need help with quadratics question

so, basically, we got this question for homework, and i have literally no idea what to do. the only thing i know is that the formula will be quadratic. so heres the problem

"There are seven boy scouts and seven girls scouts in a 15 seat canoe. They are all single seats. the girls are sitting in the front seven chairs, and the boys are sitting in the back seven chairs and they want to switch completely. the only way they can move is by moving one seat up or back, or leapfrogging over somebody else to land on their other side. what is the minimum amount of moves it would take to do this."

I really need help so any would be appreciated.

8

I don't think this has anything to do with quadratics..?

Basically there are three different symbols, B, G, and -, and the only move you're allowed to make is swapping two adjacent symbols (B/G swapping with - is your first rule and B/G swapping with adjacent B/G is your second)... and apparently you need to turn B B B B B B B - G G G G G G G into G G G G G G G - B B B B B B B via such swaps (the individual people aren't distinct beyond their gender, right?). When the problem is expressed in this simple way, it doesn't seem to me like it should be very difficult...

i think your misunderstanding the moves. lets say we start out with this G G - B B. we CAN swap a B or G with an adjacent -, but we can't SWAP a B/G with a B/G, we have to leapfrog them.
Example for leapfrogging: G G - B B ---> - G G B B.

i hope that clears it up a little

So, one person, can jump over one and only one other person (irrespective of gender..?), if this lands them where the empty space is?

yes that is completely right

Hum, how could we use mathematics to represent this then? I can see how a program can use an array to simulate and shift the values around according to the rules to achieve the desired result, but as far as obtaining the least number of moves..

Lawdy, I sure can't wait to see what Xei comes up with. Mein interest is piqued.