markov process. That is, the contagion is divided into discrete states. Once an individual has been exposed, the path of progression through the states of the infection is determined by a transition table. This transition table should then reflect the contagion being modelled. On this page, the default characteristics and transition rates have been set to COVID-19 characteristics (see Section 2.2 of Kerr et al., 2020).
Beyond the scope of this page
Of course, the model can be extended in many different ways. For example, CovaSim (Kerr et al., 2020) takes into account that COVID-19 has a different effect on different age groups. In addition, SynthPops takes a multi-layer approach to interactions, where interactions of households, schools, and workplaces are modelled separately and combined to create a more accurate model of interactions across different age groups. While these extension have the potential for making more accurate predictions of the spread of the contagion and its effects on society, they are beyond the scope of the scripts on this page.
Though this be madness…
Fitch diagrams are a way of constructing formal logic proofs in sentential logic or in predicate logic. The script on this page page (open script in separate tab) allows users to constuct these proofs and check its validity automatically.
The script allows the use of the logical connectives listed in the table below. In addition, the script allows for the use of predicates, functions, variables, and constants. The only restrictions on these is that they must start with a letter and consist only of letters, numbers, and the underscore (_) character. In particular, the typical restrictions that predicates must start with uppercase letters, while functions and variables must start with lowercase letters, is not enforced.
|Logical connective||Logic symbol||Script symbol|
Each statement in a proof has to be justified by a rule. Below, we describe each of the possible rules in more detail. In some cases, the rule alone justifies the use of a certain statement. In general, however, a rule refers to previous statements and/or subproofs. Single statements are referred to through their line number, while subproofs are referred to by the first and last line of the subproof, separated by a dash (e.g. 4-6). If a rule refers to more than one statement and/of subproof, they are separated by a comma (e.g. 3, 4-5, 7). The script on this page will automatically check whether rules are applied correctly. Below, we look at each of the supported rules in more detail.
Premises are the statements that are assumed to be true, and from which we want to derive the goal or conclusion. As a result, premise rules are always allowed, except that they must appear as a single block at the start of the proof. That is, you cannot slip in an extra premise halfway through the proof: it must appear at the top.
Assumptions, as the name suggests, are assumed to be true. However, unlike premises, assumptions are temporary. In essence, an assumption starts a subproof that has a single premise (the assumption). While a subproof can refer to any statement in proofs that contain it, there are only a few ways in which the main proof can interact with subproofs. We will visit these rules below.
A flag is like an assumption, except that a flag assumes that some constant exists rather than that some statement is true. Note that this must be a new constant, it may not already exist in some statement before the flag statement. The flag rule is only needed to introduce a universal quantifier (∀).
A tautology rule introduces a statement that is logically true (e.g. P ∨ ¬ P). In general, you should avoid introducing tautologies this way, and instead use Fitch to derive the tautologies you need. After all, if you can derive Q from premises P1, …, Pn, then (P1 ∧ … ∧ Pn) → Q is a tautology. Using this tautology to prove Q, however, would miss the point of making a proof that Q does indeed follow from premises P1, …, Pn.
When you do introduce a tautology this way, the script will check whether the formula you provided actually is a tautology. However, this check may fail for formulas that contain certain combinations of universal and existential quantifiers. If this happens, the script will trust your judgment on whether or not the formula is a tautology.
Reiteration repeats a previously derived statement. You can only reiterate statements that are in the same subproof, or a subproof containing the reiteration. Note that you never need to use reiteration, it is simply there to make the proof more readable.
Equality (=) rules
The equality symbol (=) indicates that the left-hand side is the same as the right-hand side. In terms of Fitch proofs, equality is not the same as mathematical equality. From a statement a=b, it does not follow that b=a.
|k||a = a||= Introduction|
Any constant or variable equals itself.
|m||a = b|
|n||P(b)||= Elimination: k, m|
An equality a=b allows any occurence of the left-hand side (a) of the equation to be replaced by the right-hand side (b).
Conjunction (∧) rules
The conjunction symbol (∧) indicates that both the left-hand side and the right-hand side of a statement are true.
|n||P ∧ Q||∧ Introduction: k, m|
For any two derived formulas P and Q, their conjunction P ∧ Q can also be derived.
|k||P ∧ Q|
|m||P||∧ Elimination: k|
Whenever a conjunction P ∧ Q is derived, both the left-hand side (P) and the right-hand side (Q) can also be derived.
Disjunction (∨) rules
The disjunction symbol (∨) indicates that of the left-hand side and the right-hand side of a statement, at least one of them is true (and possible both). Subproofs are needed to eliminate a disjunction: to show that R follows from P ∨ Q, you must show that R follows from assuming P, and that R also follows from assuming Q.
|m||P ∨ Q||∨ Introduction: k|
Any disjunction in which either the left-hand side or the right-hand side is a derived formula can also be derived.
|g||P ∨ Q|
|n||R||∨ Elimination: g, h-j, k-m|
Formula R can be derived from a disjunction P ∨ Q if R follows from assuming the left-hand side (P) of a disjunction, but also from assuming the right-hand side (Q) of the same disjunction.
Negation (¬) rules
The negation symbol (¬) indicates that the underlying statement is not true. Introducing a negation relies on a subproof: if assuming P results in inconsistencies, then ¬P can be derived.
|n||¬ P||¬ Introduction: k-m|
Whenever absurdity can be derived in a subproof, the assumption of that subproof can be derived to be false.
|k||¬ ¬ P|
|m||P||¬ Elimination: k|
A double negation can be eliminated.
Absurdity (⊥) rules
Absurdity (⊥) is the result of two contradicatory statements. From absurdity, any statement can be derived.
|n||⊥||⊥ Introduction: k, m|
Aburdity follows when both a formula and its negation can be derived.
|m||P||⊥ Elimination: k|
Any formula follow froms absurdity.
Implication (→) rules
The implication symbol (→) indicates that whenever the left-hand side can be derived, the right-hand side must also be true.
|n||P → Q||→ Introduction: k-m|
If formula Q can be derived from assuming P, then the corresponding conditional can be derived.
|k||P → Q|
|n||Q||→ Elimination: k, m|
If Q follows from P, and P is derived, then Q can be derived.
Biconditional implication (↔) rules
The biconditional implication symbol (↔) indicates an implication that works both ways. That is, a biconditional implication P ↔ Q means that when P is true, Q can be derived, but also that if Q is true, P can be derived.
|n||P ↔ Q||↔ Introduction: g-h, k-m|
If formula Q follows from assuming P, and P follows from assuming Q, then the corresponding biconditional can be derived.
|k||P ↔ Q|
|n||P||→ Elimination: k, m|
If P can be derived if and only if Q can be derived, then P follows from Q, and Q follows from P.
Universal quantifier (∀) rules
The universal quantifier (∀) indicates that some statement holds for all possible constants. For example, if we know that ∀x P(x) is true and that c is some constant, then P(c) is true. But be careful: a universal quantifier does not imply that a constant actually exists.
|n||∀x P(x)||∀ Introduction: k-m|
If a formula can be derived for a randomly chosen constant, it holds universally.
|m||P(a)||∀ Elimination: k|
If a formula holds universally, it holds for any (existing) constant.
Existential quantifier (∃) rules
The existential quantifier (∃) indicates that a statement holds for at least one constant, though it gives no information about the identity of that constant. For example, if you know that ∃x P(x), this tells you that there is some constant c so that P(c) holds, but it gives no information at all about whether or not for a given constant b, P(b) holds.
|m||∃x P(x)||∃ Introduction: k|
If a formula holds for some constant (a), there exists a constant for which the formula holds.
|m||P(a)||∃ Introduction: k|
If a formula holds for some constant, give that constant a name that has not previously been used.
|Yum Cimil||God of death|
|Ekahau||God of travellers|
|Ahau Kin||Sun god|
|Yum Kaax||Corn god|
1900 — 1912: MXMXI, MCMX, MCMVIII, MCMIV, MCM
1913 — 1919: MCMXIX, MCMXVII, MCMXV, MCMXIV, MCMXIII
1920 — 1945: MCMXLV, MCMXLI, MCMXXXIX, MCMXXXII, MCMXXV
1946 — : MCMXCVII, MCMLXX, MCMLXIX, MCMLX, MCMLI[+]
Read the contents of folder MCMXXXII. Talk to Jeff Akers. 2–1 Take the pin. 3 Leave the station. Pull the rope. Go to Sally McDonald’s home. Walk to the basement. Approach the safe. Use the pin on the hole. Push the round button between the dial and the hole. Dial to 1. Push the button. Dial to 2. Push the button. Dial to 9. Push the button. Dial to 3. Push the button. Dial to 2. Push the button. Use the protective equipment on the journal. Read through the journal. Take the map. Leave the safe. Walk up the stairs. Use the telephone. Call Vivian Whitmore. 1–2–2–2–1–2–3 Leave the house. Walk to the boat. Pull the rope. Go to the Moon Lake State Park Ranger Station. Talk to Jeff Akers. 1–1 Open the envelope. 4 Leave the station. Pull the rope. Go to Sally McDonald’s home. Walk to the house. Walk up the stairs. Sleep until nightfall. Leave the house. Turn right before the docks and continue to Red’s observation tree. Climb up the ladder. Talk to Red Knott. 2–2–2 Climb down the tree. Walk to the house. Walk up the stairs. Sleep until morning. Leave the house. Walk to the boat. Go to the Moon Lake State Park Ranger Station. Talk to Jeff Akers. Open the envelope. Take the key. 4 Leave the station. Pull the rope. Go to Sally McDonald’s home. Walk to the cemetery. Approach the first tombstone on the left. Use the key on the ornament. Move one of the letters. Walk to the house. Use the telephone. Call Vivian Whitmore. 2–4 Leave the house. Walk to the cemetery. Approach the first tombstone on the left. Use the key on the ornament. Use the second letter twice. Use the third letter twice. Use the fourth letter twice. Walk into the passage. Hold the lamp. Walk until the batteries run out. Turn around and walk until you hit the end of the path. Turn left. Pull the lever. Leave the passage. Walk to the boat. Pull the rope. Go to Em’s Emporium. Talk to Emily Griffen. 7–1 Take the paper. Approach the display. Arrange the cans so they resemble the example on the paper. Leave the display. Talk to Emily Griffen. 1 Use the batteries. Take the lamp. Leave the store. Pull the rope. Go to Sally McDonald’s home. Walk to the cemetery. Approach the first tombstone on the left. Use the key on the ornament. Use the second letter twice. Use the third letter twice. Use the fourth letter twice. Walk into the passage. Hold the lamp. Keep turning left until you get to the speakeasy. Approach the picture of Vitus. Approach the picture of Lucy. Approach the picture of Xander. Approach the picture of Iggy. Approach the roulette wheel. Open the top. Push the button. Close the top Leave the roulette wheel. Approach the soda spigots. Pull the red handle. Push the first button. Repeat until the first letter is X. Pull the blue handle. Push the second button. Repeat until the first letter is V. Pull the red handle. Push the yellow button. Repeat until the first letter is I. Pull the green handle. Push the fourth button. Repeat until the first letter is L. Leave the speakeasy through the tunnels. Hold the lamp. Follow the light into the picture tunnel. Approach the picture of Xander. Note the locations of the four dogs on the map. Approach the map between Xander and Lucy. Push the square at row 1, column 7. Push the square at row 3, column 11. Push the square at row 4, column 9. Push the square at row 5, column 7. Close the passage. Turn left. Walk through the upper tunnel. Walk to the kennel. Continue to the workbench. Take Malone’s key. Return to the picture tunnel. Approach the map between Xander and Lucy. Push the square at row 1, column 7. Push the square at row 3, column 11. Push the square at row 4, column 9. Push the square at row 5, column 7. Enter the passage. Approach the door. Use Malone’s key on the lock. Walk through the door. Take the valve wheel. Approach the valves. Turn the wheel. Go to the right. Turn the wheel. Put the valve wheel on the empty spot. Approach the gauge. Use the screwdriver on the hole. Leave the gauge. Turn the left wheel. Approach the gauge. Take the screwdriver. Leave the gauge. Take the valve wheel. Leave the valves. Approach the vault door. Turn the wheel. Open the door. Enter the well. Climb down. Approach the lock. Move the first number once. Move the second number twice. Move the fifth number once. Move the last number once. Note the numbers now read 50, 10, 5 and 1. Put the valve wheel on the pipe. Approach the gold. Walk up the ladder. Enter the vault. Close the door. Open the drain. Enter the drain. Climb up the other end of the sewer. Climb up the ladder.
|This is which card?|
|What card am I thinking about?|
|What card am I looking at?|
|Tell me, what card is this?|
|Which card am I thinking of?|
|What card am I concentrating on?|
|What card is this?|
|Can you tell what card this is?|
|What card am I holding?|
|Do you know what card I’m looking at?|
- Chantilly Hildegardwith the necklace
- Awful Ursula, with the red hair
- Sickly Sara, with one blue and one green eye
- Edna the Terrible, who talks when you pick her up
- Teddy Eberhardt, with his kilt
- Sadie Crawford, with two left feet
- Hagar Anderson, wearing suspenders
- Thomasina O’Neill, who is missing hair
- Yawning Alice, who is sleepy
- Naughty Tina, who is cracked
- Eliza Sandberger, with the red ribbon
Move the first lever on the top row until the hole is open.
Move the second lever on the top row until the hole is half open.
Move the third lever on the top row until the hole is open.
Move the first lever on the bottom row until the hole is half open.
Move the second lever on the bottom row until the hole is closed.
Move the third lever on the bottom row until the hole is open.
Move the far right lever.
Seek, and ye shall find
We represent a search problem as a graph, where each node is a point in the solution. For example, this could be a road map, where different nodes are different cities. But nodes can also represent different actions in a plan. For example, an agent that wants to make a cup of tea can search through his repertoire of actions and find that it should pass through the nodes of “putting on the kettle” and “pouring the hot water” to get to the goal of “enjoying a nice cup of tea”.
In our representation, agents always try to find a path from the start S to the goal G. Every arrow represents a path from one node to another, and can only be travelled in one direction. The number next to each edge shows the cost of taking that path (e.g. the time, effort, or energy consumed by taking the path). When there is no edge connecting two nodes, it is not possible to go from one node to the other directly. However, it may still be possible to go there indirectly.
Below, we describe a number of search algorithms, and show an example of the way this algorithm works in practice. This list of algorithms includes
- depth first search,
- depth limited search,
- iterative deepening search,
- breadth first search,
- uniform cost search,
- greedy best first search, and
- A* search.
Each example consists of the example network and the stack. The stack shows what options the agent can still explore. Whenever a node is put onto the stack (the agent recognizes the possibility of going to that node), the corresponding node in the network turns green. When the node is removed from the stack (the agent has finished considering the option), it turns blue. As soon as the goal node
To compare these search algorithms more directly, you can also view the search algorithm script page, which provides a simultaneous view of the network, the stack, the search tree, and the algorithm.
Depth first search
An agent that uses depth first search is always moving forward. Every time the agent reaches a node, it looks at all the options available from that point and chooses to continue searching in the last direction that the agent has observed. Backtracking to a previous point only happens when the agent reaches a dead end, and is therefore forces to turn back.
One of the main advantages of depth first search is that it requires very little memory. But because of that, depth first search may lead agents to go around in circles. Fortunately, there are no circular paths in the example above. In general, to prevent going around in circles, agents can skip visited nodes. Whenever they see a node for the second time, they ignore the possibility of going there.
Depth limited search
As mentioned above, the disadvantage of depth first search is that you may get stuck in a circular path. One way to overcome this is stop searching after a given number of steps. For example, the agent may restrict itself for paths that visit no more than three nodes. This way, the agent is sure not to get stuck in a circular path for all eternity. The downside, of course, is that if there the path from start to goal visits at least four nodes, the agent cannot find a solution even though it exists.
Iterative deepening search
The disadvantage of depth first search is that you may get stuck in a circular path. Depth limited search solves this partially by putting a limit on the length of the path. Unfortunately, this may lead the agent to be unable to find the solution, because it takes too many steps.
To solve this problem, the agent could simply increase its search limit and try again. This is exactly what iterative deepening search does. Whenever the agent is unable to find a path from start to goal, the agent increases its search depth limit and restarts the search. But the demonstration shows that this solution has its own problems: the agent may be doing the same search over and over again, forgetting what it has learned every time.
Breadth first search
If depth first search is about always moving forward, breadth first search is about not straying too far. An agent that follows breadth first search explores its options in the order it observed these options. Rather than staying on one chosen path, the agent will jump back and forth between options until it finds the solution.
Breadth first search has a huge advantage over depth first search. Because breadth first search means a meticulous search for a path to the goal, it is guaranteed to find such a path if it exists. It will even find the path that takes the fewest number of steps, though this may not be the path with the lowest cost. This advantage comes at a cost of the memory needed to remember all paths that are not yet explored.
Uniform cost search
Uniform cost search is a refinement of breadth first search. Whereas breadth first search always considers the path with the fewest steps first, uniform cost search prefers to consider paths with lower costs. An agent that follows uniform cost search orders its stack of paths to consider based on the length of the path. In the stack view of the example above, the length of the path is listed below the node. Since the agent always looks at the path with the shortest length first, as soon as the agent considers the goal node G, it has found the shortest path from start to goal.
Greedy best first search
Unlike the previous search algorithms, which were all uninformed search, greedy best first search is an informed search algorithm. That is, greedy best first search makes use of information that is not part of the problem description in the form of a heuristic. This heuristic gives an estimate for the cost of reaching the goal from any node. For example, a heuristic on a road map could be the straight-line distance between two cities. This is easier to calculate than the road distance, but still gives the agent some indication of whether it is looking in the right direction. This is the main idea of the heuristic: it should be easy to calculate, but still give information that is relevant to the search.
An agent that follows greedy best first search orders its stack based on the heuristic value, and therefore tries nodes with a low heuristic value first. That is, it first tries those nodes that are expected to be very close to the goal node already, and ignore those paths that go into the wrong direction. However, like depth first search, this can cause the agent to go around in circles. Another disadvantage of greedy best first search is that it needs a heuristic, which may not be easy to get.
Like greedy best first search, A* search is an informed search algorithm that makes use of a heuristic in addition to the problem description. But instead of relying only on the heuristic, A* search also looks at how long the path already is (similar to uniform cost search. That is, A* search makes an estimate of the total length of the path rather than the remaining distance, and orders the stack based on this estimate.
Like uniform cost search, A* search will find the shortest length path, but only if the heuristic follows a simple rule: the heuristic cannot overestimate the cost of actually reaching the goal. That is, the heuristic value for a node cannot be more than the actual cost of reaching the goal from that node. It can, however, be less. In fact, for the special case that the heuristic value is zero for all nodes, A* search is the same as uniform cost search. But for a more informative heuristic, A* search could be a lot more efficient in finding the path with the lowest cost.
> ENTER WELL > WEST > LOOK CAGES > WEST > LOOK PLAQUE > NORTH > NORTH > NORTH > UP > EAST > NORTH > UNLOCK GATE > WEST > SOUTH > ENTER TREE > SOUTH > SOUTH > SOUTH > EAST While Ennio mentions he smells snarlmeat: > WEST > EAST
> EAST > UP > EAST > EAST > EAST > NORTH > NORTH > NORTH > EAST > EAST > EAST > EAST > NORTH > NORTH > EAST > ENTER BOAT > WEST > SOUTH > WEST > NORTH > NORTH > WEST > INSERT CARD > PUSH BUTTON 5 > EAST > LOOK CUFFS > READ LABEL > HIT CUFFS WITH ZAGTONE > WEST > PUSH BUTTON 1 > EAST > SOUTH > ENTER BOAT > SOUTH > WEST > WEST > WEST > GET MUSHROOM > THROW MUSHROOM AT EYE > OPEN GATE > WEST > WEST > WEST > NORTH > SIC ENNIO AT SNARL > GIVE BOOK TO GRAMPS > OPEN JAR > PUSH SNARL IN HOOP