Logic Games Flashcards
Each of exactly five radio stations - F, J, K, L and M - plays one or more of the following four types of music: new age, oldies, rock and soul. None of the stations plays any other type of music. The following conditions apply:
F plays more types of music than any other station
K plays new age and oldies but no other type of music
Exactly three of the five stations play rock
L doesn’t play new age or rock
M plays more types of music than K
Five commuters - L, M, N, O and P - each take exactly one of two trains to work: the Highbrook or the Sullivan train. These commuters take no other train to work and the following conditions apply:
If O takes the Sullivan train then M takes the Highbrook train
If P takes the Highbrook train then L takes the Sullivan train and N takes the Highbrook train
M and L cannot take the same train
a) What do we know is P takes the Highbrook train?
b) What do we know if M takes the Sullivan train?
I will not go jogging if it is raining outside
R → /J/
J → /R/
Neither X nor Y is chosen if Z is chosen
Z → /X/
X → /Z/
Z → /Y/
Y → /Z/
A filmmaker will choose exactly five songs to use in a film project. Of the nine songs that she will choose from, three songs - F, G and H - were written in the 1960’s, three songs - J, K and M - were written in the 1970’s and three - O, P and Q - were written in the 1980’s. The following conditions apply:
Exactly two songs from the 1980’s are selected for the project
G and J cannot both be selected
H and O cannot both be selected
If Q is selected both G and H are selected
Everyone must have exactly one numbered locker (1-100)
X and W cannot both have odd numbered lockers
Neither Y nor Z can be odd if W is odd
L is selected if and only if M is also selected
L → M
/M/ → /L/
M → L
/L/ → /M/
If H is in, then G is in
Six kindergarten students - R, S, T, V, X and Y - will be assigned to one of two teachers: Mr Paulson or Mrs Henson. None of these six students will be assigned to any other teacher and the following conditions apply:
If S is assigned to Mrs Henson then V is assigned to Mr Paulson
If X is assigned to Mr Paulson then T is assigned to Mr Paulson
If R is assigned to Mrs Henson then so is V
a) What do we know if S is assigned to Mrs Henson?
b) What do we know if V is assigned to Mr Paulson?
c) What do we know if both V and X are assigned to Mr Paulson?
K is produced at some point after N but before O
Both L and J are produced at some time before N
M is produced at some time after P
R is produced at some time before O
J is produced at some time before M
P > M
J \
L - N - K - O
R /
Both T and V call at some time before M
N calls at some time after R
O calls at some time before N but after M
P calls at some time before M
T calls at some time before S
V \
P - M - O - N
T / R /
\ S
Both S and Y finish at some time before R
T finishes at some time after X
S finishes at some time after W but before V
X finsihes later than S
Y finsihes later than W
/ Y > R
W - S - V
\ X
If N occupies the third positionm, what is the earliest position that M could occupy?
5th
If M or G is selected then H must be selected
M → H
/H/ → /M/
G → H
/H/ → /G/
If Brooks is not on the bus, Traiger is not on the bus
/B/ → /T/
T → B
At Riverside high school, six athletes - Mit, Nathan, Paula, Raul, Victoria and Yolanda - were chosen as athletes of the year. Each plays one or more of the following: hockey, soccer, tennis. None of the athletes plays any other sport. The following must be true:
Nathan plays exactly two sports
Yolanda plays more of the sports than Victoria
Raul and exactly three other students play hockey
Victoria plays both soccer and tennis
Mit doesn’t play any sport that Victoria plays
Paula doesn’t play any sport that Mit plays
J and K can’t both be selected
J → /K/
K → /J/
What is the earliest position T could occupy?
4th
If Q is in then V is in but P is not
If V is in then P or R is in
If Beethoven is played, then Mozart is played
B → M
/M/ → /B/
If J occupies third position, what are the possible positions N could occupy?
4th, 5th, 6th, 7th
W and X cannot both be selected
W → /X/
X → /W/
If X is selected, then Y is selected
X → Y
/Y/ → /X/
YourHome Realty has exactly five condos on the market: P, Q, S, T and V. Each has at least one of the following three features: fireplaces, hardwood floors, modern appliances. The condos have no other features. The following conditions apply:
Q has fewer features than S
P and T have exactly one feature in common
Both Q and V have hardwood floors
P has more features than any other condo
If the tiger is not in the cage, then the lion is in the cage
/T/ → L
/L/ → T
S cannot be out unless T is in
If R is in then S is in
The characters Z and W must be played by actors of different genders
If M is selected then G of H is selected
M → G or H
/G/ and /H/ → /M/
Of the eight letters, which ones could occupy the first position?
L, J, P, R
At a conference, exactly six presentations - F, G, H, J, K and M - are given over the course of six consecutive days. Each is given exactly once and no two presentations are given on the same day. The following conditions apply:
H is presented either on the day immediately before the day on which K is presented
F is presented on day 3
G is presented on a day numbered lower that the day on which J is presented
Martinez isn’t chosen unless Jones is chosen
M → J
/J/ → /M/
T is not selected unless R is selected
T → R
/R/ → /T/
X plays volleyball only if Y plays squash
Of the seven letters, which ones could occupy the first position?
O, L
One evening a television station broadcasts exactly six programs - M, N, O, P, R and S. No two programs are braodcast simultaneously and no other programs are broadcast. Each program is either 30 or 60 minutes in length. The following must be true:
N is 60 minutes in length
The broadcast of S immediately precedes the broadcast of O
Each 30 minute program is immediately followed by a 60 minute program
P is broadcast at some time before O
A 30 minute program is broadcast fourth
Of the eight letters, which ones could occupy the first position?
T, P, V, R
FRAMES
At a conference, exactly six presentations - F, G, H, J, K and M - are given over the course of six consecutive days 1-6. Each is given exactly once and no tow presentations are given on the same day. The following conditions apply:
H and K are presented on consecutive days
F is presented on day 3
G is presented on a day numbered lower than the day on which J is presented
Good Candidate for frames - there are only six slots, F is fixed in position 3 and there is a chunk (HK or KH),
3 Frames
H/K K/H F _ _ _
_ _ F H/K K/H _
_ _ F _ H/K K/H
What is the latest position that O could occupy?
5th
Eactly eight artists - O, S, P, R, T, V, W and Y - enter an art competition. The competition judges rank the artists from 1-8. There are no ties and the rankings conform to the following:
Either P or W is ranked fourth
R is ranked either first or eighth
Y receives a ranking that is numbered two lower than that of O
T is not ranked fifth
Setting up frames not worth it - is an 8-slot setup meaning there will be many possibilities. While slot 4 is fixed there are two possibilities P or W which will double the number of possibilities. While R is limited, there are two possibilities for R. The chunk Y_O can be placed in a number of positions: 1_3, 3_5, 5_7 and 6_8
Of the eight letters, which ones could occupy eighth position?
N, S
A filmmaker will choose exactly five songs to use in a film project. Of the nine songs that she will choose from, three songs - F, G and H - were written in the 1960’s, three songs - J, K and M - were written in the 1970’s and three - O, P and Q - were written in the 1980’s.
The following conditions apply: Exactly two songs from the 1980’s are selected for the project, G and J cannot both be selected, H and O cannot both be selected, If Q is selected both G and H are selected
INFERENCES: MUTUALLY EXCLUSIVE PAIRS
O and H
O and Q - since two 1980’s songs must be chosen, P must be chosen
Of the seven letters, which ones could occupy the last position?
M, N, P, S
If V is in, then both P and Q are out
If both P and Q are selected, then R is selected
P and Q → R
/R/ → /P/ and/or /Q/
A filmmaker will choose exactly five songs to use in a film project. Of the nine songs that she will choose from, three songs - F, G and H - were written in the 1960’s, three songs - J, K and M - were written in the 1970’s and three - O, P and Q - were written in the 1980’s.
The following conditions apply: Exactly two songs from the 1980’s are selected for the project, G and J cannot both be selected, H and O cannot both be selected, If Q is selected both G and H are selected
INFERENCES: NUMBER DISTRIBUTIONS
80’s: 2, 60’s: 3, 70’s:0 → N selected → O not selected → P and Q selected
80’s:2. 60’s: 0, 70’s: 3
80’s: 2, 60’s: 2, 70’s: 1
80’s:2, 60’s: 1, 70’s: 2
(Y/N/M)
Does T come somewhere before R?
Maybe
V is selected if and only if P is selected
P → V
/V/ → /P/
V → P
/P/ → /V/
How many letters must come before O?
5
Four candidates - P, Q, R and S - interview for jobs. No other candidates are interviewed and each candidate interviewed is either hired or not. The following conditions apply:
P cannot be hired unless S is also hired
If R is hired then both Q and P are hired
a) what do we know if R is hired?
b) what do we know if R is not hired?
(Y/N/M)
Does K come somewhere before J?
No
If M is selected, both G and H must be selected
M → G
/G/ → /M/
M→H
/H/ → /M/
(Y/N/M)
Does V come somewhere before O?
Yes
If H is selected then J is selected but G is not
H → J
/J/ → /H/
H → /G/
G → /H/
Rolfson and Strapini can’t both be selected
R → /S/
S → /R/
If F and N are selected will not be
If O is selected, P and S will not be
If Raul is invited then Shauna is not invited
R → /S/
S → /R/
Exactly six items - F, G, H, J, K and L - are sold at a yard sale. They are sold one at a time and consecutively and each item is sold either for $10 or $20. The following rules govern the sale of the items:
J is sold either first or sixth
No two $10 itmes are sold consecutively
The item sold third is sold for $20
L is sold for $20
Jenny’s Juice will have a sale on at least one of the following five kinds of juice: graoe, mango, orange, pineapple and tomato. No other juices will be included in the sale. The following rules apply:
If mango juice is included in the sale, then grape juice is also included but tomato juice is not
Pineapple juice is not included in the sale unless orange juice is included
If grape juice is included then orange juice is also included
a) What do we know if mango juice is on sale?
b) What do we know if grape juice is not on sale?
c) What do we know if one and only one of either mano=go or grape juice is on sale?
Of the eight letters, which ones could occupy the eighth position?
O, M
Exactly eight artists - Osman, Park, Rainer, Samanski, Trung, Villanueva, Wallis and Yang - enter an art competition. The competition judges rank the artists from one to eight. There are no ties and the rankings conform to the following:
Either Park or Wallis is ranked fourth
Rainer is ranked either first or eighth
Yang receives a ranking that is numbered two lower that that of Osman
Trung is not ranked fifth
(Y/N/M)
Does M come somewhere before R?
Maybe
If K is selected then neither M nor N is selected
K → /M/
M → /K/
K → /N/
N → /K/
How many letters must come before J?
1
What is the latest position S could occupy?
3rd
If Y occupies the second position and V occupies the fourth position, what are the different possibilities are there for ordering the seven letters?
WYSVRXT
WYSVXRT
WYSVXTR
X plays earlier than W but later than T
Y plays later than Z
Z plays earlier than X
T - X - W
Z /
\ Y
F cannot be selected unless H is also selected
F → H
/H/ → /F/
H and J both speak at some time before N
K speaks at some time after P
P speaks at some time before H
J \
P - H - N
\ K
If J is selected, then G is selected but L is not
J → G
/G/ → /J/
J → /L/
L → /J/
If V occupies the third position, what is the earliest position R could occupy?
5th
K presents earlier than both M and N
K presents later than G
G - K - M
\ N
Exactly seven students - M, N, P, O, S, T and W - sit in the seats numbered sequentially 1-7 in the first row of a classroom. Exactly one student sits in each of the seven seats. Each student is either right handed or left handed but not both. The seating arrangement adheres to the following conditions:
No right handed student can sit in a seat numbered one lower than the seat of a left handed student
M sits in a seat numbered two lower than the seat in which P sits
A right handed student sits in seat 3
T is right handed
O sits in seat 6
How many letters must come after P?
3
L is chosen if and only if G is selected
G → L
/L/ → /G/
L → G
/G/ → /L/
If T isn’t chosen for the team, N is chosen
/T/ → N
/N/ → T
If J is out then G is out
If H is in then G is in
If M and G are selected then H is selected
M and G → H
/H/ → /M/ and/or /G/
What is the earliest position R could occupy?
4th
Both M and H are written later than N
O is written at some time before H but after J
J is written earlier than K
K is written earlier than N
/ M
J - K - N - H
\ O /
What s the earliest position O could occupy?
5th
R and T cannot both be in
G isn’t selected for the club is F is selected for the club
F → /G/
G → /F/
Exactly seven airplanes - M, N, O, P, R, S and T - land at Wiley airport on Monday. No other planes land and no two planes land at the same time. The order in which the planes land conforms to the following:
N lands at some time before P but some time after T
R lands at some time after S
T lands at some time after both M and O
S lands some time before P
O \
M - T - N > P
S - R
J leaves at some point before K but after L
L - J - K
If X is selected both Y and Z are selected
X → Y
/Y/ → /X/
X → Z
/Z/ → /X/
Yohei plays the guitar if Juan plays drums
Jd → Yg
/Yg/ → /Jd/
On Monday exactly fixe flights - P, Q, R, S and T - depart from the same airport. The flights depart one at a time and each flight departs exactly once. Two of the flights are bound for Japan, two for Germany and one for France. The following conditions apply:
No flight bound for Germany can depart until at least one flight bound for Japan has departed
Flight Q departs at some time before flight S and some time after R
The flight that departs first is not bound for Japan
Flight P is bound for Germany
B interviews at some time before F
Both D and G interview at some time before B
H interviews at some time after D
/ H
D - B - F
G /
If Sid is on the committee, then Jana is on the committee
S → J
/J/ → /S/
If T occupies the fourth position, which letters could occupy the seventh position?
VR
FRAMES
Exactly seven items - R, S, T, V, W, X and Y - are sold at a yard sale. The items are sold consecutively and no two items are sold at the same time. Th order in which the items are sold at the same time. The order in which the items are sold are subject to the following conditions:
T is sold ealier than V and exactly one item is sold between T and V
S is sold earlier than R
X is sold immediately after V
Y is sold second
Good Candidate for frames - bulky 4-slot chunk, Y is fixed in the second slot, many cross-outs below the diagram
3 Frames
TYVX _ _ _
_ YT _ VX _
_ Y _ T _ VX
Exactly seven people - Francis, Gosman, Helena, Jackson, Kielor, Lin and Miller - sit in the front row at the movie theatre. The first row contains only seven seats numbered consecutively from 1 to 7. No two people sit in a seat. The seating arrangements are governed by the following:
If Gosman sits in seat 2, then Jackson sits in seat5
Francis sits in a seat numbered lower than Jackson’s seat but higher than Gosman’s seat
Helena sits in seat 3
Miller sits in either seat 1 or 7
X is built later than Y but earlier than Z
W is built later than Y
Y - X - Z
\ W
How many letters must come after L?
4
If K is out then both L and M are in
If L is in then K is out
If L is out, M is in
If Paulson is selected then Oter is selected but Vicenza is not
P → O
/O/ → /P/
P → /V/
V → /P/
Neither H nor K is selected if L is selected
L → /H/
H → /L/
L → /K/
K → /L/
The town of Holden has exactly three movie theatres: J, K and L. Each of the three theatres shows one or more of the following movies: Rung, Stilited and Trouble. None of the three theatres shows any other movie. The following rules apply:
Any theatre that shows Rung also shows Trouble
Exactly two of the theatres show Stillted
Both R and S arrive earlier than Q
R - Q
S /
Floyd, George and Hank are each being assigned to one of only two camp activities - swimming or tennis
George and Hank cannot both be assigned to the same activity
Floyd will be assigned to swimming if and only if Hank is
If Flora is chosen, then both Land and Newsam are chosen
F → L
/L/ → /F/
F → N
/N/ → /F/
M arrives at some time after O
L arrives earlier than N
J arrives at some time after L but before P
S arrives at some time after J
N arrives later than O
O - M
> N
L - J - P
\ S
If Tamika gives a speech, then she won the speech competition
S → Won
/Won/ → /S/
