Out of six numbers 1,2,3,4,5 and 6 in some order, we know third and fourth ranked numbers in every five out of the six numbers. Find the first ranked in the order given.

for example, if the ranks were, 3 > 6 > 2 > 5 > 1 > 4

and you gave me 1,2,3,4 and 5, I'd say that third-ranked is 5 and fourth-ranked is 1. In the same way I'd give the third and fourth ranked out of any five given numbers.

How would one find the highest ranked out of all these numbers?(If it is possible at all) And in how many steps (one step is giving me one tuple of five numbers)? I'd also appreciate if one could suggest better tags for this.

EDIT:- also find the last (lowest) ranked out of all these numbers if possible

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    $\begingroup$ am I allowed to ask for ranking of say 1,1,2,2,3? because otherwise you have no way of differentiating between 1st and 2nd rank. $\endgroup$ – JMP Dec 9 '18 at 13:23
  • $\begingroup$ ThankYou for clarifying and sorry for not mentioning that the numbers are always 1,2,3,4,5,6 (hence no repitions) and the ranking is predefined (not necessarily increasing or decreasing order). $\endgroup$ – Krishna Dec 9 '18 at 13:54
  • $\begingroup$ Your edit is not clearing up confusion; it is completely changing the question at hand! Please do not edit your question to explicitly invalidate previous answers. $\endgroup$ – Deusovi Dec 10 '18 at 7:39
  • $\begingroup$ the edit now just adds another question keeping the original questions in place. It does not invalidate your answers because you answered the original single question correctly. You can try to help with the added question if possible. $\endgroup$ – Krishna Dec 10 '18 at 7:46

There's no way: you cannot compare the top two numbers. All comparisons' results will be the same if those two were switched.

With the new question, yes, it is possible. Say the numbers are secretly (a) to (f), where "a" is the highest and "f" is the lowest.There are six possible comparisons:


The sets of two distinguished elements have one pair that appears exactly once (c and e), and one pair that appears exactly twice (c and d). The set of three undistinguished elements is the same in all three of these trials, except for one of them; the element that is in two of these three sets is the lowest-ranked element.

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    $\begingroup$ Except you can't identify the first two, you can identify the rest. $\endgroup$ – iBug Dec 9 '18 at 17:03
  • $\begingroup$ ThankYou for the prompt answer. I have now edited the question asking the lowest ranked element. Can you help me finding that? $\endgroup$ – Krishna Dec 10 '18 at 7:12
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    $\begingroup$ @SriKrishnaSahoo Please do not edit your question to explicitly invalidate previous answers. Your edit changed it into a completely different question. $\endgroup$ – Deusovi Dec 10 '18 at 7:24

The new question is:



ranks 1, 2 and 6 are never returned by the answerer, and so we cannot determine their order.


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