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Boomboom joined Scout Jamboree. Every scout was said to handshake with each other. Some of them did not do. The total number of handshakes was $7$. Find the minimum number of handshakes which were not done?

sorry wrong.... there will be 3

leonardo shawon wrote:ammm,, is the answer 1? Or 2. Im not sure.

proof????

if there is $n$ scouts then the number of handshakes is $\binom{n}{2}$, if all scouts do it...
as you are to find minimum number of handshakes which were not done, just find minimum value of $n$ such that $\binom{n}{2}$ is greater than $7$...
$\binom{5}{2}=10$

ans is $3$...

I think question statement should be a little bit refined.

The part "Every scout was said to handshake with each other. Some of them did not do." should be replaced by something like "Every scout was said to handshake with each other. But some of them didn't handshake with all."

I first considered something like this, let $x$ be the number of total scout, & $y$ be the number of scout who didn't shake there hand with anyone...(blah blah blah)

i once try to figure it out with subset...