My twin brother and I invite thirteen pairs of twins to a networking session at my house. I asked everyone present to find out how many people they exchanged business cards with.It turn out that everyone questioned including my twin brother exchanged business cards with different number of people. I did not ask myself of course. Assuming no one exchanged cards with his or her siblings, how many people did my twin brother exchanged cards with?
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Interesting one, help appreciated
- Thread starter rhd1305
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My twin brother and I invite thirteen pairs of twins to a networking session at my house. I asked everyone present to find out how many people they exchanged business cards with.It turn out that everyone questioned including my twin brother exchanged business cards with different number of people. I did not ask myself of course. Assuming no one exchanged cards with his or her siblings, how many people did my twin brother exchanged cards with?
What are your thoughts?
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Not sure it is possible to tell. Example for 5 twins (1 is swap with, 0 is not swap with):My twin brother and I invite thirteen pairs of twins to a networking session at my house. I asked everyone present to find out how many people they exchanged business cards with.It turn out that everyone questioned including my twin brother exchanged business cards with different number of people. I did not ask myself of course. Assuming no one exchanged cards with his or her siblings, how many people did my twin brother exchanged cards with?
1r (twins pairs 1-5 with a r,l to differentiate between them, numbered 1 as most swaps, 2 as second most swaps, etc) can only swap with at most 8 people and, since I didn't ask me, 9 slots are needed (0-8 swaps), 1r must swap with 8 people.
Suppose I am 5l, then my twin (5r) swapped with 0 people.
| Pair/Swap | 1r | 1l | 2r | 2l | 3r | 3l | 4r | 4l | 5r | 5l | Total Swap |
| 1r | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8 |
| 1l | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 7 |
| 2r | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 6 |
| 2l | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 5 |
| 3r | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 4 |
| 3l | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 |
| 4r | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 |
| 4l | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 5r | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 5l | ? | ? | ? | ? | ? | ? | ? | ? | 0 | 0 | ? |
However suppose we were to change the table so that I was some other twin, for example 4l. Well just interchange row 4l with 5l and my twin would have swapped cards with 2 persons.
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Ishuda, I'm fairly sure that 1r can be anything from 0 to 8,
since 1r can have the same as any of the others, as he was
not one of the one questioned (only the ones questioned
are different), so 1l starts at 8, so it is possible.
The table example is for the case of my twin & I being pair (5r,5l) and each twin set having
Number_of_Swapsr = 10 - 2*pair number
Number_of_Swapsl = Swapsr - 1 [except for me]
By definition 1r is the greatest number of swaps and the number of swaps must be 8 [since all of the members other than myself were question, 9 were questioned. Since 9 were questioned and all were different, there must be 9 slots, i.e. 8 swaps, 7 swaps, 6 swaps, ...,0 swaps]. The twin pair (and l or r) for the next highest number of swaps is unknown but the table is, again, an example of 1l being the next highest number, etc.
We could also have my twin and I as pair (4r, 4l)
| Pair/Swap | 1r | 1l | 2r | 2l | 3r | 3l | 4r | 4l | 5r | 5l | Total Swap |
| 1r | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 8 |
| 1l | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 7 |
| 2r | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 6 |
| 2l | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 5 |
| 3r | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 4 |
| 3l | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 |
| 4r | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 |
| 4l | ? | ? | ? | ? | ? | ? | 0 | 0 | ? | ? | ? |
| 5r | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 5l | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |
In the 1 case, my twin had zero swaps (first example, see edit for possible greater clairity) and in another (second example), my twin had 2.
EDIT: Note that the 1 in row 5l could be in any column but the 5r or 5l column, so maybe a follow on question might be what are the number of 'equivalence classes' where the number of swaps my twin might have had defines the ''equivalence class' [quotes because I'm not sure it is a set of equivalence classes in the technical sense]
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Hi all, thanks for your efforts. I tried using simple logic. There are 14 pairs i.e. 28 people at the networking session. Each person can potentially network with 26 people excluding himself/herself and his/her sibling. It is stated that each person when questioned gave different answers. The answers can range from 0 to 26, thus 27 possible answers which agrees with the given condition, as the author did not question himself. There is no additional data or condition mentioned in the problem. Thus it can be assumed that the brother of the author, being the co-host of the session, logically would have networked with all the invitees. Therefore the brother of the author networked with 26 people. What did I miss?
The tables provided can easily be extended to any number of twins and the answer is the same. There is no unique answer and it appears that the twin that didn't ask the question may have traded business cards with anywhere from 0 to 26 people and the given conditions would be met.Hi all, thanks for your efforts. I tried using simple logic. There are 14 pairs i.e. 28 people at the networking session. Each person can potentially network with 26 people excluding himself/herself and his/her sibling. It is stated that each person when questioned gave different answers. The answers can range from 0 to 26, thus 27 possible answers which agrees with the given condition, as the author did not question himself. There is no additional data or condition mentioned in the problem. Thus it can be assumed that the brother of the author, being the co-host of the session, logically would have networked with all the invitees. Therefore the brother of the author networked with 26 people. What did I miss?