Iggy's Logic Quiz 6

Quiz Answer Key and Fun Facts

1. Four people each framed one of the other three people for robbery. Nobody was framed more than once. If there are exactly two liars, then who could've RJ framed? Drake: A truth teller framed me TJ: RJ framed Drake Glebb: I framed whoever framed me RJ: I framed a liar

Answer: Everything is contradicting

TJ cannot be telling the truth, otherwise Drake's and RJ's statements are contradicting no matter what. TJ is lying, so RJ didn't frame Drake.
If Drake is the other liar, then a liar framed Drake. TJ is the only other liar, so TJ had to have framed Drake. Since Glebb and RJ must be truthful, Glebb couldn't have framed RJ. Glebb couldn't have framed TJ either since TJ didn't frame him. Glebb couldn't have framed Drake either since TJ framed Drake. There is nobody for Glebb to frame, so Drake cannot be the other liar to begin with.
Drake is telling the truth, so the other truth teller framed him. TJ is a liar so he couldn't have framed Drake. RJ didn't frame Drake either, so Glebb had to have framed Drake. Glebb must be the other truth teller, so Drake framed him as well. This can only mean that TJ and RJ framed each other. This is contradicting because now RJ is telling the truth, making 3 truth tellers. Everything is contradicting in every scenario.

2. Four people combined inherited $30,000. The only person who's lying is the only person who didn't inherit anything. Which of these money amounts was someone's exact inheritance? Bill: I inherited more than everyone Mack: I inherited $12,000 Dale: Alan's money and mine are $2,000 away from each other Alan: Bill inherited $16,000

Answer: $6,000

If Alan is the liar, then Dale inherited $2,000. Bill had to have inherited $16,000 for the money to total $30,000. This is contradicting because now Alan isn't lying. Alan has to be telling the truth as well as Bill who has $16,000.
If Dale is the liar, then Alan has to have $2,000 for the money to total $50,000. This is contradicting because now Dale isn't lying.
Mack is the liar by process of elimination.
After subtracting Bill's money, $14,000 is left. Alan and Dale must have $6,000 and $8,000 in order for them to be $2,000 away. You can't figure out who has $6,000 (Alan or Dale), but you know that $6,000 is someone's exact inheritance.

3. Five people were in a free-for-all paintball war. Once someone was shot, they could no longer shoot and were out of the game. Nobody shot more than 1 person. If the winner is the only person telling the truth, then who was the last person standing? RJ: I shot Jake Jake: Toparnis did not shoot Drake Drake: RJ was shot by a liar Glebb: Jake shot Toparnis Toparnis: Drake didn't shoot anyone

Answer: Jake

The first person shot couldn't have shot anyone, so the 4 remaining people each shot 1 person. The second person shot had to have shot the first person, otherwise someone else would have to shoot 2 people. For the same reason, the third person shot had to have shot the 2nd person. The 4th person shot the 3rd person, and the standing person shot the 4th person.
If Toparnis is truthful, then all others are lying. If Jake is lying, then Toparnis shot Drake. This is impossible since Toparnis's statement implies that Drake was the first person shot. The first person shot could not have been shot by the last person standing. To avoid contradictions, Toparnis is lying and Drake shot someone.
If Jake is lying, then Toparnis shot Drake. Drake would also have to be lying since he was shot. If Glebb is truthful, then the order shot is: someone-Drake-Toparnis-Jake. The someone would have to be RJ, but then Drake's statement is contradictory (he's calling himself a liar). In that scenario, Glebb cannot be truthful and RJ is the only person left to tell the truth. The order shot would then have to be: Glebb-Drake-Toparnis-Jake. There is another contradiction because now Glebb's statement is true. Glebb's statement is contradictory whether it's true or false, so Jake cannot be lying to begin with. Jake has to be the winner to avoid contradictions.

4. Four people combined have $1,000. If the only person lying is the only person with no money, then what is Andrew's money plus Kris's money? Kris: I have twice as much as Trony Ethan: I have $100 more than Andrew Trony: I have $200 more than Ethan Andrew: My dollar amount is a square number

Answer: $800

Trony cannot be lying, because then Kris is a second liar.
Andrew cannot be lying, since 0 is a square number.

If Kris is the liar, then all others are truthful.
In this scenario, we get the algebraic equations:
A + 100 = E
A + 100 + 200 = T
A + T + E = 1000
There is no letter K since Kris has $0.
We can replace the bottom equation with equal variables in terms of A.
A + A + 100 + 200 + A + 100 = 1000
Subtract 400 from both sides and simplify.
3A = 600
A = 200, so Andrew would have to have $200 in this scenario. This is contradicting because now Andrew is a second liar. Kris cannot be the liar to begin with.

Ethan is the only person left to be the liar, so Trony has $200. Kris has $400, so Andrew must have $400 in order for everyone's money amounts to total $1,000.

5. There's 1 red hat, 1 blue hat, 1 yellow hat, and 1 green hat. Each of the 4 people are wearing 1 of the hats. If each person says 1 lie and 1 truthful statement, then what color is Connor's hat? Bud: Emma's hat isn't yellow. My hat isn't red. Reese: My hat is blue. Emma's hat is green. Emma: Connor's hat isn't red. My hat is orange. Connor: My hat is orange. My hat isn't orange.

Answer: blue

First we'll consider a scenario where Reese's hat is blue.
Reese's first statement would have to be true. Reese's second statement must be false so Emma's hat isn't green. If Bud's first statement is true, then Emma's hat cannot be yellow. Emma's hat already couldn't be green or blue because of Reese's statements. Emma's hat cannot be red either since both of Bud's statements would be true. There is a contradiction since Emma's hat cannot be any color. This means Bud's first statement cannot be true in this scenario. Bud's first statement is false, so Emma's hat is yellow. This means Connor and Bud have the green and red hats. Since Bud's second statement must be true, Bud can only have the green hat. This means Connor has the red hat, which is impossible because now Emma is lying twice. There is always a contradiction in this scenario, so Reese's hat is definitely not blue.
Reese's second statement has to be true since his first is false, so Emma's hat is green. Bud's first statement is now true, so he's lying that his hat isn't red. Reese and Connor have the blue and yellow hats. Since Reese's hat cannot be blue, it's yellow.
Connor's hat is blue, Reese's is yellow, Bud's is red, and Emma's is green.

6. Four people finished running a race, but only the runners know the results. If the only person who's telling the truth is the race winner, then who is it? Raul: I won the race Carlos: Raul got last place Tito: I did better than Carlos Edgar: Raul did worse than Tito

Answer: Raul

If Tito was the winner, then all others have to be lying. This is contradicting because Tito winning makes Edgar's statement true. Tito has to be lying, so he did worse than Carlos.
If Edgar is truthful, then Raul did worse than Tito. Tito already did worse than Carlos, so the order would have to be Edgar-Carlos-Tito-Raul. This is contradicting because now Carlos's statement is true. Edgar cannot be telling the truth, so Raul did better than Tito.
Now Carlos cannot be telling the truth since Raul did better than Tito. By process of elimination, Raul is the winner.

7. Five people each voted to boot one of the other four off a reality show. There wasn't a tie so the person with the most votes was booted from the show. If the booted person is the only person lying, then who was voted off the show? Simon: I voted for someone who voted for Eva Aram: I voted for a truth teller, and no liars voted for me Max: I did not vote for Simon Eva: I voted for Max Dan: I voted for someone who voted for Aram

Answer: Dan

Aram can't be the liar since he can't vote for himself.
If Max is the liar, then he voted for Simon. Everyone else is telling the truth, so Dan and Simon both voted for people who aren't Max. Aram also couldn't have voted for Max, so Eva is the only one who did. It's impossible that Max was booted with just 1 vote, so Max has to be telling the truth.
If Simon is the liar, then Aram couldn't have voted for him. Max or Eva couldn't have voted for him either since that would contradict the statements. Dan is the only person who could've voted for Simon, but Simon couldn't have been booted with just 1 vote. Simon has to be telling the truth, so someone voted for Eva.
If Eva is the liar, then at least 2 people voted for her. They couldn't have been Simon or Aram, so they have to be Max and Dan. This means Eva had to have voted for Aram in order for Dan to have voted for her. Eva couldn't have voted for Aram since that would contradict Aram's true statement. Since there is a contradiction, Eva cannot be the liar.
The liar must be Dan by process of elimination. Eva and Aram couldn't have voted for Dan, so Dan's voters have to be Max and Simon. Simon voted for Dan. Dan voted for Eva. Eva voted for Max. Max voted for Dan. Aram voted for Simon.

8. Four people combined have $30. If only one person is lying, then what is the product of Connor and Kate's dollar amount? Haley: I have $0 Kate: Ray has less money than Haley Ray: I have $15 more than Kate Connor: I have one fourth of what Ray has Don't put a $ in your answer.

Answer: 25

If Ray is the liar, then Kate and Haley are truthful. This is impossible because Ray cannot have less than $0. Ray has to be telling the truth and has at least $15. If Kate is truthful, then Haley has more money than Ray. Haley cannot have more than Ray because that results in more than $30. Kate is definitely the liar.
Here are algebraic equations showing the relations between everyone's money.
K + C + R = 30
C = R/4
K = R - 15
The letter H is not included since Haley has $0.
We can replace the K and C in the top equation with equal variables in terms of R.
R - 15 + (R/4) + R = 30
Multiply both sides by 4
4R - 60 + R + 4R = 120
Add 60 to both sides and simplify
9R = 180
Divide both sides by 9
R = 20
Ray has $20, so Kate has $5, and Connor has $5. Kate's dollar amount times Connor's is 25.

9. Four people combined have $500 in bills (nobody has change). The two richest people are both liars, while the two truth tellers have the lower money amounts. If nobody has the same amount of money, then how much does Jeremy have? Vincent: I have $108, which is less than Jeremy Christian: I have $1 more than Jeremy Eric: I have $170 Jeremy: Christian is $4 richer than Vincent Don't put a $ in your answer.

Answer: 109

Eric cannot be telling the truth since there would have to be at least two people richer than him. Two more people richer than $170 would result in more than $500. Eric must be lying and is one of the two richest. If Jeremy is the other liar, then Christian and Vincent are the truth tellers.

This is contradictory since Christian (a truth teller) cannot have more money than Jeremy (a liar). Jeremy must be truthful, so there is one liar and one honest person left. Christian is $4 richer than Vincent, so Vincent would have to be the honest person. Vincent has $108 and Christian has $112. Jeremy must have more than Vincent and less than Christian. Jeremy cannot have $111, because then Christian's statement is true. Jeremy cannot have $110, because then Eric's statement has to be true in order for everyone's money amounts to add to $500. Jeremy has to have $109 since it's the only other number between 108 and 112. Eric has $171.

10. There are three murder suspects (Sam, Joe, and Chirs), three possible murder weapons (knife, gun, and candlestick), and three rooms (kitchen, study, and lounge). The murderer is the only person lying, and they did it with one weapon in one room. Sam: The murder wasn't with the gun or candlestick Chris: The murder happened with the knife in the kitchen Joe: The murder didn't happen in the lounge For the three words in your answer, put the murderer's name first, then the name of the weapon, and then the room.

Answer: chris knife study

If Chris is telling the truth, then Joe also must be telling the truth. Sam would have to be the murderer with the knife in the kitchen. This is contradicting because now everyone's telling the truth. Chris has to be lying to avoid contradictions. Since Sam and Joe are telling the truth, Chris used the knife somewhere that isn't the lounge. If Chris used the knife in the kitchen, then he can't be lying.

The murder had to have happened in the study for there to be no contradictions. It was Chris with the knife in the study.

Source: Author iggy4

This quiz was reviewed by FunTrivia editor crisw before going online.
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You need to use some sort of logical reasoning to answer my questions. If some of the questions seem impossible, take your time and you might notice logic flaws to eliminate possible answers.

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