2022-2023年Bebras挑战练习题-Pantry Map(储藏室地图)

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!

To confuse Biberina, Castorus adds some more X's in other squares of the map, making sure that the total number of X's in each row and each column is even. (Note: 0 is also an even number).为了迷惑比贝里娜,卡斯特鲁斯在地图的其他方格中又添加了一些“X”,确保每行和每列中“X”的总数都是偶数。(注:0 也是偶数)
Then Castorus erases the two X's showing where his hiding places are. The resulting map is shown below.然后卡斯托鲁斯擦掉了显示他藏身之处的两个“X”。最终的地图如下所示。
Question: 问题:
In which two squares has Castorus hidden his food?卡斯特鲁斯把食物藏在了哪两个方格里?

(Mark them on the map and then press 'Save' when you are finished.)(在地图上标记它们,完成后点击“保存”。)

2022-2023年Bebras挑战练习题-Pantry Map(储藏室地图)

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:2022-2023年Bebras挑战练习题-Pantry Map(储藏室地图)

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:

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2022-2023年Bebras挑战练习题-Castors (8-10岁) 集合

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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2022-2023年Bebras挑战练习题-Sailor Necklace(水手项链)

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。

2022-2023年Bebras挑战练习题-Sailor Necklace(水手项链)

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。

We will name action one "B" and action two "W".我们将把第一个动作命名为“B”,把第二个动作命名为“W”。

Here are three possibilities:以下是三种可能性:

  1. You could have constructed each necklace by first locating the two starting beads and then perform a series of B and W actions. Necklace  can be made starting with the second and third beads, and then performing actions W-B-B. Necklace  can be made starting with the third and fourth beads, and then performing the actions W-W-B. Necklace  can be made starting with the second and third beads, and then performing the actions B-W-B. However, if you look at necklace , the starting beads must be the second and third beads. You can perform action W once, but then there are no actions that will construct the rest of the necklace.你可以通过先确定两个起始珠子,然后依次执行一系列的 B 和 W 操作来制作每条项链。项链 可以从第二和第三颗珠子开始,然后执行 W-B-B 操作。项链 可以从第三和第四颗珠子开始,然后执行 W-W-B 操作。项链 可以从第二和第三颗珠子开始,然后执行 B-W-B 操作。然而,如果你看项链 ,起始珠子必须是第二和第三颗珠子。你可以执行一次 W 操作,但之后没有操作可以完成项链的其余部分。
  2. This approach would not work well if the necklace was very long and had many possible starting beads. In this case, you could instead try a deconstructive approach where you repeatedly remove beads by reversing the B and W actions until you only have two starting beads left.如果项链很长且有多种可能的起始珠子,这种方法就不太管用了。在这种情况下,您可以尝试一种反向构建的方法,即反复通过反转黑白操作来移除珠子,直到只剩下两个起始珠子为止。
  3. A third strategy is to notice something about the parity of the beads. According to the sailor necklace instructions, there will always be an odd number of solid red beads and an odd number of striped blue beads. Can you see why? Necklace  has an even number of both types of beads and therefore cannot be a sailor necklace. 第三种策略是留意珠子的奇偶性。根据水手项链的制作说明,实心红珠子的数量和条纹蓝珠子的数量总是奇数。你能明白其中的原因吗?项链 两种颜色的珠子数量都是偶数,所以它不可能是水手项链。

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2022-2023年Bebras挑战练习题-Heart Graphics(心的图形)

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

2022-2023年Bebras挑战练习题-Heart Graphics(心的图形)

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

Answer: 答:

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

2022-2023年Bebras挑战练习题-Heart Graphics(心的图形)

The square needs to be rotated so that one corner is facing down. This only happens in sequences "Duplicate circle. Rotate square. Move circle. Move circle." and "Duplicate square. Rotate square. Move square. Move circle.". Next, you can see that you need two circles to create a heart.正方形需要旋转,使一个角朝下。这种情况只会在“复制圆。旋转正方形。移动圆。移动圆。”和“复制正方形。旋转正方形。移动正方形。移动圆。”这两个序列中出现。接下来,您可以看到需要两个圆才能组成一个心形。

Sequence "Duplicate square. Rotate square. Move square. Move circle." cannot be correct because it does not create a second circle. This leaves the first one: "Duplicate circle. Rotate square. Move circle. Move circle." as the only correct sequence. The images below show the shapes (made see-through) after each of the first three operations of this sequence. After the final fourth operation, the heart is created. This verifies that Tina could have used sequence "Duplicate circle. Rotate square. Move circle. Move circle."序列“复制正方形。旋转正方形。移动正方形。移动圆形。”不可能正确,因为它没有生成第二个圆形。这使得第一个序列:“复制圆形。旋转正方形。移动圆形。移动圆形。”成为唯一正确的序列。下面的图片展示了此序列前三个操作后图形(已设置为透明)的样子。在最后的第四个操作之后,心形就形成了。这证实了蒂娜可能使用了序列“复制圆形。旋转正方形。移动圆形。移动圆形。”

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2022-2023年Bebras挑战练习题-Hamburger Recipe(汉堡包配方)

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  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。
2022-2023年Bebras挑战练习题-Hamburger Recipe(汉堡包配方) 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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2022-2023年Bebras挑战练习题-Embroidery Machine(绣花机)

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:

2022-2023年Bebras挑战练习题-Embroidery Machine(绣花机)

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 → 。

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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2022-2023年Bebras挑战练习题-Lila's Guessing Game(莉拉的猜谜游戏)

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。

2022-2023年Bebras挑战练习题-Lila's Guessing Game(莉拉的猜谜游戏)  

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

Answer: 答:The paper is in bag A, the gem is in bag B and the marble is in bag C.纸在 A 袋里,宝石在 B 袋里,弹珠在 C 袋里。

Explanation: 解释:Lila switches the items three times. After the first switch, the bags look like this:莉拉将物品调换了三次。第一次调换后,袋子看起来是这样的:2022-2023年Bebras挑战练习题-Lila's Guessing Game(莉拉的猜谜游戏)  
After the second switch, the bags look like this:第二次交换之后,这些袋子看起来是这样的:
After the third and final switch, the bags look like this:在第三次也是最后一次交换之后,这些袋子看起来是这样的:

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2022-2023年Bebras挑战练习题-Colorful Tower(五彩缤纷的塔)

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:

2022-2023年Bebras挑战练习题-Colorful Tower(五彩缤纷的塔)

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:2022-2023年Bebras挑战练习题-Colorful Tower(五彩缤纷的塔)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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2022-2023年Bebras挑战练习题-Beehive(蜂巢)

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”。)

2022-2023年Bebras挑战练习题-Beehive(蜂巢)

 

 

 

 

 

 

Explanation 解释

Answer: 答案:

Explanation: 解释:

You can solve the task just by trying it out, but this can take a lot of time. A quicker way to solve this task, is by taking a closer look at the bees’ rules. In the following image, you see each bee and its rule. The cells, in which the bee can be placed according to its rule, are coloured green.

您可以通过尝试来解决此任务,但这可能会耗费大量时间。解决此任务的更快方法是仔细研究蜜蜂的规则。在下面的图片中,您可以看到每只蜜蜂及其规则。根据其规则可以放置蜜蜂的单元格被涂成了绿色。

You see that some bees can be placed in only one cell of the hive and others can be placed in different cells. For example, bee 2 can only be placed in one cell, because there is only one way to place the bee’s part of the hive in the complete hive.

您会发现有些蜜蜂只能被安置在蜂巢中的一个蜂房里,而有些蜜蜂则可以被安置在不同的蜂房里。比如,蜜蜂 2 只能被安置在一个蜂房里,因为将这只蜜蜂所占的蜂巢部分放入完整蜂巢的方式只有一种。

2022-2023年Bebras挑战练习题-Beehive(蜂巢)

To solve the task, you proceed like this: First place the bees for which only one placement is possible, that is to say bees 2, 3 and 4.

要解决这个问题,你可以按以下步骤操作:首先放置那些只能有一种放置方式的蜜蜂,也就是蜜蜂 2、3 和 4。

There is then only one possible place left for bees 1 and 5. In the same way, you place in order bee 6 and finally bee 7.

那么,蜜蜂 1 和 5 就只剩下一个可能的位置了。同样地,依次放置蜜蜂 6,最后放置蜜蜂 7。

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2022-2023年Bebras挑战练习题-Kits (6-8岁) 集合

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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