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Joined: 10 Apr 2015
Posts: 6218
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In a room of 12 people, each person shook hands with exactly 3 other p
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23 Oct 2021, 05:54
23 Oct 2021, 05:54
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In a room of 12 people, each person shook hands with exactly 3 other people. How many handshakes took place?
A) 18
B) 36
C) 55
D) 110
E) 220
A) 18
B) 36
C) 55
D) 110
E) 220
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In a room of 12 people, each person shook hands with exactly 3 other p
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24 Oct 2021, 05:49
24 Oct 2021, 05:49
1
GreenlightTestPrep wrote:
In a room of 12 people, each person shook hands with exactly 3 other people. How many handshakes took place?
A) 18
B) 36
C) 55
D) 110
E) 220
A) 18
B) 36
C) 55
D) 110
E) 220
Let's say the 12 people are A, B, C, D, ...., K and L
If each person shook hands with exactly 3 other people, then person A participated in 3 handshakes.
Similarly, person B participated in 3 handshakes.
Person C participated in 3 handshakes.
.
.
.
Person K participated in 3 handshakes.
Person L participated in 3 handshakes.
So, the total number of handshakes = (12)(3) = 36 (but the correct answer is not B)
Notice that every handshake has been counted TWICE.
For example, if B and G shook hands, then person B counted the handshake, AND person G counted the same handshake.
To account for this duplication, we'll divide 36 by 2 to get 18
Answer: A
Re: In a room of 12 people, each person shook hands with exactly 3 other p
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19 Sep 2025, 07:23
19 Sep 2025, 07:23
1
Another perspective to investigate this problem:
There are 12 people and each person shook hands with exactly 3 other people.
In other words, 12 persons x (3 handshakes / 1 person) = 36 handshakes
BUT because each handshake involves 2 people, that must mean that each handshake was counted twice.
Hence, 36 handshakes / 2 = 18 handshakes
There are 12 people and each person shook hands with exactly 3 other people.
In other words, 12 persons x (3 handshakes / 1 person) = 36 handshakes
BUT because each handshake involves 2 people, that must mean that each handshake was counted twice.
Hence, 36 handshakes / 2 = 18 handshakes
