useR GuideuseR GuidetHe deVil'stHe deVil'scAlculAtoRcAlculAtoR

hoW to plAyhoW to plAyIn the In the The Devil's CalculatorThe Devil's CalculatorThe Devil's CalculatorThe Devil's Calculator,,all normal arithmetic operatorsall normal arithmetic operators(addition, multiplication,(addition, multiplication,etc...)etc...) are replaced by a strange are replaced by a strangediamond symbol, "diamond symbol, "◇◇◇◇". This". Thisrepresents an evil mathematicalrepresents an evil mathematicaloperation, a function that doesoperation, a function that doessomething unknown to its input,something unknown to its input,and it becomes more difficult andand it becomes more difficult andobscure each level.obscure each level.

5◇=6◇ is adding one to the input

expressed ◇=f(x)=x+1

You objective is, throughYou objective is, throughinterpolation, to uncover the "interpolation, to uncover the "◇◇""function and then work backwardsfunction and then work backwardsto use it in calculating to use it in calculating 666666666666..Once the number Once the number 666666666666 has been has beencalculated using the calculated using the ◇◇ key, the key, thelevel is won. Think of it likelevel is won. Think of it likethe typical scenario of solvingthe typical scenario of solvingfor x in an algebraic expression,for x in an algebraic expression,but the but the operators themselvesoperators themselvesoperators themselvesoperators themselves

are unknown, rather than aare unknown, rather than aconstant. To add to theconstant. To add to thechallenge, numbers willchallenge, numbers willoccasionally be occasionally be on fireon fireon fireon fire and you and youwill be unable to use them to getwill be unable to use them to getdata on operands or to calculatedata on operands or to calculate666666666666..

opeRAtoRsopeRAtoRsAs you progress in the game, newAs you progress in the game, newmathematical operators aremathematical operators areunlocked. There are three, inunlocked. There are three, intotal. "total. "◇◇◇◇" is a unary operator," is a unary operator,(much like a square root(much like a square root), that), thattakes in one input and returns atakes in one input and returns anumber. "number. "ψψψψ" is a binary" is a binaryoperator, operator, (like addition or(like addition ordivision)division) that takes in two that takes in twoinputs and returns a number.inputs and returns a number.Finally, "Finally, "фффф" is a unary operator" is a unary operatorthat takes an a positive integerthat takes an a positive integeras its input, and returns theas its input, and returns theindex of a mystery integerindex of a mystery integersequence. If "sequence. If "фффф" represents" representsprime numbers, 3prime numbers, 3фф=5 since 5 is=5 since 5 isthe third prime. To conquer thethe third prime. To conquer thegame, you will need to use allgame, you will need to use allthree operators together tothree operators together tocalculate calculate 666666666666. . ""фффф" will always return" will always return

an integer and will only accept an integeran integer and will only accept an integer

as an inputas an input

◇ф(3ψ2)=666◇=x*111 | ψ=x^y | ф=digit of pi

3^2 is 9, 9th digit of pi is 6, 6*111=666

negAtionnegAtionAn early mechanic that deserves aAn early mechanic that deserves amention is negation. If you havemention is negation. If you havethe following expression,the following expression,pressing the pressing the ±±±± button will button willtoggle between four states, wheretoggle between four states, wherethe result of the function isthe result of the function isnegated, the input is negated,negated, the input is negated,and both the input and theand both the input and theresulting function are negated.resulting function are negated.

◇2 -◇2 ◇-2 -◇-2All four are very different

RecursionRecursionAn important mechanic thatAn important mechanic thatbecomes apparent rather early,becomes apparent rather early,(in level 5) is recursion.(in level 5) is recursion.Functions can and will need to beFunctions can and will need to beused many times in succession.used many times in succession.Suppose Suppose ◇◇=a^2. =a^2. ◇◇3 would3 wouldtherefore be 9 and therefore be 9 and ◇◇◇◇3 would be3 would be81, or 81, or ◇◇9. What would 9. What would ◇◇◇◇◇◇3 be?3 be?Parentheses can make it clearer:Parentheses can make it clearer:((◇◇((◇◇((◇◇3))) means the expression3))) means the expressionwould be 6561 or would be 6561 or ◇◇81.81.

◇◇◇◇2if ◇=2a-1:

2(2(2(2*2-1)-1)-1)-1 = 17

pARenthesespARentheses

It is important to remember thatIt is important to remember thatallallallall operators need to be used in operators need to be used inthe service of calculating 666,the service of calculating 666,else the level will not be won.else the level will not be won.There are some levels where it isThere are some levels where it istrivially easy to calculate 666trivially easy to calculate 666with one function, but thewith one function, but thedifficulty comes withdifficulty comes withincorporating another. Anotherincorporating another. Anothertwist is parentheses and order oftwist is parentheses and order ofoperations: operations: ◇◇(3 (3 ψψ 5) is 5) is veryveryveryvery

different from different from ◇◇3 3 ψψ 5. Let's say 5. Let's say◇◇=a+2 =a+2 ψψ=a*b. In the latter=a*b. In the latterexample, the example, the ◇◇ function will function willfirst act on the 3, and itsfirst act on the 3, and itsresult (5) will then be the firstresult (5) will then be the firstinput of the be the input of the be the ψψ function, function,resulting in 5*5=25. In the firstresulting in 5*5=25. In the firstexample, the example, the ψψ would go first, would go first,(3*5=15) and then the (3*5=15) and then the ◇◇ function functionwould act on its result. 15+2=17.would act on its result. 15+2=17.You'll notice there is no buttonYou'll notice there is no buttonfor parentheses - that is becausefor parentheses - that is becausethey are added automaticallythey are added automaticallydepending on the order in whichdepending on the order in which

the operators are added in thethe operators are added in theequation. In keeping with ourequation. In keeping with ourearlier example, if you key in 3earlier example, if you key in 3ψψ 5 and then press the 5 and then press the ◇◇ button, button,it will automatically prepend theit will automatically prepend the◇◇ function and parentheses to the function and parentheses to thebinary expression.binary expression.

◇((5ψ◇7)ψ1)Order of operations:

a=◇7, b=5ψa, c=bψ1, answer=◇c

difficultydifficultyThis game is meant to live up toThis game is meant to live up toits name. Particularly laterits name. Particularly laterlevels can be fiendishlylevels can be fiendishlydifficult. If you find yourselfdifficult. If you find yourselfstruggling, you can always skip astruggling, you can always skip alevel and return later. Consultlevel and return later. Consultthe "help" button often, it hasthe "help" button often, it has

different advice for every leveldifferent advice for every levelin the game. Look to the steamin the game. Look to the steamcommunity or Twitch | YouTubecommunity or Twitch | YouTubelet's plays for guidance, andlet's plays for guidance, andfeel free to reach out onfeel free to reach out ontwitter: twitter: @devilscalc@devilscalc..

GraphingGraphingGraphing can be a valuable assetGraphing can be a valuable assetfor inferring patterns in data.for inferring patterns in data.(There is now support for pan,(There is now support for pan,scan and zoom)scan and zoom). Each of the three. Each of the threeoperators are demarcated byoperators are demarcated bydifferent colors (red, green,different colors (red, green,blue) and their point shapes.blue) and their point shapes.Graphing can sometimes beGraphing can sometimes bedeceptive as many challenges aredeceptive as many challenges arenon-algebraic. Hitting the "p"non-algebraic. Hitting the "p"key will copy your formulakey will copy your formulahistory to the clipboard and ishistory to the clipboard and isformatted as CSV so you can bringformatted as CSV so you can bringit into your favorite spreadsheetit into your favorite spreadsheet

application and customize yourapplication and customize yourgraphs / line fit.graphs / line fit.

Graphing can offer important insights

wolfrAM AlphAwolfrAM AlphAWolfram is deeply integratedWolfram is deeply integratedwithin the game. To query wolframwithin the game. To query wolframalpha, go to the "notes" menu,alpha, go to the "notes" menu,and tap the 'wolfram' button toand tap the 'wolfram' button toinput a search. As the game isinput a search. As the game ismore logic based, you are notmore logic based, you are not

expected to do algebraexpected to do algebra(particularly multivariate(particularly multivariatealgebra) and using Wolfram Alphaalgebra) and using Wolfram Alphawith the flag "over the integers"with the flag "over the integers"can save enormous amounts ofcan save enormous amounts oftime. If you determine that time. If you determine that ψψ==(a+5)/b, then you can type (a+5)/b, then you can type ""(a+5)/b=666 over the integers"(a+5)/b=666 over the integers"and wolfram will list integerand wolfram will list integerpairs. This is also helpful forpairs. This is also helpful forrecursive functions: if recursive functions: if ◇◇=3a+5,=3a+5,you can test if there is anyou can test if there is aninteger answer for integer answer for ◇◇◇◇X=666 byX=666 bytyping in typing in "3*(3a+5)+5=666 over"3*(3a+5)+5=666 overthe integers."the integers." You can also enter You can also enterthe field blank, to upload yourthe field blank, to upload yournotes for Natural Languagenotes for Natural LanguageProcessing.Processing.

The over the integers flag is a lifesaver

if you suspect your answer is an integer

Holding down the screen in theHolding down the screen in the"help" or "hint" menu will open"help" or "hint" menu will openup unique links to Wolframup unique links to WolframMathWorld to point you in theMathWorld to point you in theright direction on the puzzle.right direction on the puzzle.Holding down the graph screenHolding down the graph screenwill open a scatterplot of yourwill open a scatterplot of yourcurrent data on wolfram alpha.current data on wolfram alpha.Holding down the screen in theHolding down the screen in the"notes" menu will open wolfram"notes" menu will open wolframnotebooks for you to betternotebooks for you to betterorganize your strategies with theorganize your strategies with thelevel. Created levels will soonlevel. Created levels will soonsupport links to Wolfram cloudsupport links to Wolfram cloudAPI functions. A helpful trickAPI functions. A helpful trickwith the "over the integers" flagwith the "over the integers" flagis the following:is the following:Floor(a*100)/100=666Floor(a*100)/100=666Floor(a*100)/100=666Floor(a*100)/100=666 over the over theintegers will provide answers upintegers will provide answers upto two decimal points.to two decimal points.

Wolfram MathWorld is a mathematical

encyclopedia that has entries for

virtually every type of puzzle in the

game

otheR toolsotheR toolsPlayers can access a scientificPlayers can access a scientificcalculator provided by calculator provided by DesmosDesmoseither by going into the "notes"either by going into the "notes"menu or holding the screen down.menu or holding the screen down.This is important since you areThis is important since you arenot expected to do computationsnot expected to do computationsmanually. A link to OEIS becomesmanually. A link to OEIS becomes

available once its operator isavailable once its operator isunlocked, and consulting itsunlocked, and consulting itsdatabase is recommended fordatabase is recommended fordeciphering the logic behind adeciphering the logic behind alevel.level.

xkcd is the best

MeMoRy keysMeMoRy keysMemory keys are an important toolMemory keys are an important tooland their utility may not beand their utility may not be

immediately obvious. In additionimmediately obvious. In additionto being able to keep specificto being able to keep specificcalculations handy if needed,calculations handy if needed,their real usefulness is in statetheir real usefulness is in statemanagement. Once you unlockmanagement. Once you unlockmultiple operators, you'll needmultiple operators, you'll needto use all three together toto use all three together tocalculate 666. You cancalculate 666. You cancompartmentalize this task usingcompartmentalize this task usingmemory keys, since saving amemory keys, since saving acalculation to a memory key savescalculation to a memory key savesthe operators used in thatthe operators used in thatcalculation (why the buttonscalculation (why the buttonslight up). This way you can avoidlight up). This way you can avoidhaving to build a long equationhaving to build a long equationfrom scratch and instead buildfrom scratch and instead buildupon work you've saved over theupon work you've saved over thecourse of the level.course of the level.

◇5=74 → M1 :

M1ψ9=666You can save the result 74 along with the ◇

state for easy recall

dlc | onlinedlc | onlineModeMode

In the "graph" menu, there is theIn the "graph" menu, there is the"levels" button. This allows you"levels" button. This allows youto replay levels from the regularto replay levels from the regulargame and to check if there is newgame and to check if there is newDLC. The next DLC willDLC. The next DLC willautomatically load when pressed.automatically load when pressed.You may skip the level and returnYou may skip the level and returnto it anytime using the replayto it anytime using the replaymenu. if there are no new DLCmenu. if there are no new DLClevels, you have the option oflevels, you have the option ofplaying community challenges evenplaying community challenges evenif you have not yet beaten theif you have not yet beaten thegame, though this is discouraged,game, though this is discouraged,as the concepts introduced lateras the concepts introduced laterin the game may be necessary forin the game may be necessary forsuccess.success.

DLC levels can prove even more

challenging than the regular game.

level cReAtelevel cReAteAnyone can suggest levels for DLCAnyone can suggest levels for DLCinclusion inclusion herehere, but from within, but from withinthe game, you can build andthe game, you can build andupload levels without moderation.upload levels without moderation.Click "graph" -> "levels" ->Click "graph" -> "levels" ->"create" and you will be prompted"create" and you will be promptedfor a username. Once inputted,for a username. Once inputted,

you can design levels usingyou can design levels usingmath.jsmath.js between ternary between ternary ififififconditions. "a" is always theconditions. "a" is always thefirst input of a function, andfirst input of a function, and"b" if there is a second."b" if there is a second.

a%2 ? a/2 : a+3will divide by 2 when the input is

odd and add 3 when even

Everything between ternaryEverything between ternaryoperators will be fed intooperators will be fed intomath.evalmath.eval, which supports simple, which supports simpleexpressions and advancedexpressions and advancedfunctionality. For questions,functionality. For questions,contact us on twitter:contact us on twitter:@devilscalc@devilscalc, or submit a level, or submit a levelvia our via our online formonline form and we can and we cancode it for you.code it for you.

a==b ? a*b : a/bwill multiply both inputs together

when they are the same, and divide them when

different

Integer sequence functions can beInteger sequence functions can begenerated with a manual series orgenerated with a manual series orarray of numbers array of numbers i.e.i.e.'[0,1,1,2,3,5,8,13,21,34][a]''[0,1,1,2,3,5,8,13,21,34][a]'would be the start of Fibonacci,would be the start of Fibonacci,or you can compute themor you can compute themdynamically:"dynamically:"

string(pi)[a]will return the (a)th digit of pi

AdVAncedAdVAncedtRickstRicks

ΔΔ: a,j,[ψψ: s,k,]φφ: d,l,\\Equals: Enter, =

Hold Hold '+/-''+/-''+/-''+/-' or type or type '_''_''_''_' on ondesktop to mute sound effects. Ondesktop to mute sound effects. Onmobile, enter mobile, enter '.0900''.0900''.0900''.0900' followed followedby equals to supress haptics.by equals to supress haptics.Enter Enter '.000''.000''.000''.000' followed by equals followed by equalsto clear online level data. Typeto clear online level data. Type'.00000''.00000''.00000''.00000' followed by equals to followed by equals toreset your game data (purchasereset your game data (purchasehistory will remain).history will remain).

You can jump quickly from levelYou can jump quickly from levelto level by entering a period,to level by entering a period,followed by the level number,followed by the level number,another period, and then hittinganother period, and then hittingequals. i.e. equals. i.e. '.XX.''.XX.''.XX.''.XX.' will take will takeyou to level XX. To skip theyou to level XX. To skip theentire game and go directly toentire game and go directly tothe postgame, you can enterthe postgame, you can enter.4973..4973..4973..4973. followed by equals. For followed by equals. Fordesktop, a list of keyboarddesktop, a list of keyboardshortcuts is below:shortcuts is below:

Clear: backsp,esc, c

AC: Delete, shift+C

Calc: #

help: right arrow

notes:left arrow

Wolfram: w , OEIS: o

MR1: shift+1

MR2: shift+2

MR3: shift+3

MS1: alt+1

MS2: alt+2

MS3: alt+3

SFX/Mute: _

graph: up/dn arrow

Server Sync: *

CopyClip: p

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