There were 7 guests at a party + a host. 1st guest shook hands with 1 guy, 2nd guest with 2 guys .... kth guest with k guys. How many people did the host shake hands with? k was either 6 or 7, probably 7 – I don’t remember exactly

Question

Accepted Answer

At a party with 7 guests and a host, each guest shakes hands with a certain number of people. How many people did the host shake hands with?

The first guest shakes hands with 1 person, the second with 2 people, and so on.
The kth guest shakes hands with k people.
The host shakes hands with all 7 guests, so the number of people the host shakes hands with is the sum of 1 to 7.
The sum of 1 to n is n(n+1)/2, so the host shakes hands with 28 people.

Accepted Answer

initially remaning shakes sequence for guests (1 2 3 4 5 6 7) => 1 2 3 4 5 6 7

and the hosts had shakes =>0

When 7th will shakes with all others => 0 1 2 3 4 5 0

and the hosts had shakes =>1

When 6th will shakes with all others except 1 & 7 => 0 0 1 2 3 0 0

and the hosts had shakes =>2

When 5th will shakes with 3, 4, G => 0 0 0 1 0 0 0

and the hosts had shakes =>3

4th with the host only => 0 0 0 0 0 0 0

and the hosts had shakes =>4

Hence 4 is the answer.

Accepted Answer

There were 7 guests at a party + a host. 1st guest shook hands with 1 guy, 2nd guest with 2 guys .... kth guest with k guys. How many people did the host shake hands with? k was either 6 or 7, probably 7 – I don’t remember exactly

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