分类： 赛事动态

Maria found a box containing hidden treasure, but the box was locked.玛丽亚发现了一个装有隐藏宝藏的盒子，但盒子是锁着的。

To unlock the box, she needs to use the correct combination of three shapes.要打开这个盒子，她需要使用三个图形的正确组合。

Help Maria unlock the box by following the given hints on the right of the combinations shown below.请按照下面组合密码右侧给出的提示帮助玛丽亚打开这个盒子。

Question:问题:

Which of the following combinations will unlock the treasure box?以下哪一种组合能打开宝箱？

A.

B.

C.

D.

   

 

 

 

 

 

Explanation 解释

Answer: 答案:

Explanation: 解释:

We will start by eliminating the shapes that do not fit into the combination that unlocks the box.我们将从排除那些不符合能打开盒子的组合的形状开始。

In the second row of hints, we see that nothing belongs in our combination, which means that the Christmas three , diamond  and arrow  do not lead to unlocking the box.在第二行提示中，我们看到没有任何东西属于我们的组合，这意味着圣诞树、菱形和箭头都不能打开这个盒子。

In the last row of hints, we see that one shape is correct, but placed incorrectly.在最后一行提示中，我们看到有一个形状是正确的，但位置放错了。

We have previously concluded that the Christmas tree and the arrow are not used, so the shape we need is a star , but it is placed incorrectly.我们之前已经得出结论，圣诞树和箭头没有用到，所以我们需要的形状是星星，但它的位置放错了。

The possible positions of the start are as follows:起点可能的位置如下：

 or 或We can continue to find the other two shapes.我们可以继续找出另外两种形状。

From the first row, we see that one form is correct and in the right place. We reject the arrow because it does not belong to the final combination, so it follows that one of these combinations is correct:从第一行来看，有一种形式是正确的，并且处于正确的位置。我们排除箭头，因为它不属于最终的组合，所以可以得出结论，这些组合中有一个是正确的：

 or 或From the third row, we see that two shapes are correct, but placed incorrectly.从第三行来看，有两个图形是正确的，但位置放错了。

We definitely need the star, but its position is not in the middle, so now we have definitely found the position of the star and that position is given in the following picture:我们确实需要那颗星，但它的位置不在中间，所以现在我们已经确切地找到了那颗星的位置，其位置在下面的图片中给出：

We found one shape and it's correct position. Likewise, we continue this process to find the remaining two shapes.我们找到了一个形状及其正确位置。同样地，我们继续这个过程来寻找剩下的两个形状。

From the first row, we had:从第一行，我们有： or 或

Since we found the star to be in the first position, the triangle can't be in the first position. So, it follows that the moon is in its correct position. This leaves us with:既然我们发现星星处于第一个位置，那么三角形就不能在第一个位置。所以，月亮就在其正确的位置。这样就剩下：

From the fourth hint, we see that one shape is correct, but incorrectly placed. The triangle  is out, and the only position left is the middle position. The heart  can't be correct, because it is in the middle position. Thus, the only shape that can be in the middle position is the circle .从第四个提示中可以看出，有一个图形是正确的，但位置放错了。三角形被排除在外，剩下的唯一位置就是中间位置。心形不可能正确，因为它在中间位置。所以，唯一能放在中间位置的图形就是圆形。

There are other possible ways to determine the answer other than the explanation above. All these different ways will still lead to the correct answer.除了上述解释之外，还有其他可能的方法来确定答案。所有这些不同的方法最终都会得出正确的答案。

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In a land called Mysteria, there lives a wizard. 在一片名为神秘之地的大陆上，住着一位巫师。

The wizard can transform items into an assortment of other items. The order of these items will always be the same.这位巫师可以把物品变成各种各样的其他物品。这些物品的排列顺序总是固定的。

For example: if a coin is transformed into a potion and a dragon, the potion will always be on the left of the dragon.例如：如果一枚硬币被转化成一瓶药水和一条龙，那么药水总是会在龙的左边。

The table below shows the two possible ways a wizard can transform a diamond and the two possible ways he can transform a coin:下表展示了巫师将钻石进行转化的两种可能方式以及将硬币进行转化的两种可能方式：

Before 之前	After 后

  These magical transformations can happen any number of times, in any order. That is, any diamond and any coin can be transformed at any time. In this way, a long line of magical things can be created from a single diamond or coin.这些神奇的变化可以以任意次数、任意顺序发生。也就是说，任何一颗钻石和任何一枚硬币都可以在任何时候进行变化。通过这种方式，从一颗钻石或一枚硬币出发，可以创造出一长串神奇的事物。

Question:
问题:

Starting with a single diamond, which line is not possible to obtain?从一颗钻石开始，哪一行是无法得到的？

A.

B.

C.

D.

   

 

 

 

 

 

Explanation 解释

The correct answer is: 正确答案是：

Suppose the magical transformations are numbered 1 through 4 as follows:假设这些神奇的变形按如下方式编号为 1 至 4：

Number 数量	Before 之前	After 后
1
2
3
4

can be obtained by starting with a single wizard and applying transformations, 1, 4, 2 and 3 in that order.可以通过从一个巫师开始，并依次应用变换 1、4、2 和 3 来获得。

can be obtained by starting with a single wizard and applying transformations 2, 2, 3, 4, and 1 in that order.可以通过从一个巫师开始，并依次应用变换 2、2、3、4 和 1 来获得。

can be obtained by starting with the single wizard and applying transformations 2, 1, 3 and 3 in that order.可以通过从单个巫师开始，并依次应用变换 2、1、3 和 3 来获得。

One quick way to see that  is not possible is to notice that the transformation rules always create a potion and a dragon at the same time. Therefore, the number of potions in Mysteria will always equal the number of dragons, which is not the case in this answer option.要快速看出这是不可能的，只需注意到转化规则总是同时生成一瓶药剂和一条龙。因此，神秘岛上的药剂数量总是等于龙的数量，而这在该选项中并非如此。

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The Little Beaver is in a maze. The maze is made up of two floors, each with its own grid of obstacles.小海狸被困在了一个迷宫里。这个迷宫由两层组成，每层都有自己的障碍网格。

The Little Beaver can move between two adjacent cells within one floor if there is no wall between the cells; this takes one second.小海狸可以在同一层内相邻的两个格子之间移动，前提是这两个格子之间没有墙；这需要花费一秒钟。

The Little Beaver can also use her magic wand to move to the corresponding cell of the other floor; this takes five seconds.小海狸还可以用她的魔法棒移动到另一层对应的单元格；这需要五秒钟。

For example, if the Little Beaver is in cell A, there are three possible moves:例如，如果小海狸在 A 单元格，那么有三种可能的移动方式：

1. Move left. This move takes 1 second.1. 向左移动。此动作耗时 1 秒。

2. Move down. This move takes 1 second.2. 向下移动。此动作耗时 1 秒。

3. Move to the corresponding cell of the other floor. This move takes 5 seconds.3. 移动到另一层对应的单元格。此移动耗时 5 秒。

The Little Beaver starts at cell A and wants to reach cell B as soon as possible. 小海狸从 A 单元格出发，想要尽快到达 B 单元格。

Question:问题:

What is the shortest time needed for the Little Beaver to reach cell B, if starting from cell A?如果小海狸从 A 单元格出发，那么它到达 B 单元格所需的最短时间是多少？

A. 16

B. 17

C. 18

D. 20

 

 

 

 

 

Explanation 解释

Troy has a collection of gems.特洛伊收藏了一些宝石。

He ranks his gems from his overall favorite to his least favorite.他将自己收藏的宝石从最喜爱的到最不喜爱的依次排列。

Sarah knows which gems are in Troy's collection, but she does not know how he has ranked them.萨拉知道特洛伊收藏的宝石都有哪些，但她不知道他是如何给这些宝石排序的。

Sarah has a plan to find out which gem is Troy's overall favorite:萨拉有个计划，要弄清楚特洛伊最喜欢哪种宝石：

• Sarah chooses four of Troy's gems and asks Troy: "Out of this group of four, which gem is your favorite?"萨拉从特洛伊的宝石中挑了四颗，然后问特洛伊：“在这四颗宝石中，哪一颗是你最喜欢的？”
• Sarah chooses a new set of four gems and asks her question again.萨拉挑选了一套新的四颗宝石，再次提出了她的问题。
• Then she chooses a third set of four gems and asks her question for the last time.然后她挑选出第三组四颗宝石，并最后一次提出她的问题。

Note: When Sarah chooses her second and third set of four gems, she may sometimes include gems she has chosen before.注意：当萨拉选择她的第二组和第三组四颗宝石时，有时可能会包含之前选过的宝石。

Question:问题:

If Sarah is to successfully find Troy's overall favorite gem, what is the largest possible number of gems in Troy's collection?如果萨拉要成功找到特洛伊最喜欢的宝石，那么特洛伊收藏的宝石最多可能有多少颗？

A. 8

B. 10

C. 11

D. 12

 

 

 

 

 

Explanation 解释

Answer: 答案:

10

Explanation: 解释:

With 10 gems, Sarah can ask Troy about eight different gems with the first two requests. Troy's answer to each of these requests is a candidate to be his favourite of all his gems, but the other three cannot be. Therefore, with Sarah's third and final request, she can include these two candidates and the two gems that have not yet been part of a request. Troy's answer to this third request must be his favourite gem.萨拉有 10 颗宝石，她可以用前两次询问来询问其中的 8 颗。特洛伊对这两次询问的回答可能是他所有宝石中最喜欢的那颗，但另外三颗则不可能。因此，在萨拉的第三次也是最后一次询问中，她可以把这两个可能的答案以及之前未被询问过的两颗宝石都包括进去。特洛伊对这次询问的回答一定是他最喜欢的那颗宝石。

We have shown that there is a strategy of Sarah's that works if there are 10 gems. (Note that there are other correct strategies that work for 10 gems.)我们已经证明，如果宝石有 10 颗，那么萨拉有一种策略是可行的。（请注意，对于 10 颗宝石，还有其他正确的策略也是可行的。）

If Troy has at least 11 gems, we consider Sarah's first two requests.如果特洛伊至少有 11 颗宝石，我们就考虑萨拉的前两个请求。

If at least one gem is part of both requests, then at least four gems will be unconsidered after the first two requests. In this case, Sarah must ask about these four unconsidered gems, because if she doesn't, an unconsidered gem could be Troy's favourite. On the other hand, she won't have any information about Troy's favourite among the last four unconsidered gems compared to the other seven gems. In this case, her strategy cannot determine which gem is Troy's most favourite.如果至少有一颗宝石同时属于两个请求，那么在前两个请求之后，至少会有四颗宝石未被考虑。在这种情况下，萨拉必须询问这四颗未被考虑的宝石，因为如果不这样做，未被考虑的宝石中可能就有特洛伊最喜欢的那颗。另一方面，与另外七颗宝石相比，她对最后四颗未被考虑的宝石中哪一颗是特洛伊最喜欢的毫无头绪。在这种情况下，她的策略无法确定哪颗宝石是特洛伊最喜欢的。

If there is no gem that is part of Sarah's both first two requests, then candidates for Troy's favourite include the two answers to these requests and the three remaining unconsidered gems. This is a total of five possibilities for Troy's most favourite gem, and Sarah does not have any information about how they rank, so her strategy cannot work.如果莎拉最初的两个请求中没有共同包含的宝石，那么特洛伊最喜欢的宝石候选者就包括这两个请求的答案以及剩下的三颗未被考虑的宝石。这样特洛伊最喜欢的宝石就有五种可能性，而莎拉对它们的排名毫无头绪，所以她的策略就行不通了。

We have shown that there is not a strategy of Sarah's that works, if there are more than 10 gems.我们已经证明，如果宝石数量超过 10 颗，那么萨拉的任何策略都无法奏效。

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2022-2023年Bebras挑战练习题

Cadets (12-14岁) 集合

名称	类型
Hamburger Recipe 汉堡包配方	A
Flower Garden 花园	A
Sailor Necklace 水手项链	A
Embroidery Machine 绣花机	A
Pantry Map 储藏室地图	A
Rug Weaving 地毯纺织	B
Nuts and Bolts 螺母和螺栓	B
Lights On 亮着灯	B
Cipher 8 密码8	B
Mary's Neighbors 玛丽的邻居	B
Lists 列表	C
Listen and Walk 听和走	C
Tic-Tac-Toe 井字	C
Favorite Movie 最喜欢的电影	C
Hangar Carousel 机库旋转木马	C

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At Beavertown Airfield, six planes are parked on a rotating turntable in a round hangar.在比弗敦机场，六架飞机停放在圆形机库中一个可旋转的转盘上。

The turntable can be rotated left or right by using a control panel with two arrows ◄►. One button press rotates the turntable exactly one parking position, either left or right. The gate of the hangar is wide enough for one plane to roll out. The turntable is very slow to rotate, so having fewer button presses will avoid delays.转盘可通过带有两个箭头“◄►”的控制面板向左或向右旋转。按一次按钮，转盘就会精确地旋转一个停车位的位置，要么向左，要么向右。机库的门足够宽，可供一架飞机驶出。转盘旋转速度非常慢，因此减少按钮按压次数可避免延误。

In the mornings, when pilots come to pick up their planes, the parking position 1 is always at the gate. In the best case scenario, the arrow keys need to be pressed five times to get all planes to roll out. In these cases pilots will access the parking positions in the order: 1, 2, 3, 4, 5, 6 by pressing ► five times, or in the order: 1, 6, 5, 4, 3, 2 by pressing ◄ five times.早上，当飞行员来取飞机时，1 号停机位总是在登机口。在最佳情况下，需要按五次方向键才能让所有飞机驶出。在这种情况下，飞行员会按顺序访问停机位：1、2、3、4、5、6，方法是按五次“右箭头”键，或者按顺序访问停机位：1、6、5、4、3、2，方法是按五次“左箭头”键。

But what is the worst case scenario? That is, what order of accessing the parking positions will require the maximum number of button presses for all planes to be rolled out?但最糟糕的情况会是怎样？也就是说，哪种取车顺序会让所有飞机都驶出车位所需的按键次数最多？

Task:任务:

Provide one of such worst case order for pilots to access the parking positions 1 - 6 by dragging the numbers into the right spots.请将飞行员进入 1 至 6 号停机位的最糟糕的顺序之一通过将数字拖到正确的位置来提供。

 

 

 

 

 

Explanation 解释

A group of friends wants to choose which of seven movies to watch.一群朋友想要从七部电影中选一部来看。

Each friend rates each movie from highest to lowest: , ,  .每位朋友都按照从高到低的顺序给每部电影打分。

A movie is called a "favorite movie" if none of the friends has given another movie a higher rating.如果朋友中没有人给另一部电影打出更高的评分，那么这部电影就被称为“最喜爱的电影”。

Example:例子:

Movie 1 is NOT a favorite movie because Niklaus gave a higher rating to Movie 4.电影 1 不是最喜欢的电影，因为尼克劳斯给电影 4 的评分更高。

Task:任务:

Make as few changes as possible to the ratings so there is a favorite movie.尽量少改动评分，以便能选出一部最受欢迎的电影。

There are multiple ways to do this.有多种方法可以做到这一点。

(Click on a rating to change it and press 'Save' when you are finished.)（点击一个评分来更改它，完成后点击“保存”。）

 

 

 

 

 

Explanation 解释

Tic-tac-toe is a paper-and-pencil game for two players. 井字棋是一种供两人玩的纸笔游戏。

Rules:规则:

Players choose who uses X as their marker and who uses O. One player starts, then both players take turns marking the spaces in a three-by-three grid with an X or an O. The player who succeeds in placing three of their markers in a horizontal, vertical, or diagonal row is the winner. If no one succeeds and all nine boxes are filled, the game ends in a tie. 玩家选择谁用 X 作为自己的标记，谁用 O。一名玩家先开始，然后两名玩家轮流在三乘三的网格中用 X 或 O 标记空格。成功将三个自己的标记连成一条横线、竖线或对角线的玩家获胜。如果没有人成功且所有九个格子都被填满，游戏以平局结束。

Example:例子:

The following images show the first two moves each player made, and the last move they made in a game.以下图片展示了每位玩家在一场游戏中所下的前两步棋以及他们所下的最后一步棋。

(The moves made on each turn are highlighted.)（每回合所下的棋步均以高亮显示。）

The image on the right is what we call the 'result sheet' of a completed game. Not all sheets that are filled randomly with X or O are valid result sheets according to the rules presented above.右边的图像是我们所说的已完成游戏的“结果表”。并非所有随意填满 X 或 O 的表格都符合上述规则，是有效的结果表。

Question:问题:

Which of the following images is the only valid result sheet of a completed game according to the rules above?根据上述规则，以下哪张图片是唯一有效的已完成游戏的成绩单？

A.

B.

C.

D.

   

 

 

 

 

 

Explanation 解释

Answer: 答案

:

Explanation: 解释:

This is a valid game because it was won by player O and then stopped.这是一场有效的游戏，因为是玩家 O 赢得了比赛，然后游戏停止了。
Answer    is not correct. 答案不正确。

Player X has won the game, but player O has placed more marks than player X, which is not possible.玩家 X 赢得了游戏，但玩家 O 放置的标记比玩家 X 多，这是不可能的。

Since the winning player always places the last mark, they can only have more or an equal number of marks but not less.由于获胜的玩家总是放置最后一个标记，所以他们拥有的标记数量只能更多或相等，而不会更少。

Answer  is not correct because there are 5 X-marks but only 3 O-marks. That is not possible. The difference between the numbers can only be 0 or 1.答案不正确，因为有 5 个叉号，但只有 3 个圈号。这是不可能的。数字之间的差值只能是 0 或 1。

Answer  is not correct because a winner had not been determined and the fields were not all filled completely.答案不正确，因为当时尚未决出胜者，而且表格也未全部填满。

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Tina, who is blind, walks through the city along the roads using her talking glasses.失明的蒂娜戴着会说话的眼镜沿着城市道路行走。

The talking glasses have cameras and an intelligent object recognition system.这款会说话的眼镜配备了摄像头和智能物体识别系统。

The glasses can recognize: a house , a tree , a road and lawn .这副眼镜能够识别：房屋、树木、道路和草坪。

 When Tina enters a new road square, the talking glasses tell her - in this order - what is on her left, what is in front of her and what is on her right.  For example: "tree, road, house".当蒂娜走进一个新的道路广场时，会说话的眼镜会依次告诉她她的左边、正前方和右边分别有什么。例如：“树、路、房子”。

Tina starts at the arrow, facing in the direction of the arrow, and listens to her talking glasses.蒂娜从箭头处开始，面向箭头所指的方向，听从她那会说话的眼镜的指引。

This is what they tell her (beginning with the starting square):这就是他们告诉她的（从起始方格开始）：

• tree, road, house 树，路，房子
• road, road, lawn 路，路，草坪
• tree, road, tree 树，路，树
• road, road, road 路，路，路
• tree, road, tree 树，路，树
• tree, house, road 树，房子，路
• road, road, tree 路，路，树
• house, road, tree 房子，路，树

At the end, Tina has arrived at one of the squares labeled with a letter.最后，蒂娜来到了标有字母的一个方格处。

Question:问题:

At which letter on the map has Tina arrived?蒂娜在地图上的哪个字母处到达了？

(Click on the letter to select it. Press 'Save' when you are finished.)（点击字母以选中它。完成后按“保存”。）

 

 

 

 

 

 

Explanation 解释

We can represent a list of numbers 3,5,2,4,1 visually as follows.我们可以将数字列表 3、5、2、4、1 以如下方式直观地表示出来。

(The smaller red numbers above indicate the positions in the list named 'X.')（上面较小的红色数字表示在名为“X”的列表中的位置。）

We write (X 2) to describe the number at position 2. So (X 2) is 5. Similarly (X 5) is 1.我们用 (X 2) 来表示位置 2 上的数字。所以 (X 2) 是 5。同样地，(X 5) 是 1。

The positions can be indicated indirectly, for example:这些位置可以间接表明，例如：

(X (X 3)) is 5 because (X 3) is 2, so (X (X 3)) = (X 2) = 5.(X (X 3)) 等于 5，因为 (X 3) 等于 2，所以 (X (X 3)) = (X 2) = 5。

Here are three lists, A, B and C.这里有三个列表，分别是 A、B 和 C。

Question:问题:

What is the number described by (A (B (C 3)))?由 (A (B (C 3))) 描述的数字是多少？

A. 1

B. 2

C. 3

D. 4

E. 5

 

 

 

 

 

Explanation 解释