Hello, Tara!
]The object is to state how many line segments would be in a circle that has seven dots.
I have done it a few times and come up with the answer of 21. . . . right!
However, part of me also wants to say 42 lines because each dot can reach out to all the other dots.
Your second approach is fine ... but there are some duplications.
If we list all 42 connections, we have a table like this:
. . . (A,B), (A,C), (A,D), (A,E), (A,F), (A,G)
. . . (B,A), (B,C), (B,D), (B,E), (B,F), (B,G)
. . . (C,A), (C,B), (C,D), (C,E), (C,F), (C,G)
. . . . . . . . . and so on.
But notice that we have both (A,B) and (B,A)
. . . They are the
same connection, but we've counted it twice.
. . . And we've done this with <u>every</u> pair: (D,G) and (G,D), etc.
So our list is
twice as long as it should be.
. . . Therefore:
. 42 ÷ 2
.=
.21 . . . which verifies your original count.
