分类： 赛事动态

Tina started with one circle and one square: 蒂娜从一个圆和一个正方形开始：

Then she created this heart from these shapes:然后她用这些形状拼出了这颗心：

Tina only used these kinds of operations on the shapes:蒂娜仅对这些图形使用了以下这些操作：

• Rotate: Rotate the shape by any amount in either direction.旋转：可将图形沿任意方向旋转任意角度。
• Move: Move the shape anywhere.操作：将图形移动到任何位置。
• Duplicate: Create a copy of the shape in the same location.复制：在相同位置创建形状的副本。

Question:问题:

Which of the following sequence of operations could Tina have used?以下哪一系列操作是蒂娜可能用过的？

A. Duplicate circle. Rotate square. Move circle. Move circle.复制圆。旋转正方形。移动圆。移动圆。

B. Duplicate square. Rotate square. Move square. Move circle.复制正方形。旋转正方形。移动正方形。移动圆形。

C. Duplicate circle. Rotate circle. Move circle. Move square.复制圆。旋转圆。移动圆。移动正方形。

D. Move circle. Move circle. Duplicate circle. Move square.移动圆。移动圆。复制圆。移动正方形。

 

 

 

 

Explanation 解释

Beaver Jessica is making hamburgers according to the rules below.

海狸杰西卡正在按照以下规则制作汉堡包。

Buns 面包	Meat 肉	Sauce 酱汁	Pickles 泡菜	Lettuce 生菜	Onions 洋葱	Cheese 奶酪

1. The sauce should be right above the meat.酱汁应该正好在肉的上方。
2. Meat and cheese should be below the pickles, lettuce, and onions.肉和奶酪应该放在泡菜、生菜和洋葱的下面。
3. Onions should not be in contact with the buns.洋葱不应与面包接触。

Question:问题:

Which hamburger is correctly made according to the rules?哪个汉堡是按照规则正确制作的？

A.

B.

C.

D.

 

 

 

      

Explanation 解释

Answer: 答案:

D.

Explanation: 解释:

	This hamburger follows rules #1 and #2, but the onion touches the top bun, so it doesn't follow rule #3.这个汉堡符合规则 1 和 2，但洋葱碰到了上面的面包，所以不符合规则 3。
	This hamburger follows rule #1, but the lettuce is below the meat and the cheese, so rule #2 was not followed.这个汉堡符合规则 1，但生菜在肉和奶酪下面，所以没有遵循规则 2。
	The cheese is between the meat and the sauce, so it doesn't follow rule #1奶酪在肉和酱汁之间，所以它不符合规则 #1 。
	This hamburger satisfies all the rules, so this is the correct answer!这个汉堡包符合所有规则，所以这就是正确答案！

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（Bebras每日一练部分展示）

Havel has a programmable sewing machine. The machine can sew a  stitch or a   stitch and can also move the fabric forward 1 stitch space.哈维尔有一台可编程的缝纫机。这台机器可以缝制 1 针或 2 针，还能将布料向前移动 1 针的距离。

The sewing machine can sew both of these stitches in the same place (in any order), to get a stitch.缝纫机可以在同一位置缝这两种针脚（顺序不限），从而得到一种针脚。

The program for the machine consists of a sequence of characters +, x and →.该机器的程序由一系列字符 、x 和 → 组成。

The machine keeps repeating the program while the pedal of the sewing machine is held down.只要踩住缝纫机的踏板，机器就会不断重复这个程序。

Example:例子:

Running the program + → + x → x → will sew this pattern: 运行此程序 → x → x → 将会缝制出这种图案：

Question:问题:

Which program did Havel enter into the machine to get the following pattern?哈维尔输入了哪个程序到机器里才得到了下面这个图案？

 

 

 

 

 

 

Explanation 解释

Answer: 答案:

x → x → x + → x → + x →

Explanation: 解释:

Looking at the program, we see that the repeating pattern is .

查看该程序，我们发现重复的模式是 。

The first stitch is , after which the fabric should be moved, so the program starts with x →.

第一针缝完后，应移动布料，因此程序以 x → 开始。

The same for the second  stitch.

第二个针脚也是如此。

Then we have to sew a star - which can be done by sewing x and + on the same place (the order does not matter) and only then the fabric is moved.

然后我们要缝制一颗星——这可以通过在相同位置缝制 x 和 来完成（顺序无关紧要），只有这样布料才会移动。

To do this, we add x + → or + x → to our program.要做到这一点，我们在程序中添加 x → 或者 x &rarr； 。

Another cross is "made" by commands x → and another star by the + x → or x + → commands.

另一个十字是通过命令 x → 来“制作”的，而另一颗星则是通过 x → 或 x → 命令来生成的。

So the whole program is x → x → x + → x → + x →.

所以整个程序就是 x → x → x → x → x → 。

Option A: x → x → x + → x → + x → x → x → is incorrect, because it sews a sequence of  which is not the pattern that Havel got.

选项 A：x → x → x → x → x → x → x → 是错误的，因为它拼接了一个序列，这并非哈维尔所得到的模式。

Option B: x → x → x + → x → x → is incorrect, because the resulting pattern is , which is not the pattern Havel was aiming for.

选项 B：x → x → x → x → x → 是错误的，因为这样得到的模式是 ，这并非哈维尔所期望的模式。

Option D: + x → + x → x → + x → x → is also incorrect. The beginning of the program + x → + x → will sew  which is not in Havel's pattern.

选项 D：x → x → x → x → x → 也是错误的。程序的开头 x → x → 会缝合出 ，这不符合哈维尔模式。

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（Bebras每日一练部分展示）

Lila and her friends are playing a guessing game.莉拉和她的朋友们正在玩猜谜游戏。

To start the game, Lila puts a marble in bag A, a gem in bag B, and a piece of paper in bag C.要开始游戏，莉拉把一颗弹珠放进袋子 A，一块宝石放进袋子 B，还把一张纸放进袋子 C。

 

Then, while her friends' eyes are closed, Lila moves the items in the bags.然后，在朋友们都闭上眼睛的时候，莉拉把袋子里的东西挪了挪位置。

1. First, she switches the items in bags A and B.首先，她把 A 袋和 B 袋里的东西调换了。
2. Then, she switches the items in bags A and C.然后，她把 A 袋和 C 袋里的东西对换了。
3. Lastly, she switches the items in bags B and C.最后，她把 B 袋和 C 袋里的东西调换了。

Question 问题:

Where are Lila's items now?莉拉的东西现在在哪里？

(Drag them into the correct bag and press "Save.")（将它们拖入正确的袋子，然后点击“保存”。）

 

 

 

 

 

Explanation 解释

Sam has 30 hexagonal puzzle pieces, 10 of each of these three types:山姆有 30 块六边形拼图，这三种类型各 10 块：

When Sam places three pieces in the following pattern, the three pieces must EITHER 1) all be the same color -OR- 2) all different colors.当山姆以如下模式放置三枚棋子时，这三枚棋子要么 1）颜色完全相同，要么 2）颜色各不相同。

Question:问题:

Fill in all the white tiles with the correct colors.用正确的颜色填满所有的空白瓷砖。

(Click on a tile to change its color. Press 'Save' when you have finished the puzzle.)（点击一个方块来改变其颜色。完成拼图后按“保存”。）

 

 

 

 

 

Explanation 解释

Answer: 答案:Explanation: 解释:

When we know the colours of two pieces beside each other, we know what the colour of the piece above them must be. For example, consider the bottom left unknown piece. Since the two pieces below it are green, it must also be green. On the other hand, the piece to its right must be blue because the two pieces below it are green and yellow. We can use this idea to work from the bottom to the top of the tower. There is only one possible answer.

当我们知道相邻两块的颜色时，就能确定它们上方那块的颜色。比如，考虑左下角那块未知的积木。由于它下面的两块是绿色的，所以它也一定是绿色的。另一方面，它右边的那块一定是蓝色的，因为下面的两块分别是绿色和黄色。我们可以用这个思路从塔的底部往上推导。答案只有一个。

Note that we can work in any order on each row of the tower.

请注意，对于塔的每一行，我们可以按任意顺序进行操作。

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（Bebras每日一练部分展示）

Can you help the bees find their compartment in the hive?你能帮蜜蜂找到它们在蜂巢里的隔间吗？   Underneath each bee is a picture that tells the bee a rule about where its compartment is. In each rule, the bee's position is represented by the darker orange cell. To help the bees understand the rules, the compartment turns dark orange when a bee is not allowed to be there, and green when the bee is allowed to be there.每只蜜蜂下方都有一张图片，向蜜蜂展示其所在隔间的位置规则。在每条规则中，蜜蜂的位置由颜色更深的橙色单元格表示。为了帮助蜜蜂理解规则，当蜜蜂不允许在某个隔间时，该隔间会变成深橙色；当蜜蜂被允许在该隔间时，隔间则会变成绿色。

bee is allowed here 蜜蜂可以在这里 bee is not allowed here这里禁止养蜂。

Task:任务:

Drag and drop all of the bees into the hive, following each bee's rule.按照每只蜜蜂的规则，将所有蜜蜂拖放到蜂巢中。

(Press 'Save' when you have finished.) （完成后请按“保存”。）

 

 

 

 

 

 

Explanation 解释

2022-2023年Bebras挑战练习题

Kits (6-8岁) 集合

名称	类型
Coloring Page着色页面	A
Most Popular Book 最受欢迎的书	A
Put Your Shirts Away 把你的衬衫收起来	A
Tube of candy 一管糖果	B
Pearls 珍珠	B
Pick Up Sticks 捡起棍子	B
Go Green 走绿色	C
Strawberry Hunt 草莓狩猎	C
Tortoise and Hare 乌龟和野兔	C

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（Bebras每日一练部分展示）

A tortoise and a hare are going to race against each other on the track shown below.一只乌龟和一只野兔将在下面所示的赛道上进行赛跑。

Beavers love to play a game called "Strawberry Hunt."海狸们喜欢玩一个叫做“草莓狩猎”的游戏。

Rules: 规则:

1. A different number of strawberries is put on each area of a field.在一块田地的不同区域放置了数量不等的草莓。
2. Starting from any field, take 3 steps.从任何一块田地开始，走三步。
3. Each step can be one of:每一步都可以是以下之一：
   • move up one area 向上移动一个区域
   • move down one area 向下移动一个区域
   • move right one area 向右移动一个区域
   • move left one area 向左移动一个区域
4. Eat all the strawberries you found.把你找到的所有草莓都吃掉。

Examples:例子:

Choosing the path on the left, a beaver will eat 9 + 1 + 6 + 5 = 21 strawberries.

Choosing the path on the right, the beaver will eat  7 + 1 + 5 + 8 = 21  strawberries as well. 

选择左边的路，一只海狸会吃掉 9 + 1 + 6 + 5 = 21 个草莓。选择右边的路，海狸也会吃掉  7 + 1 + 5 + 8 = 21  个草莓。

Little Beaver is playing on this grid:小海狸正在这个网格上玩耍：

Question:

How many strawberries can Little Beaver eat at most?小海狸最多能吃多少颗草莓？

 

 

 

 

 

Explanation 解释

Answer: 答案:23

Explanation: 解释:

Though there are 51 possible ways to finish the game (see table below), we don't have to check all 51 total sums of strawberries. Here is how:

尽管完成游戏有 51 种可能的方式（见下表），但我们不必检查所有 51 种草莓的总和。方法如下：

We know that each player can reach 4 areas that in their short path. These paths can only make the following shapes:

我们知道每个玩家在其短路径中可以到达 4 个区域。这些路径只能形成以下形状：

Now, we check these shapes including any of the areas with 9 or 8 strawberries (including all shapes with both of these areas). Since checking field combinations with 9 or 8 strawberries will also cover those fields with 5, 6 or 7 strawberries, all grids with larger numbers of strawberries will be covered. Then, we can find the largest total number of strawberries:

现在，我们检查这些形状，包括任何有 9 个或 8 个草莓的区域（包括所有同时具有这两种区域的形状）。由于检查有 9 个或 8 个草莓的田地组合也会涵盖那些有 5 个、6 个或 7 个草莓的田地，所以所有草莓数量更多的格子都会被涵盖。然后，我们就能找到草莓总数的最大值：

Now, note that without the areas with 8 and 9 strawberries, the maximum sum of strawberries on any other combination of four areas is 7 + 6 + 5 + 5 = 23. That is, also without areas 8 and 9, 23 cannot be exceeded. Therefore, Little Beaver can eat at most 23 strawberries.

现在请注意，如果没有 8 个和 9 个草莓的区域，那么其他任意四个区域的草莓总数最大为 7 + 6 + 5 + 5 = 23 个。也就是说，即便没有 8 个和 9 个草莓的区域，总数也无法超过 23 个。因此，小海狸最多能吃 23 个草莓。

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（Bebras每日一练部分展示）

The beavers are painting pictures, made of different shapes, on a computer.海狸们正在电脑上绘制由不同形状组成的图画。

They can paint any shape by selecting one of four colors and then clicking on the shape.他们可以通过选择四种颜色中的一种，然后点击形状来给任何形状上色。

Example:例子：

The beavers could paint the 'face'  completely blue with just two moves: 海狸只需两步就能把“脸”完全涂成蓝色：

1. Select yellow, paint the red part to get: 选择黄色，将红色部分涂成黄色得到：
2. Then select blue, paint the yellow part to get: 然后选择蓝色，将黄色部分涂成蓝色，得到：

Task 任务:

Make the pattern below completely green with the fewest number of moves possible.

(Press 'Save' when you have finished.)（完成后请按“保存”。）用尽可能少的步数将下面的图案全部涂成绿色。

 

 

 

 

 

Explanation 解释