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第五十一期“學生智慧擂臺”優秀作業(育才小學東區校五年級)
作者: 點擊數:134 更新時間:2019年6月20日 文章錄入:育才小學東區校
   

1.桌上放了25根火柴,甲乙二人輪流每次取走13根。規定誰取走最后一根火柴誰就獲勝。如果雙方采用最佳方法,甲先取,那么誰將獲勝?

=1   =1  1+1=2

        =2  1+2=3

       =3  1+3=4

=2   =1  2+1=3

        =2  2+2=4

       =3  2+3=5

=3   =1  3+1=4

        =2  3+2=5

       =3  3+3=6

25 ÷ 4 = 6……1

甲先拿1根,然后無論乙拿幾根,甲拿的根數都和乙湊成4,所以甲將獲勝。

2.如圖,正方形的邊長是4厘米,求陰影部分的面積。


4×4×π÷2=8π(cm²)

4×4=16cm²)

8π-16=9.12cm²)                  

育才小學東區校五(1  周一鳴

 

 

 

1.桌上放了25根火柴,甲乙二人輪流每次取走13根。規定誰取走最后一根火柴誰就獲勝。如果雙方采用最佳方法,甲先取,那么誰將獲勝?
:甲獲勝。方法如下:甲先取一根,然后無論乙取幾根,甲取的根數加上乙取的根數的和保持是四根就可以了。因為254的倍數多一根,所以只要保持第二次之后順延的兩次和是4就行了。

第一題:

2+2=4

25÷4=6輪……1

甲拿到最后1

答:甲勝

 

 

第二題:

4×4=16平方厘米)


16平方厘米

4×4×3.14÷4=12.56平方厘米

4×4×3.14÷4=12.56平方厘米

(①+③+②+③)-(①+②+③)=25.12-16=9.12平方厘米

答:面積是9.12平方厘米

 

育才小學東區校五(1 王婧萱

 

 

 

 

桌上放了25根火柴,甲乙二人輪流每次取走13根。規定誰取走最后一根火柴誰就獲勝。如果雙方采用最佳方法,甲先取,那么誰將獲勝?

答:用倒推的方法,誰想獲勝就得留一根火柴給自己,二人輪流每次取走13根,所以得給對方留1+3=4根,倒推再向前一次,就得給對方再留4根,一共8根,以此類再向前推,想獲勝的一方給對方留4的倍數,就一定會贏。甲先取,如果想贏就得留4的倍數:25÷4=6……1,就是說甲先拿1,下面每次控制留給乙4的倍數的火柴就必定會贏。

 

2.如圖,正方形的邊長是4厘米,求陰影部分的面積。


由圖1變成圖2

第一步:邊長變成圓的半徑,求出大圓的面積除以4份等于四分之一圓:4×4×л÷4=4л(cm²)


第二步:求正方形的面積除以2等于三角形的面積:4×4÷2=8cm²)

第三步:大面積減小面積得到一半的陰影面積,再乘以2

4л-8)×2=12.56-8)×2=9.12cm²)

答:陰影部分的面積為9.12cm²。

 

育才小學東區校五(1 吳宇軒

 

 

 

2.如圖,正方形的邊長是4厘米,求陰影部分的面積。

 


分析:我們可以把這個陰影部分連著一塊空白部分,看做一個扇形。

 4×4×3.14÷4

=50.24÷4

=12.56(平方厘米)

用這個扇形的面積減去沿對角線劃的一個三角形的面積。

 

4×4÷2=8(平方厘米)

然后相減。

12.56-8=4.56(平方厘米)

這個4.56平方厘米是陰影部分的一半,所以要乘以二。

4.56×2=9.12(平方厘米)

:陰影部分的面積是9.12平方厘米。

育才小學東區校  五(2)班      季欣悅

 

 

 

如圖,正方形的邊長是4厘米,求陰影部分的面積。

答:求這個陰影部分可以用大面積減小面積,那先算出正方形積,4×416,再用16×3.1450.24。接著算空白面積,是

16÷44,4×28,8×3.1425.12。最后大面積減小面積,50.2425.129.12。所以最后答案是9.12平方厘米。                                          

                                   育才東區校  五(2)班  周宇豪

 

 

                                                  

樂樂和多多在玩取火柴游戲,媽媽進來說:“我來考考你們,桌上共有25根火柴,你們輪流每次取走13根,誰取走最后一根火柴誰就獲勝,樂樂先取,怎么才能獲勝?”樂樂想了一會,高興的說,這可難不倒我:“25除以41,我先拿1根,剩下的24根火柴正好能被4整除,然后不管多多拿幾根,我都拿4減去她拿的根數,這樣保證兩個人每次拿的火柴根數之和都是4,就能確保我拿到最后一根,我就穩贏了,哈哈,我聰明吧!”,媽媽微笑著說:“真不愧是智慧小能手呢。”

2、解題思路:

正方形的邊長是4厘米,即正方形相鄰兩邊構成的扇形的邊長為4厘米,所在圓的半徑為4厘米。

正方形的面積為4×4=16平方厘米;

扇形所在圓的面積為4×4×3.14=50.24平方厘米;

因正方形相鄰兩邊構成直角,所以扇形的面積為所在圓面積的四分之一,即扇形面積為50.24÷4=12.26平方厘米;

題中陰影是兩個扇形的重復部分,面積為12.26×2-16=9.12平方厘米。

育才東區校  五(2)班  司禮樂

 

 

 

 

 

1.解: 1.假設只有4個火柴,按照規則,理論上誰先抽誰輸

       2.假設只有5個火柴,按照規則,理論上誰先抽誰贏(先抽1個)

       3.假設只有6個火柴,按照規則,理論上誰先抽誰贏(先抽2個)

       4.假設只有7個火柴,按照規則,理論上誰先抽誰贏(先抽3個)

       綜上所述

       5.如果有8跟火柴,無論抽幾個都會讓對方觸發2 3 4方案,所以必輸

       6.如果9根火柴,抽一個,必贏

       7.如果10根火柴,抽2個,必贏

       8.如果11根火柴,抽三個,必贏

        如果12根火柴,無論抽幾個都會讓對方觸發6 7 8 方案, 所以必輸

到這里可以發現4個一循環

所以

25÷4=6余下1

所以說誰先抽誰贏

: 因為甲先抽,所以甲勝利

育才東區校五(2) 鄒酉婕

 

 

 

 

1、桌上放了25根火柴,甲乙二人輪流每次取走13根。規定誰取走最后一根火柴誰就獲勝。如果雙方采用最佳方法,甲先取,那么誰將獲勝?

解:甲先取1根,再根據乙的取法而變化,如果乙取1根,甲就取3根;乙取2根,甲也取2根;乙取3根,甲就取1根,那么甲就可獲勝。

 

2.如圖,正方形的邊長是4厘米,求陰影部分的面積。


解:根據題意,陰影面積為:  4×4×π÷4×24×4

=8π116

=25.1216

=9.12平方厘米

 

育才小學東區校五(2)班  王麒順

 

   
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