The Biggest benefit

1. The Biggest benefit Li Mengyuan 13122687 Xu Junjie 13122364 Geng Yong 13123949 Ma Yinxiang 13121754

2. outline 1.Explain the game. 2.One of Simple analyses. 3.Mathematicl expectation. 4.To make the game end.

3. 1.Explain the game. A He won 8 million lottery. B He is A’s good friend.

4. a b B A 1. a > b , A will give B the money a . 2.b > a , A will give B the money (b-a)/a . 3. a = b , A will give B the money (a+b) .

5. ? There are some interesting things. Whatshould they give figures to make to maximize their own interests ?

6. VOTE 2.Analyze simply. • The number of B • 8million ( ) • 4million-8million ( ) • 4million ( ) • 10w-4million ( ) • 10w ( ) • 1w-10w ( ) • 1w ( )

7. If you vote for 8 million. You maybe right in 2 cases. Case 1: A is a rich man. He didn’t care about the money. Case 2: A want to give you a test, so he would choose 8 million.

8. ? Then, let’s think about the case that is different from the above 2 cases. So which number is best?

9. a>b x Ok，It’s time to slove the problem. For A: From 1 to 8000000 a=b For example : a=50 x x . . . . . . a<b x x

10. a>b For A: From 1 to 8000000 a=b . . . . . . a<b

11. Plus all the situations, we get the final formula: S(a)=

12. x61 x62 . . . b<a x7999999 x8000000 b=a For B: From 1 to 8000000 For example : b=60 x x . . . . . . b>a x x

13. For A: From 1 to 8000000 For example : b=60 b=a (b+1) (b+2) . . . . . . . . . b>a b<a 7999999 8000000

14. Also，plus all the situations we get the final formula: S(b)=

15. We have written down the function S(a) and S(b) ,but how to deal with them ? S(a)= S(b)= Derivative！！！ S’(a)>0 a∈【1，8000000】 So , the function is always increasing . And for A , at 1 will has the minimum expense .

18. THANKS！