The Discus Throw
This year at the Puzzlarian Annual Games event, the discus throw was quite popular. After many rounds of competition, the field was narrowed to 4 people:
Knightmare
Neal
Kapakoi
Jin
Because of inexperienced judges, there were discrepancies in the distance measures. Cam, a game expert was asked to evaluate the results and to determine a winner. He decided the first thing to do would be to interview the 4 participants. Their comments are listed:
(note: no two make the same number of false statements)
Knightmare:
1. Kapakoi did not win the discus throw.
2. I was second.
3. Kapakoi and I trained together.
Neal:
1. Knightmare was the winner.
2. I placed a close second.
3. Kapakoi and I trained together.
Kapakoi:
1. Neal was the winner.
2. I did not train with anyone.
3. Knightmare was second.
Jin:
1. Knightmare was not the winner.
2. Neal was second.
3. Kapakoi and I trained together.
To whom did Cam present the discus throw trophy?
Knightmare
Neal
Kapakoi
Jin
Because of inexperienced judges, there were discrepancies in the distance measures. Cam, a game expert was asked to evaluate the results and to determine a winner. He decided the first thing to do would be to interview the 4 participants. Their comments are listed:
(note: no two make the same number of false statements)
Knightmare:
1. Kapakoi did not win the discus throw.
2. I was second.
3. Kapakoi and I trained together.
Neal:
1. Knightmare was the winner.
2. I placed a close second.
3. Kapakoi and I trained together.
Kapakoi:
1. Neal was the winner.
2. I did not train with anyone.
3. Knightmare was second.
Jin:
1. Knightmare was not the winner.
2. Neal was second.
3. Kapakoi and I trained together.
To whom did Cam present the discus throw trophy?
posted by Zaux at
10:55 AM
17 Comments:
My suspicion is that Cam presented Knightmare with the Trophy.
I'll let Cam explain the mathematics of it, as I can't :-) Thanks Cam.
(I do think it's TFF, TTT, FFF, TTF)
I found 4 possible solutions (examining all combinations in Knightmare's statements):
TTT FFF TFT TFF, Neal wins
TFT TTT FFF FTF, Knightmare wins
TFF TTT FFF TTF, Knightmare wins
FFT FTT FFF TTT, Kapakoi wins.
there is one solution only not four and it is the scenario where neal wins.
sry i guess i cant find any flaws in your 2nd scenario listed TFT TTT FFF FTF but in your third scenario u have jin as TTf and nightmare win. look at that again. and in your fourth scenario u assume that kapakoi trained with everybody.
that's interesting ... I worked through it and found only one solution, which agrees with the source solution ...
guess we'll let a few others comment before revealing :)
FTPmon ...
you are right ... Neals gets the trophy
ok, now i know why i said only neal could have won. in your second scenario where i said i couldnt find problem u also have it listed as though 2 different people both trained with kapakoi. Now, because the problem doesnt tell us whether or not Kapakoi trained with 1 or more people we have 3 scenarios where it is possible 2 of which mean that someone isnt telling the whole truth. they are simply saying "kapakoi and i trained together" when they should have said, "we all trained together" or "the 3 of us trained together". However, if we are to assume there is only one answer here it is the scenario where neal wins.
If no 2 people make the same number of false statements, then:
1 makes 1 false
1 makes 2 false
1 makes 3 false
1 makes 0 false
I decided to look for the person making 3 true statements (0 false).
Let:
A - Knightmare
B - Neal
C - Kapakoi
D - Jin
If A is the 3 truth teller:
B - 3F
C - 1T, 1F
D - 1F
If B is the 3 truth teller:
A - 3F
C - 3F
D - 1T, 2F
If C is the 3 truth teller:
A - 1T, 1F
B - 3F
C - 1T, 2F
If D is the 3 truth teller:
A - 1T, 2F
B - 1F
C - 2F
Therefore C is the 3 truth teller because:
A tells 1F
D tells 2F
B tells 3F
Since C is the 3 truth teller, he says that B was the winner.
B - Neal
Cam presented the trophy to Neal.
D'oh ! I've no idea how I ended up with TFF, TTT, FFF, TTF when Jin's 1st T does indeed negate Knightmare winning. That'll teach me to not double check things !
Noticed an error in my previous post:
In the "If C is the 3 truth teller" section, the C - 1T,2F should have been D - 1T,2F.
sorry 'bout that
The Discus Throw:
TOTAL FALSE: 0+1+2+3=6
For "Kapakoi and I trained together:" Assume 3F statements i.e. he either trained with 1 other guy or noone
minimum # false statements for each scenario:
KE 1st: 4F (KE2+KA1+KA3+JI1)
KE 2nd: 3F (NE1+NE2+JI2)
KE 3-4th: 3F (KE2+NE1+KA3)
NE 1st: 3F (NE1+NE2+JI2)
NE 2nd: 3F (KE2+KA1+KA3)
NE 3-4th: 3F (NE2+KA1+JI2)
Find overlaps with KE and NE positions.
Overlap KE 1st: -3 with NE 2nd: Total 4
Overlap KE 2nd: -3 with NE 1st: Total 3
Overlap KE 3rd: -2 with NE2: Total 4
Only way to get total 6F is Neal 1st, Knightmare 2nd.
Check arrangement:
Knightmare:
1. Kapakoi did not win the discus throw. T
2. I was second. T
3. Kapakoi and I trained together. T
Neal:
1. Knightmare was the winner. F
2. I placed a close second. F
3. Kapakoi and I trained together. F
Kapakoi:
1. Neal was the winner. T
2. I did not train with anyone. F
3. Knightmare was second. T
Jin:
1. Knightmare was not the winner. T
2. Neal was second. F
3. Kapakoi and I trained together. F
Note: Kapakoi training noone works too. KE becomes TTF and KA becomes TTT
Answer:
Neal wins
Cam
Zaux,
Would you be able to post the below puzzle for me. I sent an e-mail to trick of mind a week ago, but no success. Thanks in advance.
"
Serial Killer
Given the following series:
56__194__442__848__1484__2446__3854__?
What is the number corresponding to the 8th term ?
What is the number corresponding to the 42nd term ?
What is the number corresponding to the 200th term ?
"
Cam
Cam, you should be able to do it yourself now that you've got an account. Just go to www.blogger.com and sign in.
I'll put it up for you; in case you've got a weird account.
This post has been removed by the author.
Knightmare-3 true
1. True
2. True
3. True
Neal
1. False
2. False
3. False
Kapakoi
1. False / true
2. False
3. True
Jin
1. true
2. False
3. False / true
I did this presuming that Knightmare only stated the truth. It leads to a lot being left to chance actually-but it fits the scenario (Neal said all false due to Kapokoi and Jin having 1 true).
HOWEVER
Either Neal or Jin recieved the trophy - it can be either. If Kapokoi did True false True and Jin did True False False....Neal won. If Kapokoi did FALSE false true and Jin did True false true... JIN won.
I have come to the conclusion that not enough information was given-although I'm probably wrong. Would'nt be the first time :(
Soli
Cam...if you have a google account,then it's easy to get a gmail account.send your gmail account to ToM (trickofmind@gmail.com) asking to become auther
Zaux...you have posted some good logic problems recently,but this is the first one i couldn't get!
keep up the good picks :}
Post a Comment
Links to this post:
Create a Link
<< Home