Olympiad strategy questions, the following three questions have to write the process, thank you.

1. Think of it this way: if you want to grab 30, you must grab 27, so that the other party will report 28, or 28, 29, 30 in your hands. And to report to 27, you must grab 24; And so on, you have to grab it

That is, you must grab to win.

2. In the same way, you must grab it

That is, you must grab to win.

3. In the same way, you must grab it

That is, you must grab to win.

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This type of problem can be inferred backwards, i.e., backward reasoning. As in the first question. If you want to get 30, you must first get 27

Because you get 27, regardless of whether the opponent takes one or two, you can choose to take one or two and get 30Of course, in this process, you have to understand that the other party takes one and you take two, and the other party takes two and you take one, so as to ensure that the number is increased in multiples of three. In the same way, 50 you have to get 47 first, but you have to grab 2 at the beginning, and then follow the 3 rule to grab up until you grab the same way, first grab 1 and then 4, 7 ......The last 100

Hope you understand,!

1. Let the other party count first, and you will make up 3. You're going to win.

2. You count first, and you make up the number of 3 less than 1.

3. The other party counts first, and you make up the number of 1 more than 3.

1 Let the other party count first, you make up three, and win. 2 The other party counts first, and you get more than three and one, and you win. 3 If you count first, make up the number less than three, and you win.

A cylinder is vertically cut into two parts along the diameter of the base, and the sum of the surface areas of the two parts is more than the surface area of the cylinder, and the area of the rectangle with a long base is the diameter and the width is the height of the cylinder.

The area of a rectangle: 2010 2 = 1005 square centimeters.

Cylindrical side area: square centimeters.

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It is 2010 square centimeters larger than the surface area of the cylinder, which means that the area of the two new rectangles is 2010 square centimeters.

The length of the rectangle is the diameter of the base, and the width of the rectangle is the height of the cylinder.

So, d*h=2010 2=1005 square centimeters.

Comparison: c*h=s side.

That is, the d*h=s side.

Cm.

Height * bottom diameter * 2 = 2010 (square centimeters).

Height * bottom diameter = 2010 2 = 1005 (square centimeters) and, i.e. two rectangles. 14*Bottom Diameter*High.

Therefore, the side area = bottom circumference * height = 3, and the side area = the surface area increased after the incision are two sections.