Please help me solve this question:
The kitchen floor of Emily’s house is made from 40 square tiles, as shown below:
(Picture: http://hkgshare.com/di-YMJT.png)
As the tiles become worn out over the years, Emily decided to replace them. Unfortunately, she was only able to obtain matching rectangular tiles. Each rectangular tile will cover exactly two of the original square tiles.
Is it possible for Emily to replace all the original square tiles with the new rectangular tiles and fit the kitchen floor exactly? Explain.
(Hint: Colour kitchen floor as a checkerboard.)
Mathematics and Problem Solve
2013-11-01 4:54 am
回答 (3)
2013-11-01 5:56 am
✔ 最佳答案
It is impossible.Colour kitchen floor as a checkerboard as follow :
..■□■□■
■□■□■□■
□■□■□■□
■□■□■□■
□■□■□■□
■□■□■□■There are 21 black square tiles and 19 white square tiles.
If it is possible , as each rectangular tile will cover exactly two of the original square tiles(1 black , 1 white), there should be 20 black and 20 white square tiles(contradiiction).
2013-11-01 8:13 pm
It seem look like IVE - ICT Mathematics and Problem Solving Techniques (ITE3107) Assignment 's question .
2013-11-01 6:06 am
多謝你的指導呀～
但可惜今次我都係排第二咋～
下次我會努力！！
☆ヾ(◕‿◕)ノ
2013-11-02 23:17:18 補充：
Au Chin Tao, thank you for your information.
I would notice that from now on.
Thanks!
但可惜今次我都係排第二咋～
下次我會努力！！
☆ヾ(◕‿◕)ノ
2013-11-02 23:17:18 補充：
Au Chin Tao, thank you for your information.
I would notice that from now on.
Thanks!
收錄日期: 2021-04-21 22:29:55
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20131031000051KK00198