*Fishing boat*
Ten Men are fishing from a boat, five in the front, five in the back, and there is one empty seat in the middle.
The five in front are catching all the fish, so the five at the back want to change seats.
To avoid capsizing the boat, they agree to do so using the following rules:
1.A man may move from his seat to and empty seat next to him.
2.A man may step over only one man to an empty seat.
3.No other move are allowed.
What is the minimum number of moves necessary for the men to switch places?
If there are n men from each side, how many moves is needed for the swap?
*渔船*
十个人在船上钓鱼，五个在前面，五个在后面，中间有一个空座位。
前面的五个人都有鱼获，所以后面的五个人想换座位。
为避免翻t船，他们同意使用以下规则：
1.一个人可以从他的座位移动到他旁边的空座位。
2.个人只能跨过另一人到一个空位。
3.不允许其他动作。
交换位置所需的最少移动次数是多少呢？
*如果双方各有 n 个人，交换需要多少个步骤？*
Leapfrog
no of no of no of total no
pegs slides Jumps Moves
1. 2. 1. 3
2. 4. 4. 8
3. 6. 9. 15
4. 8. 16. 24
n. 2n. n^2. n(n+2)
Strategic:
1. Simplify the problems
2. Critical concepts, critical moves?
3. Total shifts : 2n(n+1)
Jumps: n^2
1 jump =2 shifts
Total Slides
= Totalshifts-2x total jumps
= 2n(n+1)-2n^2
=2n
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