分类： 赛事动态

Two beavers live in lodges separated by a large forest.

两只海狸分别住在被大片森林隔开的窝里。

They decide to send messages to each other by shooting fireworks into the sky above the trees.

他们决定通过向树梢上方的天空发射烟花来互相传递信息。

Each message is a sequence of words, though the beavers only know five different words.

每条信息都是一串单词，不过海狸们只认识五个不同的单词。

The beavers can shoot two types of fireworks, one after the other, and know the following codes:

海狸们能够依次发射两种烟花，并且知晓以下代码：

For example, to send the (rather strange) message "food, log, food", a beaver would shoot:

例如，要发送（相当奇怪的）信息“食物，原木，食物”，一只海狸会这样射击：

Question: 问题:

How many different meanings can the following sequence of fireworks have?

下面这一系列烟花能有多少种不同的含义？

 

 

 

 

 

 

Explanation 解释

The correct answer is 4. The message could mean any of the following:

正确答案是 4。该消息可能表示以下任何一种意思：

• log, rock, food, river 日志，岩石，食物，河流
• log, log, log, river 木头，木头，木头，河流
• rock, tree, river 岩石、树木、河流
• rock,food, log, river 岩石、食物、原木、河流

To convince yourself that there are no more possibilities, you can systematically count them:

要让自己确信没有其他可能性，你可以系统地进行计数：

- Start with the first firework. It is not a message, so you can assign a zero to it.

从第一个烟花开始。它不是信息，所以你可以给它赋值为零。

- The first two fireworks can only mean log. Assign number one to the second firework.

前两束烟花只能表示“木”。给第二束烟花标上数字 1。

- We are now at the third firework. It can have a meaning of any shorter sub-sequence plus one new word. Yet we see that there is no way to prolong the previously examined sequences (of length 1 and 2), so we only have one possible meaning (rock) and assign 1 to the third firework.

现在我们来到了第三个烟花。它可以表示任何更短的子序列加上一个新词的意思。然而我们发现无法延长之前考察过的序列（长度为 1 和 2 的），所以我们只有一个可能的意思（“岩石”），于是给第三个烟花赋值 1 。

- The fourth firework is somewhat interesting! It can either add the word log to the first two fireworks, or food to the first three fireworks, as shown by the arrows below. So we sum the two numbers at the 2^nd and 3^rd firework and assign it to the 4^th (1+1=2).

第四个烟花有点意思！它要么把单词“log”加到前两个烟花上，要么把“food”加到前三个烟花上，如下方箭头所示。所以我们把 2 号和 3 号烟花上的两个数字相加，并把这个和赋值给 4 号烟花（1 + 1 = 2）。

- We proceed applying the same idea to each firework to the right. We look one, two and three fireworks back. If those shorter messages can be prolonged with a correct word, we mark this fact with an arrow. Then we just sum the numbers “brought” by the arrows to the currently examined firework.

我们接着将同样的思路应用于右侧的每一个烟花。我们向后看一个、两个和三个烟花。如果那些较短的信息能用一个正确的词加以延长，我们就用箭头标出这一事实。然后，我们只需将箭头“带来”的数字加到当前正在考察的烟花上。

- At the last firework we will have the number of all possible meanings.

在最后一束烟花绽放时，我们将拥有所有可能意义的数量。

The systematic approach when we build our solution systematically step by step and using the previous steps is called dynamic programming. It makes the process much easier.

当我们逐步系统地构建解决方案，并利用之前的步骤时，这种系统的方法被称为动态规划。它使整个过程变得容易得多。

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For his homework, Thomas had to write words on cards and connect them with rubber bands.托马斯的家庭作业是把单词写在卡片上，然后用橡皮筋把它们连起来。   The teacher told him to connect any two words that differ by exactly one letter.老师让他把仅相差一个字母的任意两个单词连接起来。 Thomas did this, as you can see in the picture on the right.托马斯就是这样做的，如您在右边的图片中所见。 When Thomas returned from having a break he got a surprise.托马斯休息回来时吃了一惊。 Peter, his little brother, had erased all the words!彼得,他的小弟弟把所有的字都擦掉了！
	Also, the cards were completely mixed up, as you can see in the image on the left.而且，正如您在左边的图片中所看到的那样，这些卡片完全被打乱了。 Importantly, the rubber bands still connected them as before.重要的是，橡皮筋仍像之前那样把它们连在一起。 Thomas was sure he could put the words back in the correct place.托马斯确信他能把那些词放回正确的位置。

Question: 问题:

Which of the pictures below contains the words in exactly the right places?

下面哪张图片中的单词位置完全正确？

A.

B.

C.

D.

 

 

 

 

 

Explanation 解释

A factory produces sets of 6 bowls of different sizes. A long conveyor belt moves the bowls one by one, from left to right.

一家工厂生产每套 6 个不同尺寸的碗。一条长长的传送带将碗一个接一个地从左向右移动。

Bowl production places the 6 bowls of each set onto the conveyor belt in a random order.

碗的生产过程是将每套的 6 个碗以随机的顺序放置在传送带上。

Before packing the bowls, they need to be sorted to look like this:

在打包碗之前，需要将它们分类整理成如下这样：

To help with the sorting, the factory places workers along the conveyor belt.

为了便于分类，工厂在传送带上安排了工人。

When a set of bowls passes a worker, he will swap any two neighboring bowls which are in the wrong order.

当一组碗经过一名工人时，他会交换任何两个顺序错误的相邻碗。

He will keep doing this until the set of 6 bowls has finished passing him.

他会一直这样做，直到那套 6 个碗全部从他面前传过。

See how the order of a set of bowls changes as it passes one worker: 

观察一组碗在经过一名工人时其顺序是如何变化的：

Question: 问题:

How many workers should be put along the line to sort the following set of bowls?

要将下面这组碗进行分类，应该在流水线上安排多少名工人？

 

 

 

 

 

Explanation 解释

The answer is: 4 

答案是：4

As shown in the question, the original order of the set of bowls is: 5 6 3 2 1 4

如问题中所示，碗的原始排列顺序为：5 6 3 2 1 4

Remember that swapping of neighboring bowls happens from right to left.

记住，相邻碗的交换是从右往左进行的。

After passing a first worker, the order of the bowls is: 1 5 6 3 2 4 (4 swaps, all with bowl 1)

经过第一个工人处理后，碗的顺序是：1 5 6 3 2 4（共交换了 4 次，都是与 1 号碗交换）

After passing a second worker, the order is: 1 2 5 6 3 4 (3 swaps, all with bowl 2)

经过第二个工人之后，顺序为：1 2 5 6 3 4（共交换了 3 次，都是与 2 号碗交换）

After passing a third worker: 1 2 3 5 6 4 (2 swaps, all with bowl 3)

经过第三个工人之后：1 2 3 5 6 4（共进行了 2 次交换，均与第 3 个工人交换）

After passing a fourth worker, the set of bowls is sorted: 1 2 3 4 5 6 (2 swaps, all with bowl 4)

经过第四位工人后，碗的排列顺序已整理好：1 2 3 4 5 6（共交换了两次，都是与 4 号碗交换）

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Seven beavers are in an online social network called Instadam.

七只海狸在一个名为“Instadam”的在线社交网络里。

Instadam only allows them to see the photos on their own page and on their friends' pages.Instadam

只允许他们查看自己页面和朋友页面上的照片。

In this diagram, if two beavers are friends they are joined by a line.

在这个图中，如果两只海狸是朋友，它们之间就会有一条线相连。

After the summer holidays everybody posts a picture of themselves on all of their friends' pages.

暑假过后，每个人都会在所有朋友的主页上发一张自己的照片。

Question: 问题:

Which beaver's picture will be seen the most?

哪只海狸的照片会被看到最多？

A. Ari

B. Bob

C. Chio

D. Dmitri

E. Ehab

F. Fritz

G. Gerald

 

 

 

 

 

Explanation 解释

The correct answer is Chio.

正确答案是 Chio。

In order to find the beaver whose picture gets seen by most beavers, you have to count the beavers that are at most two steps away. The beavers that are one step away are those on whose page the pictures will be posted and the beavers that are two steps away are those who can see these pages.

为了找出其照片被最多海狸看到的那只海狸，你得计算出距离它最多两步的所有海狸。距离为一步的海狸是指那些照片会发布在其页面上的海狸，而距离为两步的海狸则是那些能看到这些页面的海狸。

当然，任何一只海狸只能算一次。

The following table shows the names of these beavers as from the starting point of each beaver.

下表列出了从每只海狸的起点算起这些海狸的名字。

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Stella the beaver loves to draw stars. She has devised a system for labeling her stars according to their shape. She uses two numbers:

海狸斯特拉喜欢画星星。她设计了一套根据星星形状给它们编号的系统。她使用两个数字：

• A number of dots for the star.给这颗星星画上一些点。
• A number indicating if a line from a dot is drawn to the nearest dot (the number is 1), the second closest dot (the number is 2), etc.一个数字，表示从一个点到最近的点（数字为 1）、第二近的点（数字为 2）等所画的线。

Here are four examples of Stella's labeling system:    

以下是斯特拉标签系统的四个示例：

Question: 问题:

How would Stella label the following star?

斯特拉会如何给下面这颗星命名？

A. 9:3

B. 9:4

C. 10:4

D. 10:5

 

 

 

 

 

Explanation 解释

The correct answer is:10 : 4 

正确答案是：10 : 4 

The star has 10 dots and it is possible to draw a line to the fourth nearest dot.

这颗星有 10 个点，可以画一条线连到第四个最近的点。

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（Bebras每日一练部分展示）

Edgar is looking for a new home to live in.

埃德加正在寻找一个新家来居住。

He searched the internet and found a perfect flat for a very good price.

他在网上搜索，找到了一套价格非常划算的完美公寓。

He sent an e-mail to Francis, who is selling the flat, and received a quick reply:

他给正在出售这套公寓的弗朗西斯发了一封电子邮件，很快就收到了回复：

Hi,
Thank you for your interest in my flat.
Although I am not in town, I can send you the key to the flat so you can inspect it, but I need a security deposit of $5.000,- beforehand.
To show my trustworthiness, I attach a copy of my ID.
Cheers,
Francis


Edgar is unsure what to do and is asking for your help.

埃德加不知所措，正在向你求助。

Question: 问题:

What would be your best advice?

您最好的建议会是什么？

A. Don’t pay the deposit, there is a high chance that this is a mail fraud.

B. That is perfect. If you like the flat, you can keep the key right away. 

C. Pay the deposit. With the ID you can always go to the police if you don't get the deposit back.

D. Pay the deposit, go and have a look and decide later on.

 

 

 

 

 

Explanation 解释

Statement 1 would be the best advice, since there are multiple spelling errors and another name at the end of the email, the name and ID must not be real.

第一条陈述是最恰当的建议，因为邮件中有多处拼写错误，而且末尾还有一个名字，所以名字和身份证号肯定不是真实的。

Statements 2 and 4 are not good as the chance is high to not even receive the key.

陈述 2 和 4 不好，因为很有可能根本收不到密钥。

Statement 3 is not good since the authenticity of the ID can’t be proven.

陈述 3 不好，因为无法证明身份证件的真实性。

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（Bebras每日一练部分展示）

All members of a beaver family have abilities.

河狸家族的所有成员都有本领。

• A daughter inherits all her abilities from her mother.女儿的所有能力都遗传自母亲。
• A son inherits all his abilities from his father.儿子的所有能力都遗传自父亲。
• Each family member also has one extra ability.每个家庭成员还拥有一项额外的能力。

The diagram below shows the relationships between the beavers. It also shows the extra ability for each beaver.

下面的图表展示了海狸之间的关系。它还展示了每只海狸的额外能力。

Examples: 例子:

• Mother Jennifer has inherited the ability to sing from Grandmother Maria, and she also has the ability to program.詹妮弗妈妈从玛丽亚奶奶那里继承了唱歌的天赋，而且她还具备编程的能力。
• Lisa inherits two abilities from her mother and also has the ability of writing. This means she can write, program and sing. 丽莎从母亲那里继承了两项能力，还拥有写作的才能。这意味着她会写作、编程和唱歌。

Question: 问题:

Look at the diagram above. Which of these answers is true?

请看上面的图表。以下哪个答案是正确的？

A. Tom’s abilities are riding, painting and photography.

B. Sarah has abilities in reading, programming and singing.

C. Tom inherits from Grandmother Margot the ability to calculate.

D. Aunt Mary has abilities in dancing and swimming.

 

 

 

 

 

Explanation 解释

Statement 1 is correct, because Tom inherits painting from his grandfather and photography from his father.

陈述 1 是正确的，因为汤姆从祖父那里继承了绘画，从父亲那里继承了摄影。

Statement 2 is not correct, because Sarah does not inherit reading from her brother Charles.

陈述 2 不正确，因为萨拉的阅读能力并非从她哥哥查尔斯那里遗传而来。

Statement 3 is not correct, because Tom cannot inherit abilities from his grandmother.

陈述 3 不正确，因为汤姆无法从他的祖母那里继承能力。

Statement 4 is not correct, because Aunt Mary does not inherit swimming from her father.

陈述 4 不正确，因为玛丽阿姨的游泳技能并非遗传自她的父亲。

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The beavers have created a clever irrigation system for their fields. The water flows from a lake at the top of the hill all the way down to the fields numbered 1 to 6 at the bottom.

海狸们为它们的田地设计了一个巧妙的灌溉系统。水从山顶的湖一直流到山脚编号为 1 至 6 的田地。

Along the water canals, the beavers have installed four water gates, where the water can only flow either to the left or to the right.

沿着水渠，海狸们安装了四道水闸，水只能向左或向右流动。

Click on the arrows, so that only the fields numbered 2, 4, 5 and 6 are irrigated.

点击箭头，使只有编号为 2、4、5 和 6 的区域得到灌溉。

 

 

 

 

 

Explanation 解释

The left top gate must remain as it is, irrigating fields 1 and 2.

左上角的闸门必须保持现状，为 1 号和 2 号农田灌溉。

The left bottom gate must be clicked to the right, diverting the irrigation to only field 2.

必须点击左下角的闸门向右，将灌溉水只引向 2 号田。

The right top gate must remain as it is, irrigating fields 5 and 6.

右上闸门必须保持现状，为 5 号和 6 号田地灌溉。

The right bottom gate must be clicked to the left, diverting the irrigation also to field 4.

必须点击右下角的闸门向左，这样灌溉水也会流向 4 号田。

The wrong possibilities only differ from the correct solution in that they irrigate one field too much or too few. 

错误的可能性与正确的解决办法唯一的区别在于，它们要么灌溉了一块田地过多，要么灌溉过少。

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2015年Bebras挑战练习题

Cadet (12-14岁) 集合

名称	类型
Animal Competition（动物竞争）	A
Cross Country（越野）	A
Animation （动画）	A
Bracelet （手镯）	A
Geocaching （地图）	A
Beaver Logs （海狸日志）	B
Dream Dress （梦想礼服）	B
Beaver Lunch （海狸的午餐）	B
Binary Hotel （二进制酒店）	B
Drawing Patterns （绘图模式）	B
Theatre （剧院）	C
Chakhokhbili	C
Throw the dice （掷骰子）	C
You Won't Find It （你不会找到的）	C
Stack Computer （堆栈的电脑）	C

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（Bebras每日一练部分展示）

The Stack Computer is loaded with boxes from a conveyer belt. The boxes are marked with a Number or an Operator (+, -, * or /).

堆栈计算机从传送带上装载着标有数字或运算符（加号、减号、乘号或除号）的盒子。

The computer is loaded until the top box is a box marked with an operator. This operator is then used on the two boxes below it. The three boxes are then fused into one single box and marked with the outcome of the calculation.

计算机一直加载，直到最上面的盒子是一个标有运算符的盒子。然后，该运算符用于其下方的两个盒子。这三个盒子随后融合成一个盒子，并标上计算结果。

In the Stack Computer, calculations are entered in a different way to a normal calculator.

在堆栈计算机中，输入计算的方式与普通计算器不同。

Try these examples: 试试这些例子：

Enter your solution in the input box, and use the buttons to try it out on the Stack Computer.

在输入框中输入您的解决方案，然后使用按钮在堆栈计算机上进行测试。

• 2+3 must be entered as 2 3 +
• 10-2 must be entered as 10 2 -
• 5*2+3 must be entered as 5 2 * 3 +
• 5+2*3 must be entered as 5 2 3 * +
• (8-2)*(3+4) must be entered as 8 2 - 3 4 + *

Question: 问题:

How should the following computation be entered: 4*(8+3)-2?

以下计算应如何输入：4*(8 3)-2？

 

 

 

 

 

Explanation 解释

The correct answer is 4 8 3 + * 2 -.

正确答案是 4 8 3 + * 2 -。

However, the following answers are also acceptable as they all produce the correct output.

然而，以下答案也是可以接受的，因为它们都能产生正确的输出。

• 4 3 8 + * 2 -
• 8 3 + 4 * 2 -
• 3 8 + 4 * 2 -

These inputs all lead to the same result, even though the order of the operators and operations are not the same as intended in the given expression.

这些输入都会得出相同的结果，尽管运算符和运算的顺序与给定表达式中预期的顺序不同。

From left to right, we first have 4*(8+3), so we need 4 and the result of 8+3 on the stack. We achieve that by writing:

从左到右，我们首先有 4*(8 3)，所以我们需要 4 和 8 3 的结果在栈上。我们通过写入以下内容来实现：

4 8 3 +

We then have 4 and 11 on the stack, so we add a * to multiply the two numbers. We now have 44 on the stack, we add a 2 and a – for the final subtraction.

此时栈上有 4 和 11，所以我们添加一个 * 来将这两个数字相乘。现在栈上有 44，我们再添加一个 2 和一个 - 用于最后的减法运算。

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（Bebras每日一练部分展示）