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A few days ago, I saw two scholars discussing in front of a blackboard.

One scholar said that A and B were twins. The other scholar said that A and C were twins.

So I thought B and C were also twins. But, they said B and C were not twins.

Can you explain it?

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    $\begingroup$ Not a very interesting riddle IMO. Basically just "which non-transitive relation that happens be called twin am I thinking of?". $\endgroup$ – Jack M Apr 14 '18 at 19:21

13 Answers 13

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I think they are talking about

Twin primes

In particular

$A= 5$, $B=3$ or $7$ and $C=7$ or $3$

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  • $\begingroup$ if B and C are both 3 or both 7 then they are also technically twins $\endgroup$ – RenaissanceProgrammer Apr 14 '18 at 0:47
  • $\begingroup$ I don't know what you mean by "both 3 or both 7". B and C are two distinct number. If B= 3 and C= 7 they are both primes but they are NOT twin primes. $\endgroup$ – user247327 Apr 14 '18 at 19:31
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They might be talking about

Twinned cities

For example,

(A) Nassau, Bahamas; (B) Shanghai, China; and (C) Kish, Iran. (A) is twinned with (B) and (C), but (B) is not twinned with (C).

evidence:

https://en.wikipedia.org/wiki/Sister_city

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    $\begingroup$ Could you add a Wikipedia link to your spoiler explaining what the term means? (There definitely is one, but I don't want to link it in a comment) $\endgroup$ – Nic Hartley Apr 13 '18 at 17:21
  • $\begingroup$ @NicHartley thanks for the suggestion $\endgroup$ – fanjie Apr 14 '18 at 6:18
  • $\begingroup$ "Sister Cities" is NOT the same as "Twin Cities"! $\endgroup$ – user247327 Apr 14 '18 at 19:32
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    $\begingroup$ @user247327 Ignoring the spoiler, but, uh, yes, they are? Click the link. $\endgroup$ – Nic Hartley Apr 15 '18 at 2:00
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Could they be talking about

Two completely separate pairs of twins, where the name A happens to be a shared name between two of the twins, one from each pair?

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How about

A = twin 1, B = twin 2, C = twin 2

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4
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Nobody yet mentioned but:

One of the scholars simply lied. Based himself on incorrect information (if scholar meant as a researcher) or deserved the F (or european 1) grade (if scholar meant as a student)

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3
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Easy:

B and C are the same person

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  • $\begingroup$ It seems your answer is identical to Statman's $\endgroup$ – Riley Apr 13 '18 at 14:09
  • $\begingroup$ @Riley - ah. I didn't understand Statman's answer when I glanced at it first. I can see now that he meant what I said. I'll mark him up. $\endgroup$ – Lee Leon Apr 13 '18 at 14:20
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A and B are identical twins (related). A and C are also both teammates on the Minnesota Twins baseball team. B and C are not related so they are not twins (B is also not a member of the baseball team).

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  • $\begingroup$ Now that's pretty good! $\endgroup$ – user247327 Apr 14 '18 at 19:33
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At least one of them (let's say B) is indeed a twin, but from a different pair of twins (siblings B and D), but then they meant that B and C are not mutual twins. Kind of inconsistent, but that means the scholars were not mathematicians and thus not talking about twin primes...

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B and C are Siamese twins as opposed to JUST twins
A is the triplet of B and C.
So A is the twin of B, A is the twin of C, B is the SIAMESE twin of C.
Splitting hairs/heirs .......... maybe

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  • $\begingroup$ Welcome to Puzzling.SE! Could you edit your answer to include spoiler tags, so as to avoid spoiling the solution for anyone who wants to have a go at the puzzle themselves? Thanks! $\endgroup$ – F1Krazy Apr 13 '18 at 16:43
  • $\begingroup$ how is that done? $\endgroup$ – Peter Apr 13 '18 at 16:45
  • $\begingroup$ Put >! at the start of each line, and put an extra line break between every line, otherwise it won't quite work. $\endgroup$ – F1Krazy Apr 13 '18 at 16:46
  • $\begingroup$ OK I'll give it a shot $\endgroup$ – Peter Apr 13 '18 at 16:47
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I can think of 3 solutions, though (2) and (3) make some additional assumptions:

Solution 1

The puzzle question does not mention that the 2 scholars agreed with each other on the first two statements ("A and B are twins" and "A and C are twins"). So we may assume that the scholars are discussing 3 different entities, A, B and C, and that whether 2 entities are "twins" in their subject of expertise is not a straight-forward to infer (so they are still hypothesizing), or alternatively that concept may have been poorly defined and so is subjective. The 2 scholars are researching the relationship between the 3 entities and currently they both agree only the relationship between B and C, but differ on the relationship between A and the remaining two entities.

Solution 2

A, B and C are 3 conjoined infants, with A and B being joined together and A and C being joined together at birth but B and C were not joined. The scholars specifically meant "conjoined twins" when they said "twins". The scholars may be anthropologists studying abnormal birth conditions.

Solution 3

The scholars are architects discussing tall building structures. A, B and C are a sequence of 3 connected similar towers. A is the middle tower that is connected by bridges to both B and C, but B and C are not connected directly to each other. The scholars consider 2 towers to constitute "twin towers" only if they are right next to each other and perhaps also require them to be connected to each other directly through a bridge.

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Does 'twins' mean:

Set membership. A twinned to B implies $A,B\in S$ for some S. So $A,B\in S$, $A,C\in T$ but no set in the universe contains B and C.

For example let $S=\{1,2\}, T=\{1,3\}$ and no other such sets. Then $A=1, B=2, C=3$ satisfy the questions criteria.

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It is Like This

Let A = 1 , B = 2 , C = 3 B-A = 1 C-B = 1 hence they are twin but C-A = 2 hence its not

kind of stupid logic:-P

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  • $\begingroup$ But AB and AC are twins and BC arent... Maybe too stupid logic? :-P $\endgroup$ – Ckankonmange Apr 13 '18 at 13:24
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They said B and C are not twins.
But you thought that B and C are twins.
But according to them A and B or A and C are twins.
Over all from your response I get that:

None of them are twins. They all just look similar.

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    $\begingroup$ Welcome to Puzzling.SE! I originally flagged this as rude/abusive, but instead I've edited out the offensive statement about Chinese people and retracted my flag. Please be aware of StackExchange's "Be Nice" policy. $\endgroup$ – F1Krazy Apr 13 '18 at 16:49

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