Lateral Thinking XVIII

[Holmes]

Just to keep these running and not let them be forgotten in the past.

But another question: where the hell is Sayumi ?!?!?!?!? She also disappeared from the Mathematical Thinking, perhaps she´s got a lot of work ... but well, the ones that are still in this logical problems are ayw and S.H.

Let´s see ...


Five competitors -- A, B, C, D, and E -- enter a swimming race that awards gold, silver, and bronze medals to the first three to complete it. Each of the following compound statements about the race is false, although one of the two clauses in each may be true.

â—¦A didn't win the gold, and B didn't win the silver.
â—¦D didn't win the silver, and E didn't win the bronze.
â—¦C won a medal, and D didn't.
â—¦A won a medal, and C didn't.
â—¦D and E both won medals.
Who won each of the medals?

[S.H.]

Just a question, is "D and E both won medals." included in the "Each of the following compound statements about the race is false." ? Thanks 

[Sayumi]

Sorry guys 
I'm still around, but my teachers had the great idea to bury me in assignments, so I didn't have much time to work on LT/MT problems. I hope the next weeks will be a bit calmer though chances are slim... anyway I'll work on this problem as soon as I can 


EDIT:

Just a question, is "D and E both won medals." included in the "Each of the following compound statements about the race is false." ?
Thanks 

I just assumed that it is...

Okay I think I got it 

Spoiler:

gold:A
silver: D
bronze: C

I started off like this:
knowing that D and E both won medals can't be true I knew that at least one part of
D didn't win the silver, and E didn't win the bronze had to be true.
Then I just assumed that E didn't win bronze and D won silver.
Since B didn't win silver, A had to win gold. (First statement)
A won a medal was then true, so C had to win a medal as well. (Fourth statement)
Then I checked whether at least one part of the other statements was false:

Everything that' true is green, everything that's false is red
â—¦A didn't win the gold, and B didn't win the silver.
â—¦D didn't win the silver, and E didn't win the bronze.
â—¦C won a medal, and D didn't.
â—¦A won a medal, and C didn't.
â—¦D and E both won medals.

[S.H.]

I assumed that the last statement is included also..Couldn't wait anymore 

Spoiler:

D and E both won medals.
3 possibilities: D and E = no medal (Impossible because of 3rd statement)
                    > If D didn't win medal then "C won medal" = false , which lead us to C didn't win medal. But it is impossible because
                       only 2 people are possible to have no medal.
    D = no medal E = medal(Impossible because of 3rd and 4th statement)
                    > If D didn't win medal then "C won medal" = false , which lead us to C didn't win medal. (<3rd statement) If C didn't
                       win medal then "A won medal = false, which leads us to A didn't win medal. Again it is impossible because only 2
                       people didn't win medal.
    D = medal E = no medal(Only possible)

Conclusion 1 : D = medal E = no medal


â—¦D didn't win the silver, and E didn't win the bronze.

E didn't win the bronze = true based from Conclusion 1
D didn't win the silver = false (Because the other one is true)

Conclusion 2 : D won the silver medal



â—¦A didn't win the gold, and B didn't win the silver.

A didn't win the gold = false (Because the other one is true)
B didn't win the silver = true based from Conclusion 2

Conclusion 3 : A won the gold medal



A won a medal, and C didn't.

A won a medal = true based from Conclusion 3
C didn't = false (Because the other one is true)

Conclusion 4 : C won a medal

Conclusion 5 : D,A and C won medals

Conclusion 6 : A won gold, D won silver, C won bronze (Because it is the only medal missing)

@Sayumi We have the same answer, but I wonder how you got your answer though  I think we answered it in a different way..

[Holmes]

Correct Both!!!! As expected though,