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