mathbyvemuri
Branch Unspecified
14 May 2012

# Vemuri's Brain Teaser-2

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

Dancer_Engineer

Branch Unspecified
6 years ago

Only one man can communicate in both the languages, let's call him the main person M.
The rest are J1, J2, C1, C2, C3.
Suppose these 5 men are standing in a row.

M will sequentially listen to their secrets and exchange his secret with them. When he reaches C3, he is the first man to know all 6 secrets while the others know their secrets, M's secret and the mens' secret who are standing before them in the row. M exchanges his secret with C3, thus making him the 2nd man to know all the 6 secrets. M will now move backwards in the row and exchange with each men the secret of the men standing after them in the row. Thus making 9 calls in all.

Is it correct?

mathbyvemuri

Branch Unspecified
6 years ago
Dancer_Engineer, Kudos, explained it very well...

mathbyvemuri

Branch Unspecified
6 years ago
Yes the answer is 9. Dancer_Engineer explained it very well. I will give the sequence of calls:
let us name the three Japaneese as J1,J2 and J3, and the three Chinese as C1,C2,C3.
Let us consider the only Japanese knowing both Japanese and Chinese languages be J1.

PhoneCall --Between --Who knows-What?
1 -----------C1-C2 ----C1 Knows secret of C2
2 -----------C1-C3 ----C1 Knows secret of C3
3 -----------J1-J2 -----J1 Knows secret of J2
4 -----------J1-J3 -----J1 Knows secret of J3
5 -----------J1-C1 -----By this call both J1 and C1 get to know all the secrets
6 -----------J1-J2 -----J2 knows all secrets
7 -----------J1-J3 -----J3 knows all secrets
8 -----------C1-C2 ----C2 knows all secrets
9 -----------C1-C3 ----C3 knows all secrets

Dancer_Engineer

Branch Unspecified
6 years ago
mathbyvemuri, there are 3 Chinese men not 4.

Continue posting the rest of the Brain Teaser series. 👍

mathbyvemuri

Branch Unspecified
6 years ago
Dancer_Engineer, Thanks, I have edited it.
The link for next Brain Teaser:
Brain Teaser-3