Semester at school is coming to an end. Here comes our summer vacation.

I'm going to go to the countryside to enjoy the vacation with my family. My grandparents live there. They will tell me numerous intersting stories. I miss them much.

Along the dikes on big paddy fields, I will fly kites with my brother and the children there. We will also go fishing together. There will be lots of fresh fruits and I will have a chance to enjoy them all. 

My summer vacation will certainly be great. I will have much leisure to relax and play.

I have itchy feet, so I always have a detailed plan for the next holiday trip in mind.

This time, I am going to wait for my children’s summer vacation so that I can take the whole family on a trip together. I am a family person and I love to travel with my loved ones. And, you know, summer won’t be complete without sun tan and beach snapshots. Therefore, my destination must be a seaside city and Vinh Hy Bay is my ideal place. I have heard about this place a long time ago, a friend of mine highly recommended this place after her trip there. It is known for its natural scenic beauty and delicious fresh seafood at an affordable price.

I was curious, but couldn’t find time to travel there due to my tight working schedule. But this summer we are going to make it. It’s only a 4-hour ride from our city to the bay, so I am going to go by bike as if I were going backpacking. One reason luring us to this place is that it’s a pristine island, which means it won’t be crowded with tourists and the food here won’t be overpriced. Un other beaches which offer a variety of water sports canoeing, scuba-diving, water-skiing, and skydiving, there will not be many activities to do in Vinh Hy bay apart from sun-bathing and eating seafood. But this is going to be family time, and to me, spending time together is already enough.

In case my children get bored, so I am going to bring some family games UNO and castle-building tools to enjoy time on the beach together. I am in dire need of this vacation as I want to escape from a stressful workload and pressure from city life for a while with my kids and my spouse. Also, I think it is a good idea to reward my children with a trip after studying hard throughout the school year

1/2+5/6+11/12+19/20+29/30+41/42+55/56+71/72+89/90 =
1-1/2+1-1/6+1-1/12+1-1/20+1-1/30+1-1/42+1-1/56+1-1/72+1-1/90 =
9 – (1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90) =
9 – [1/(1x2)+1/(2x3)+1/(3x4)+1/(4x5)+1/(5x6)+1/(6x7)+1/(7x8)+1/(8x9)+1/(9x10)] =
9 – ( 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10) =
9 – (1 – 1/10) = 9 – 9/10 = 81/10

Dễ thấy tổng của 2012 số này là một số chẵn

Khi lấy ra 2 số,xét 3 trường hợp:

TH1: 1 số chẵn,1 số lẻ. Số thay vào là hiệu của chúng nên nó là số lẻ nên tổng của các số sau khi thay là số chẵn

TH2: 2 số chẵn. Số thay vào sẽ là số chẵn nên tổng của các số sau khi thay là số chẵn

TH3 2 số lẻ.Số thay vào sẽ là số chẵn nên tổng của các số sau khi thay là số chẵn

Vậy khi lấy ra 2 số bất kì thay bằng hiệu của chúng thì tổng của chúng sau khi thay là số chẵn nên trên bảng không thể còn số 3