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TableofContents
TitlesinTheIQWorkoutSeries
TitlePage
CopyrightPage
Introduction
Section1-Puzzles,tricksandtests
Chapter1-Theworkout
Chapter2-Thinklaterally
Chapter3-TestyournumericalIQ
Chapter4-Funumeration
Chapter5-Thinklogically
Chapter6-Thelogicofgamblingandprobability
Chapter7-Geometricalpuzzles
Chapter8-Complexitiesandcuriosities
Section2-Hints,answersandexplanations
Hints
Chapter1
Chapter2
Chapter4
Chapter5
Chapter6
Chapter7
Chapter8
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Answersandexplanations
Chapter1
Chapter2
Chapter3
Chapter4
Chapter5
Chapter6
Chapter7
Chapter8
Glossaryanddata
Glossary
Algebra
Aliquotpart
Arabicsystem
Area
Arithmetic
Automorphicnumber
Binary
Cubenumber
Decimalsystem
Degree
Dodecahedron
Duodecimal
Equality
Equation
Factorial
Fibonaccisequence
Geometry
Heptagonalnumbers
Hexagonalnumbers
Hexominoes
Hexadecimal
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Icosahedron
Magicsquare
Mersennenumbers
Naturalnumbers
Octagonalnumbers
Palindromicnumbers
Parallelogram
Pentagonalnumbers
Percentage
Perfectnumber
Pi
Polygon
Primenumber
Product
Pyramidalnumbers
Quotient
Rationalnumbers
Reciprocal
Rectangle
Rhombus
Sexadecimal
Siderealyear
Solaryear
Squarenumber
Sum
Tetrahedral
Topology
Triangularnumbers
Data
Section4Appendices
Appendix1-Fibonacciandnature’suseofspace
TheFibonacciseries
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Nature’suseofspace
Appendix2-Pi
Appendix3-TopologyandtheMobiusstrip
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TitlesinTheIQWorkoutSeries
IncreaseYourBrainpower:Improveyourcreativity,memory,mentalagilityand
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Psychometric Testing: 1000 ways to assess your personality, creativity,
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Copyright©2004byPhilipCarterandKenRussell
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Introduction
I’mverywellacquaintedtoowithmattersmathematical,
Iunderstandequations,boththesimpleandquadratical.
W.S.Gilbert
Bertrand Russell oncesaid that ‘Mathematicsmaybedefined asthesubjectin
which we never know what we are talking about, nor whether what we are
sayingistrue’.
The subject of mathematics can be challenging, fascinating, confusing and
frustrating,butonceyouhavedevelopedaninterestinthescienceofnumbers,a
whole new world is opened up as you discover their many characteristics and
patterns.
Weallrequiresomenumericalskillsinourlives,whetheritistocalculateour
weeklyshoppingbillortobudgethowtouseourmonthlyincome,butformany
people mathematics is a subject they regard as being too difficult when
confrontedbywhatareconsideredtobeitshigherbranches.Whenbrokendown
andanalysed,andexplainedinlayman’sterms,however,manyoftheseaspects
can be readily understood by those of us with only a rudimentary grasp of the
subject.
Thebasicpurposeofthisbookistobuildupreaders’confidencewithmaths
by means of a series of tests and puzzles, which become progressively more
difficult over the course of the book, starting with the gentle ‘Work out’ of
Chapter1tothecollectionof‘Complexitiesandcuriosities’ofChapter8.There
isalsotheopportunity,inChapter3,forreaderstotesttheirnumericalIQ.For
many of the puzzles throughout the book, hints towards finding a solution are
provided, and in all cases the answers come complete with full detailed
explanations.
Manyoftheproblemsinthisbookarechallenging,butdeliberatelyso,asthe
moreyoupractiseonthistypeofpuzzle,themoreyouwillcometounderstand
the methodology and thought processes necessary to solve them and the more
proficient you will become at arriving at the correct solution. Of equal
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importance,wesetouttoshowthatdealingwithnumberscanbegreatfun,and
to obtain an understanding of the various aspects of mathematics in an
entertainingandinformativewaycanbeanupliftingexperience.
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Section1
Puzzles,tricksandtests
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Chapter1
Theworkout
Allintellectualimprovementarisesfromleisure.
SamuelJohnson
Everyworkout,beitphysicalormental,involvesalimberingupsession.
Thepuzzlesinthischapteraresuchalimberingupsession.Theyhavebeen
specially selected to get you to think numerically and to increase your
confidence when working with numbers or faced with a situation in which a
mathematicalcalculationisrequired,and,likeallthepuzzlesinthisbook,they
aretheretoamuseandentertain.
Whenlookingatapuzzle,theanswermayhityouimmediately.Ifnot,your
mind must work harder at exploring the options. Mathematics is an exact
science, and there is only one correct solution to a correctly set question or
puzzle; however, there may be different methods of arriving at that solution,
somemorelaboriousthanothers.
As you work through this first chapter you will find that there are many
differentwaysoftacklingthistypeofpuzzleandarrivingatasolution,whether
itbebylogicalanalysisorbyintelligenttrialanderror.
1.Twogolferswerediscussingwhatmighthavebeenaftertheyhadplayed
apar5.
Harry said ‘if I had taken one shot less and you had taken one shot
more,wewouldhavesharedthehole’.
Geoffthencounteredbysaying‘yes,andifIhadtakenoneshotless
andyouhadtakenoneshotmoreyouwouldhavetakentwiceasmany
shotsasme’.
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Howmanyshotsdideachtake?
2.Anumberbetween1and50meetsthefollowingcriteria:
itisdivisibleby3
whenthedigitsareaddedtogetherthetotalisbetween4and8
itisanoddnumber
whenthedigitsaremultipliedtogetherthetotalisbetween4and
8.
Whatisthenumber?
3.Onarrivingatthepartythesixguestsallsay‘Hello’toeachotheronce.
On leaving the party the six guests all shake hands with each other
once.
Howmanyhandshakesisthatintotal,andhowmany‘Hello’s?
4.Whattwonumbersmultipliedtogetherequal13?
5.Workingatthestablethereareanumberofladsandlasseslookingafter
thehorses.Inallthereare22headsand72feet,includingalltheladsand
lassesplusthehorses.
Ifalltheladsandlassesandallthehorsesaresoundinbodyandlimb,
howmanyhumansandhowmanyhorsesareinthestable?
6.Howmanyboxesmeasuring1m×1m×50cmcanbepackedintoa
containermeasuring6m×5m×4m?
7.Bywhatfractionalpartdoesfour-quartersexceedthree-quarters?
8.
Whatweightshouldbeplacedonxinordertobalancethescale?
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9.Myhousenumberisthelowestnumberonthestreetthat,whendivided
by2,3,4,5or6,willalwaysleavearemainderof1.
However,whendividedby11thereisnoremainder.
Whatismyhousenumber?
10.Mybrotherislessthan70yearsold.
Thenumberofhisageisequaltofivetimesthesumofitsdigits.In9
yearstimetheorderofthedigitsofhisagenowwillbereversed.
Howoldismybrothernow?
11.AgreengrocerreceivedaboxfulofBrusselssproutsandwasfurious
uponopeningtheboxtofindthatseveralhadgonebad.
He then counted them up so that he could make a formal complaint
andfoundthat114werebad,whichwas8percentofthetotalcontents
ofthebox.
Howmanysproutswereinthebox?
12.Ifsevenmencanbuildahousein15days,howlongwillittake12men
tobuildahouseassumingallmenworkatthesamerate?
13.Attheendofthedayonemarketstallhaseightorangesand24apples
left.Anothermarketstallhas18orangesand12applesleft.
Whatisthedifferencebetweenthepercentagesoforangesleftineach
marketstall?
14.PeteristwiceasoldasPaulwaswhenPeterwasasoldasPaulisnow.
ThecombinedagesofPeterandPaulis56years.
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HowoldarePeterandPaulnow?
Thenexttwopuzzlesareofaverysimilarnature.
15.Abagofpotatoesweighs25kgdividedbyaquarterofitsweight.How
muchdoesthebagofpotatoesweigh?
16.Onebagofpotatoesweighed60kgplusone-quarterofitsownweight
andtheotherbagweighed64kgplusone-fifthofitsownweight.Which
istheheavierbag?
17.
An area of land, consisting of the sums of the two squares, is 1000
squaremetres.
Thesideofonesquareis10metreslessthantwo-thirdsofthesideof
theothersquare.
Whatarethesidesofthetwosquares?
18.Findfournumbers,thesumofwhichis45,sothatif2isaddedtothe
firstnumber,2issubtractedfromthesecondnumber,thethirdnumberis
multipliedby2andthefourthnumberisdividedby2,thefournumbers
soproduced,i.e.thetotaloftheaddition,theremainderofthe
subtraction,theproductofthemultiplicationandthequotientofthe
division,areallthesame.
19.JackgaveJillasmanysweetsasJillhadstartedoutwith.Jillthengave
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JackbackasmanyasJackhadleft.JackthengaveJillbackasmanyas
Jillhadleft.ThefinalexchangemeantthatpoorJackhadnoneleft,and
Jillhad80.
HowmanysweetseachdidJackandJillstartoutwith?
Thereisahinttosolvingthispuzzleonpage52.
20.BrianandRyanarebrothers.ThreeyearsagoBrianwasseventimesas
oldasRyan.Twoyearsagohewasfourtimesasold.Lastyearhewas
threetimesasoldandintwoyearstimehewillbetwiceasold.
HowoldareBrianandRyannow?
21.SumsarenotsetasatestonErasmus
PalindromeshavealwaysfascinatedHannah.Herboyfriend’snameis
Bob,shelivesaloneathercottageinthecountrynamedLonelyTylenol,
anddrivesherbelovedcar,whichisaToyota.
A few days ago Hannah was driving along the motorway when she
glancedatthemileageindicatorandhappenedtonoticethatitdisplayed
apalindromicnumber;13931.
Hannah continued driving and two hours later again glanced at the
odometer,andtohersurpriseitagaindisplayedanotherpalindrome.
What average speed was Hannah travelling, assuming her average
speedwaslessthan70mph?
22.Theaverageofthreenumbersis17.Theaverageoftwoofthese
numbersis25.Whatisthethirdnumber?
23.Youhave62cubicblocks.Whatistheminimumnumberthatneedsto
betakenawayinordertoconstructasolidcubewithnoneleftover?
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24.Iboughttwowatches,anexpensiveoneandacheapone.Theexpensive
onecost£200morethanthecheaponeandaltogetherIspent£220for
both.HowmuchdidIpayforthecheapwatch?
25.If
6applesand4bananascost78pence
and7applesand9bananascost130pence
whatisthecostofoneappleandwhatisthecostofonebanana?
26.Thecostofathree-courselunchwas£14.00.
Themaincoursecosttwiceasmuchasthesweet,andthesweetcost
twiceasmuchasthestarter.
Howmuchdidthemaincoursecost?
27.Mywatchwascorrectatmidnight,afterwhichitbegantolose12
minutesperhour,until7hoursagoitstoppedcompletely.Itnowshows
thetimeas3.12.
Whatisnowthecorrecttime?
28.Aphotographmeasuring7.5cmby6.5cmistobeenlarged.
Iftheenlargementofthelongestsideis18cm,whatisthelengthof
thesmallerside?
29.Astatueisbeingcarvedbyasculptor.Theoriginalpieceofmarble
weighs140lb.Onthefirstweek35%iscutaway.Onthesecondweek
thesculptorchipsoff26lbandonthethirdweekhechipsofftwo-fifths
oftheremainder,whichcompletesthestatue.
Whatistheweightofthefinalstatue?
30.Theagesoffivefamilymemberstotal65betweenthem.
AliceandBilltotal32betweenthem
BillandClaratotal33betweenthem
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ClaraandDonaldtotal28betweenthem
DonaldandElsietotal7betweenthem.
Howoldiseachfamilymember?
31.FiveyearsagoIwasfivetimesasoldasmyeldestson.TodayIam
threetimeshisage.
HowoldamInow?
32.Atmyfavouritestoretheyareofferingadiscountof5%ifyoubuyin
cash(whichIdo),10%foralong-standingcustomer(whichIam)and
20%atsaletime(whichitis).
InwhichordershouldIclaim thethreediscountsin ordertopaythe
leastmoney?
33.Addyoutome,dividebythree,
Thesquareofyou,you’llsurelysee,
Butmetoyouiseighttoone,
Onedayyou’llworkitoutmyson.
34.Intwominutestimeitwillbetwiceasmanyminutesbefore1pmasit
waspast12noon25minutesago.
Whattimeisitnow?
35.Findthelowestnumberthathasaremainderof
1whendividedby2
2whendividedby3
3whendividedby4
4whendividedby5
and5whendividedby6.
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36.
There are 11 stations on line AB. How many different single tickets
mustbeprintedtocaterforeverypossiblebookingfromanyoneofthe
11stationstoanyother?
37.Inagameofeightplayerslastingfor45minutes,fourreservesalternate
equallywitheachplayer.Thismeansthatallplayers,includingthe
reserves,areonthepitchforthesamelengthoftime.
Forhowlong?
38.Between75and110guestsattendedabanquetattheTownHalland
paidatotalof£3895.00.Eachpersonpaidthesameamount,whichwas
anexactnumberofpounds.Howmanyguestsattendedthebanquet?
39.MysistersAprilandJuneeachhavefivechildren,twinsandtriplets.
April’stwinsareolderthanhertripletsandJune’stripletsareolderthan
hertwins.
WhenIsawAprilrecently, sheremarkedthatthesumoftheagesof
herchildrenwasequaltotheproductoftheirages.LaterthatdayIsaw
June,andshehappenedtosaythesameaboutherchildren.
Howoldaremysisters’children?
40.Thedifferencebetweentheagesoftwoofmythreegrandchildrenis3.
Myeldestgrandchildisthreetimesolderthantheageofmyyoungest
grandchild, and my eldest grandchild’s age is also two years more than
theagesofmytwoyoungestgrandchildrenaddedtogether.
Howoldaremythreegrandchildren?
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41.Atraintravellingataspeedof50mphentersatunnel2mileslong.The
lengthofthetrainis mile.Howlongdoesittakeforallofthetrainto
passthroughthetunnelfromthemomentthefrontenterstothemoment
therearemerges?
Thereisahinttothispuzzleonpage52.
42.Howmanyminutesisitbefore12noonif28minutesagoitwasthree
timesasmanyminutespast10am?
43.ThehighestspireinGreatBritainisthatofthechurchofStMary,called
SalisburyCathedral,inWiltshire,England.Thecathedralwascompleted
andconsecratedin1258;thespirewasaddedfrom1334to1365and
reachesaheightof202feet,plushalfitsownheight.
HowtallisthespireofSalisburyCathedral?
44.Amanufacturerproduceswidgets,butnottoaveryhighstandard.
Inatestbatchof16,fiveweredefective.
Thentheycarriedoutalongerproductionrun,inwhich25of81were
defective.
Hadtheyimprovedtheirqualitycontrolperformanceafterthetestrun?
45.Aballisdroppedtothegroundfromaheightof12feet.Itfallstothe
groundthenbouncesuphalfofitsoriginalheight,thenfallstothe
groundagain.Itrepeatsthis,alwaysbouncingbackuphalfofthe
previousheight.
Howfarhastheballtravelledbythetimeitreturnstothegroundfor
thefifthtime?
46.Inaraceoffivegreyhounds,redjacket,blue,black,stripedandwhite,
inhowmanydifferentwaysisitpossibleforthefivedogstopassthe
winningpost?Forexample:black,red,white,striped,bluewouldbeone
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way.
47.Amanisplayingontheslotmachinesandstartswithamodestamount
ofmoneyinhispocket.Inthefirst5minuteshegetsluckyanddoubles
theamountofmoneyhestartedwith,butinthesecond5minuteshe
loses£2.00.
In the third 5 minutes he again doubles the amount of money he has
left,butthenquicklylosesanother£2.00.Hethengetsluckyagainand
doublestheamountofmoneyhehasleftforthethirdtime,afterwhich
hehitsanotherlosingstreakandlosesanother£2.00.
Hethenfindshehasnomoneyleft.
Howmuchdidhestartwith?
Thereisahinttothispuzzleonpage52.
48.Bypermittingjusttwoofthethreemathematicalsigns(+,-,×)andone
othermathematicalsymbol,plusbrackets,canyouarrangethreefoursto
equal100?
Thereisahinttothispuzzleonpage52.
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