分类： 赛事动态

Beaver Sofia and her group of friends are playing a game called 'Lights On.'海狸索菲亚和她的朋友们正在玩一个叫“开灯”的游戏。

The game has 8 large buttons which, when stood upon, send a signal down a wire.该游戏有 8 个大按钮，踩上去就会通过电线发出信号。

These wires pass through some triangular or square boxes before eventually reaching a light bulb.这些电线在最终通向灯泡之前，会穿过一些三角形或方形的盒子。

• A triangle will only send a signal if BOTH incoming wires send it a signal.一个三角形只有在两条输入线都向其发送信号时才会发送信号。
• A square will send on a signal if only ONE of the incoming wires send it a signal.如果仅有一根输入线向一个方块发送信号，那么该方块就会发送信号。
• The friends win the game if they can turn the light on.如果朋友们能打开灯，他们就赢得比赛。

Task:任务:

Select which buttons the beavers could stand on to turn on the light and win the game. 选择海狸可以踩踏的按钮，以点亮灯光并赢得游戏。

(Click on the switches to place and remove beavers. Press 'Save' when you have finished.)（点击开关放置和移除海狸。完成后按“保存”。）

 

 

 

 

 

Explanation 解释

Answer: 答案:

There are 16 possible combinations of the 8 buttons that will turn the light-bulb on. One is shown below:有 8 个按钮的 16 种可能组合可以点亮灯泡。其中一种组合如下所示：

Explanation: 解释:

A good approach to this question is to work backwards. The light-bulb at the end is connected to a wire in column 4 that comes from a triangle. For this wire to be ON, we know that the two wires leading into the triangle must also be ON.解决这个问题的一个好办法是从后往前推。最末端的灯泡与第 4 列的一根导线相连，这根导线来自一个三角形。要使这根导线处于接通状态，我们知道通向这个三角形的两根导线也必须处于接通状态。

These wires are connected to a triangle and a square.这些电线连接着一个三角形和一个正方形。

We know this triangle must be ON, therefore the wires connecting to it must both be ON.我们知道这个三角形一定是亮着的，所以连接到它的两根线也一定是亮着的。

We know the square must be ON, therefore one of the wires connecting to it must be ON, and the other must be OFF.我们知道这个方块一定是亮着的，所以连接它的两条线中必有一条是亮着的，另一条是熄灭的。

For columns 1 and 2, we will look at the wires in the top half and bottom half separately.对于第 1 列和第 2 列，我们将分别查看上半部分和下半部分的电线。

Top half:

Both wires in column 2 must be ON. Therefore, the top 2 buttons in column 1 must be pressed, and exactly one of the buttons of the bottom 2 buttons must be pressed. 上半部分:第二列的两根电线都必须接通。因此，第一列的上面两个按钮必须按下，而下面两个按钮中必须且只能按下其中一个。

Bottom half:

Given the square is in the ON position, exactly one of the wires leading into it must be ON, and the other is OFF. Therefore, either the triangle leading into it must be ON and the square OFF or vice versa. There are multiple ways of doing this - the solution shown above demonstrates one possible approach. Here, the triangle is ON and therefore the top two buttons must be pressed, meaning the square must be OFF and the bottom two buttons are either both pressed or not pressed (in this case, both are not pressed). 下半部分:鉴于正方形处于开启状态，进入它的两条线中必有一条开启，另一条关闭。因此，进入它的三角形要么开启而正方形关闭，要么相反。实现这一目标的方法不止一种——上面展示的解决方案只是其中一种可能的途径。在此，三角形开启，所以上面的两个按钮必须按下，这意味着正方形关闭，而下面的两个按钮要么都按下，要么都不按（在这种情况下，两个按钮都没有按）。

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John wants to visit his friend Mary, but he doesn't know where she lives. Fortunately, he has a map and some information:约翰想去拜访他的朋友玛丽，但他不知道她住在哪里。幸运的是，他有一张地图和一些信息：

• The Island People think of themselves as neighbors if they can visit each other by crossing only one wooden walkway.岛上的居民认为，如果彼此之间只需穿过一条木板路就能互相拜访，那他们就算是邻居了。
• Mary, Zac, and Pan have four neighbors.玛丽、扎克和潘有四个邻居。
• Zac and Pan are neighbors with Niki.扎克和潘是尼基的邻居。
• Niki has no other neighbors.妮基没有其他邻居。

Question:问题:

Where is Mary's house?  玛丽的房子在哪里？ 

 

 

 

 

 

 

Explanation 解释

Answer: 答案:

House 4 shown below. 如下所示的 4 号房屋。

Explanation: 解释:

To solve the problem, it is necessary to focus on the paths, that go from each house. We first need to identify the houses with four paths. There are three such houses: 4, 5 and 7.

要解决这个问题，有必要关注从每栋房屋出发的道路。首先，我们需要找出有四条道路的房屋。这样的房屋有三栋：4 号、5 号和 7 号。

So Mary, Zac and Pan live in one of these three houses, but we need to find out where exactly Mary lives.所以玛丽、扎克和潘住在这三栋房子中的一栋，但我们得弄清楚玛丽到底住在哪一栋。

The other two pieces of information describe Niki's house. We can deduce that there are only two paths from it. So Niki lives in one of the houses with numbers 1, 2 or 6.另外两条信息描述了妮基的房子。我们可以推断出那里只有从那里有两条路。所以妮基住在 1 号、2 号或 6 号房子中的一所。

As Niki is neighbour with Pan and Zac, we can further deduce that:由于妮基与潘和扎克是邻居，我们还可以进一步推断出：

• Niki lives in house number 6尼基住在 6 号房子。

• Zac and Pan live at numbers 5 and 7 (or the other way around) 扎克和潘分别住在 5 号和 7 号（或者反过来）。Thus, there is only one house with four paths that can be Mary's house. It is the one with the number 4! 因此，只有一座房子有四条路可以通往那里，那座房子可能是玛丽的家。它就是那座有数字4！

 

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Castorus found two good hiding places for his food.卡斯特鲁斯找到了两个藏食物的好地方。

He uses a map divided into squares to help him remember where his food is hidden. He wants to mark the squares, where his hiding places are, on his map with an X. However, if his rival Biberina finds the map, she would know where to look!他用一张划分成方格的地图来帮助自己记住食物藏在哪里。他想在地图上用 X 标出藏食物的地方所在的方格。然而，如果他的对手比贝里娜发现了这张地图，她就会知道该去哪里找！

Explanation 解释

Answer: 答案:

To find them, we look at the original map and find that there are two rows and two columns where the number of “X”s is not even: Rows 2 and 5 (from the bottom), and columns 3 and 5 (from the left).要找到它们，我们查看原始地图，发现有两行两列的“X”数量不是偶数：从下往上数的第 2 行和第 5 行，以及从左往右数的第 3 列和第 5 列。

This shows the rows and columns involved in yellow:这会将涉及的行和列以黄色显示：

The two erased “X”s showing the real hiding spots must have been in them! So we must find a way to add them back into these rows and columns to restore the even constraint.那两个被擦掉的表示真正藏匿点的“X”肯定就在其中！所以我们必须想办法把它们重新加回到这些行和列中，以恢复偶数约束条件。

There are 4 squares at the intersection of the yellow rows and columns. The upper red intersection square is marked with an “X” already: it cannot be a hiding place, since we know Castorus has erased the “X”s from the true hiding places. So in order to recover an even number of “X”s on that second row, we have to add it in the upper left yellow intersection square: we now know one hiding place.在黄色行和列的交叉处有 4 个方格。上面红色交叉方格已标有“X”：它不可能是藏匿处，因为我们知道卡斯特鲁斯已从真正的藏匿处擦掉了“X”。所以为了在第二行恢复偶数个“X”，我们得在左上角的黄色交叉方格加上一个“X”：现在我们知道了一个藏匿处。

The second hiding place can be determined as follows: Once we’ve found the first one, we cannot place the second one in the bottom left red intersection square, as this would result in 3 “X”s in the second column, and 3 is not even. The only choice left is the lower right intersection square, which gives the answer shown above.第二个藏匿点的确定方法如下：一旦我们找到了第一个藏匿点，就不能将第二个藏匿点放在左下角的红色交叉方格内，因为这样会导致第二列出现 3 个“X”，而 3 是奇数。唯一的选择就是右下角的交叉方格，这给出了上面所示的答案。

This shows the map before Castorus erased “X”s, with an even number of “X”s in each row and column:这展示了卡斯特鲁斯擦掉“X”之前的地图，每行和每列的“X”数量均为偶数：

2022-2023年Bebras挑战练习题

Castors (8-10岁) 集合

名称	类型
Coloring Page 着色页面	A
Tube of candy 一管糖果	A
Most Popular Book 最受欢迎的书	A
Pick Up Sticks 捡起棍子	A
Beehive 蜂巢	B
Colorful Tower 五彩缤纷的塔	B
Tortoise and Hare 乌龟和野兔	B
Lila's Guessing Game 莉拉的猜谜游戏	B
Embroidery Machine 绣花机	C
Hamburger Recipe 汉堡包配方	C
Heart Graphics 心的图形	C
Sailor Necklace 水手项链	C

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（Bebras每日一练部分展示）

Here are instructions for making a sailor necklace using blue striped beads and solid red beads:以下是使用蓝色条纹珠子和纯红色珠子制作水手项链的说明：

1. Every sailor necklace starts by placing one blue striped bead and one red bead on a string.每条水手项链都是先在一根线上串上一颗蓝色条纹珠子和一颗红色珠子开始的。
2. The sailor necklace can then be made longer by either:水手项链随后可以通过以下任一方式变长：

• Adding two blue striped beads to the right end of the string;在串珠的右端加上两颗蓝色条纹珠子；
• Or adding a red bead to each end of the string.或者在绳子的两端各加上一颗红色的珠子。

These two actions can be done many times in any order to build longer and longer necklaces.这两个动作可以以任意顺序重复多次，从而制作出越来越长的项链。

Question:问题:

Which necklace below is NOT a sailor necklace? 下面哪条项链不是水手项链？

A.

B.

C.

D.

    

 

 

 

 

Explanation 解释

The correct answer is D. .  There are many ways you could have solved this task.解决这个任务的方法有很多。

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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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）