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
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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.
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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Agreed, and that's how I solved it as well.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.
Good question, Vemuri!
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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.
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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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:
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:
RaviSankar Vemuri
Join my Google Group on Math:
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My Blog on Math:
https://mathbyvemuri.blocked/
Some concepts for GMAT:
https://mathbyvemuri.blogspot.in/2012/05 ... -data.html
https://mathbyvemuri.blogspot.in/2012/05 ... dates.html
https://mathbyvemuri.blogspot.in/2012/05 ... es-of.html
Join my Google Group on Math:
https://groups.google.com/group/mathbyvemuri
My Blog on Math:
https://mathbyvemuri.blocked/
Some concepts for GMAT:
https://mathbyvemuri.blogspot.in/2012/05 ... -data.html
https://mathbyvemuri.blogspot.in/2012/05 ... dates.html
https://mathbyvemuri.blogspot.in/2012/05 ... es-of.html