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Four players with first names Ahmad, Ali, Amir and Nima participated in a tournament. The highest ranked player defeated the other three, the second ranked player defeated the players in rank three and four, and the player in third rank defeated the player in rank four.

Furthermore the following information are available (where ln = Last name,):

  • Ali Koohi (fn & ln) defeated Amir (fn) and Rezayi (ln) defeated Nima (fn)
  • Ahmad (fn) is not in the third rank.
  • Akbari (ln) is not in the last rank.
  • Nazari (ln) whose first name is not Ahmad, is exactly one rank after Ali.

What is Ali Koohi's rank?

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  • 1
    $\begingroup$ Darmok and Jalad, at Tanagra $\endgroup$ – Irishpanda Nov 23 '15 at 18:07
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3rd place.

- The first clue has two last names that cannot be in last place, as they defeated someone: Koohi and Rezayi.
- Per clue #3, Akbari is also not in last, so spots 1-3 are Koohi, Rezayi, and Akbari, in some order.
- Per clue 4, Nezari must be in last place, and per that same clue, Ali Koohi is one spot ahead of them: in 3rd.

To be complete:

Per the first clue, and his place at #3, Ali defeated only one person, Amir. This means Amir's last name is Nezari. This leaves Akbari and Rezayi. Since Rezayi defeated Nima, they cannot be the same person, therefore Nima is Akbari, and Ahmad is Rezayi.

The full list:

1st Ahmad Rezayi
2nd Nima Akbari
3rd Ali Kohi
4th Amir Nezari

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  • $\begingroup$ In the first clue, couldn't Amir be same person as Rezayi? $\endgroup$ – IanF1 Nov 22 '15 at 22:58
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    $\begingroup$ Fair point. Edited the answer, though that fact actually doesn't change the answer! $\endgroup$ – Irishpanda Nov 23 '15 at 14:35
4
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Here is a summary of the available information:

  • The four first names are: Ahmad, Ali, Amir, Nima.
  • The four last names are: Akbari, Koohi, Nazari, Rezayi
  • Ali Koohi is one name pair
  • Rezayi beats Nima, and hence Nima Rezayi is not a name pair
  • Ahmand Nazari is not a name pair

This leaves three possible name matchings:

(1) Ali Koohi, Amir Rezayi, Ahmad Akbari, Nima Nazari
(2) Ali Koohi, Amir Akbari, Nima Nazari, Ahmad Rezayi
(3) Ali Koohi, Amir Nazari, Nima Akbari, Ahmad Rezayi

Now let us work through the three cases one by one.
In case (1) Ali beats Amir and Amir beats Nima. Hence Ali and Nima Nazari cannot be on adjacent ranks (as Amir is inbetween). In the remaining cases (2) and (3), Ali beats Amir and Ahmad beats Nima. This yields six possible rankings:

  • (a) Ali > Amir > Ahmad > Nima
  • (b) Ali > Ahmad > Amir > Nima
  • (c) Ali > Ahmad > Nima > Amir
  • (d) Ahmad > Nima > Ali > Amir
  • (e) Ahmad > Ali > Nima > Amir
  • (f) Ahmad > Ali > Amir > Nima

Now as Ahmad is not on the third place, (2a) and (3a) are eliminated.
As Ali and Nazari are on neighboring places (in this order), this eliminates (2b), (3b), (2c), (3c), (2d), (3e), and (2f).
We are left with (3d), (2e) and (3f).

Finally we use that Akbari is not in last place: In (2e) Amir Akbari is in last place, and in (3f) Nima Akbari is in last place.

This leaves (3d) as only possible solution:

Ahmad Rezayi > Nima Akbari > Ali Koohi > Amir Nazari
Hence Ali Koohi reached the third place.

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  • $\begingroup$ Your solution doesn't meet: "Nazari (ln) whose first name is not Ahmad, is exactly after Ali." $\endgroup$ – Zerris Nov 22 '15 at 17:41
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Ali Koohi's rank is 3rd.

Solution:
From all the clues, Ali's last name is Koohi. There are three possibilities of First and last name for remaining three players.

1. Ahmad Rezayi - Amir Akbari - Nima Nazari.
2. Ahmad Rezayi - Nima Akbari - Amir Nazari.
3. Amir Rezayi - Ahmad Akbari - Nima Nazari.

Let's talk about first case.

Case 1. Ahmad Rezayi - Amir Akbari - Nima Nazari

=> From the clues, the possible ranks of all the players for this case are:

1. Ali Koohi = 1, 2
2. Ahmad Rezayi = 1, 2
3. Amir Akbari = 2, 3
4. Nima Nazari = 2, 3
=> For this case, no one is following under rank 4. So, this case is not valid.

Case 2. Ahmad Rezayi - Nima Akbari - Amir Nazari

=> From the clues, the possible ranks of all the players for this case are:

1. Ali Koohi = 1, 2, 3
2. Ahmad Rezayi = 1, 2
3. Nima Akbari = 2, 3
4. Amir Nazari = 2, 3, 4
=> So, the possible rankwise order for this case is:
Ahmad Rezayi - Nima Akbari - Ali Koohi - Amir Nazari -----------> This is a valid scenario.

Case 3. Amir Rezayi - Ahmad Akbari - Nima Nazari

=> From the clues, the possible ranks of all the players for this case are:

1. Ali Koohi = 1, 2, 3
2. Amir Rezayi = 2, 3, 4
3. Ahmad Akbari = 1, 2
4. Nima Nazari = 3, 4
=> From the clues, there is no any possible rankwise order for this case.

Conclusion:

From all the possible cases, only case 2 is possible and hence the answer is, Ali is at 3rd position.

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2
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Update: solution is unique.

One possible Answer:

Third Place!

1: Ahmad Rezayi
2: Nima Akbari
3: Ali Koohi
4: Amir Nazari

Logic, for my own reference

FN:
Ali (Koohi) (1, 2, 3*)
Ahmad (1*, 2, 4) Rezayi*
Amir (2, 3, 4*)
Nima (not Rezayi) (2*, 3, 4) Akbari*

LN:
Koohi (Ali) (1, 2, 3*)
Rezayi (not Nima) (1*, 2, 3) Ahmad*
Akbari (1, 2*, 3) Nina*
Nazari (not Ahmad) (2, 3, 4*)

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  • In clue 1 we have have two last names (Koohi & Rezayi) that defeated someone else, so those names can't be last.
  • In clue 3, a third last name (Akbari) is also not last.
  • Therefore, the only remaining last name - Nazari - must be last.
  • Ali (one rank above Nazari according to clue 4) must be 3rd.

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