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Vemuri's Brain Teaser-2

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by mathbyvemuri » Wed May 09, 2012 12:56 am
Three Japanese-men and three Chinese-men work for the same firm. Every one of them knows a secret not known to others. They need to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets. None of the Chinese-men knows Japanese and only one Japanese-man knows Chinese. What is the minimum number of phone calls needed for the above purpose?
(A) 5 (B) 9 (C) 10 (D) 15 (E) 18

check Brain Teaser-1 here: https://www.beatthegmat.com/vemuri-s-bra ... 11169.html
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by Neo Anderson » Wed May 09, 2012 2:20 am
IMO 9

2 between 3 Japanese,
2 between 3 Chinese and
1 between a Japanese and a Chinese.
again
2 between 3 Japanese, and
2 between 3 Chinese
thus 9.
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by Bill@VeritasPrep » Wed May 09, 2012 8:32 am
Neo Anderson wrote:IMO 9

2 between 3 Japanese,
2 between 3 Chinese and
1 between a Japanese and a Chinese.
again
2 between 3 Japanese, and
2 between 3 Chinese
thus 9.
Agreed, and that's how I solved it as well.

Good question, Vemuri!
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by JARoberts » Thu May 10, 2012 10:53 am
I agree with 9 but there's another way to order it.

Use the Japanese man who speaks Chinese as a central communicator. (He'll be J1, the other Japanese men are J2 and J3, the Chinese men are C1, C2, C3.)

J1-J2 - both know each other's secrets
J1-J3 - J3 and J1 know all Japanese secrets
J1-C1 - C1 and J1 know all Japanese secrets and the first Chinese secret
J1-C2
J1-C3 - At this point J1 and C3 know all six secrets - all future calls will involve filling the other men in on secrets that J1 had not discovered when he called them the first time.
J1-C2
J1-C1
J1-J3
J1-J2

It's still 9 but I find it easier to map from one person than to try to map the intermingling of different people.
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by siliveru » Sat May 12, 2012 3:27 am
Answer is Nine
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by mathbyvemuri » Sun May 13, 2012 9:47 pm
Yes, the answer is 9 calls.Thanks to all for replies.
Let us name the three Japaneese as J1,J2 and J3, and the three Chinese as C1,C2 and C3.
Let us consider the only Japanese knowing both Japanese and Chinese languages to be J1.
Pl check the attachment for information on sequence of calls. This sequence may vary a bit to get the same answer:
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