Spy math puzzle

scipio_major

Right there are ten spies, each of which has to get a piece of information. Each of them has to get all ten pieces but they only get one from the source the other nine come from the other spies. All communication is carried out through e-mail. What is the minimum number of e-mails that must be sent for every spy to assemble the complete set of info?

After much drawing on scraps of paper, cursing and pulling my hair, I continue to get an answer the same answer but I'm certain I'm wrong. I won't give it to ya yet so you're not biased. I NEED TO KNOW IF I'M RIGHT GODDAMMIT.

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Scipio_major

bonkey

I can do it with 18 emails off the top of my head, but I havent checked to see if thats the minimum yet. If your answer is larger than 18 then you are incorrect.

jc

Victor

I would say 10. Each spy e-mail send one e-mail and cc.s it to everyone else

1. A -> B,C,D,E,F,G,H,I,J
2. B -> A,C,D,E,F,G,H,I,J
3. C -> A,B,D,E,F,G,H,I,J
4. D -> A,B,C,E,F,G,H,I,J
5. E -> A,B,C,D,F,G,H,I,J
6. F -> A,B,C,D,E,G,H,I,J
7. G -> A,B,C,D,E,F,H,I,J
8. H -> A,B,C,D,E,F,G,I,J
9. I -> A,B,C,D,E,F,G,H,J
10. J -> A,B,C,D,E,F,G,H,I

Alternatively, seeing as they are spies (and spy D shouldn't know about spy G, his sworn enemy), each spy sends one e-mail to the ring-leader (9 e-mails) and the ring-leader bcc.s (blind) a summary to everyone (10th e-mail)

bonkey

In fact, having thought about it, I'm pretty sure I can prove that 18 e-mails (at a minimum) are required.

So - why can I prove this when Victor has just come up with a figure of 10?

Simple.

I am, of course, consdering that sending one e-mail to n recipients counts as n e-mails, because although you only send one mail message from your client, multiple copies get generated and sent.

If you dont count cc-ing as multiple mails, then the answer must be 10, as each spy must send his code out (requiring a minimum of 10 messages) before everyone can have all codes. So the answer cannot be less than 10.

jc

Victor

Originally posted by bonkey
In fact, having thought about it, I'm pretty sure I can prove that 18 e-mails (at a minimum) are required.

It all really depends on the definition of one "e-mail".

And if only the ring leader needed to know you would only need 9. Then he could ICQ the others

ykt0di9url7bc3

i see it as a ring of one email being sent around until all have gotten the info

scipio_major

By a majority a majority vertict I think we can assume that 18 is the answer. And yes that is what I got (Nine of the spies sent their bits of information to the tenth who puts it all together in a news letter and sents it back out to the nine). From that you'll see that I was counting carbon-copies as seperate e-mail, although I should have specified. Thanks.

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Scipio_major

Bob the Unlucky Octopus

A simple tree structure shows a Hamiltonian solution of 18

Occy

Winning Hand

18 if you count each email as being only availably to be sent to one person.
1 tells everything he knows (f*ck all) to 2
2 tells 3 everything he knows (f*ck all X 2)
3 tells 4........................
10 ends up with the complete picture (9 emails)
It is then his mission, should he choose to accept it, to relay the full info to his other compatriots, another 9 adding up to 18

Cerberus

I suppose it depends how you interpret the question. If you take "All communication is carried out through e-mail" as meaning that there is an e-mail sent in order for each spy to get their unique piece of info from their sources then you would have to add on 10 emails onto the total of 18 making 28. But as I said, it depends on how you take up the question.

Victor

It only ask how many e-mails to assemble the information, not how many to source and assemble (the first sentence is misleading in this regard.).

scipio_major

Thanks Victor. You all know why I try to avoid telling jokes in public, I *always* mess them up.

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Scipio_major

Victor

No, no, in fairness, I'm a picky git who will find any actual or potential discrepancy. Feel honoured