分类： 赛事动态

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

The Flower Garden is a video game where the aim is to find the flowers without stepping on them.《花之园》是一款视频游戏，其目标是在不踩到花朵的情况下找到它们。

Rules:规则:

Players can click on a square where they don't think there is a hidden flower with the A button. This will either reveal a number or, if there is a hidden flower, they are said to have "stepped on the flower" and have lost the game. When a number is revealed, it shows how many neighboring squares have flowers in them. When a player knows where a flower is, they should "make it grow" by clicking on the square with the B button. If the player finds all the hidden flowers before stepping on one, they win the game.玩家可以点击他们认为没有隐藏花朵的方格，点击 A 键。这要么会显示出一个数字，要么如果那里有隐藏的花朵，玩家就会被说成“踩到了花朵”，从而输掉游戏。当显示数字时，它表示相邻方格中有多少朵花。当玩家知道花朵的位置时，应点击该方格的 B 键“让花朵生长”。如果玩家在踩到花朵之前找到了所有隐藏的花朵，他们就赢得游戏。

Example of a game still in progress:正在进行中的游戏示例：

2022-2023年Bebras挑战练习题

Benjamins (10-12岁) 集合

名称	类型
Lila's Guessing Game 莉拉的猜谜游戏	A
Beehive 蜂巢	A
Most Popular Book 最受欢迎的书	A
Tortoise and Hare 乌龟和野兔	A
Colorful Tower 五彩缤纷的塔	A
Heart Graphics 心的图形	B
Pantry Map 储藏室地图	B
Sailor Necklace 水手项链	B
Embroidery Machine 绣花机	B
Hamburger Recipe 汉堡包配方	B
Mary's Neighbors 玛丽的邻居	C
Lights On 亮着灯	C
Rug Weaving 地毯纺织	C
Nuts and Bolts 螺母和螺栓	C
Cipher 8 密码8	C

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（Bebras每日一练部分展示）

An octagon has groups of three or four letters written at the vertices. An arrow points from the center of the octagon to a letter group. The arrow can rotate clockwise.一个八边形的顶点处写着三或四个字母组成的组。有一支箭从八边形的中心指向一组字母。这支箭可以顺时针旋转。

Messages can be encrypted using the octagon and arrow.消息可以使用八角形和箭头进行加密。

At the beginning of the encryption of a new message, the arrow always points to the letters ABC.

We encrypt each letter of the message so that:我们对消息中的每个字母进行加密，以使：在对新消息进行加密的开始阶段，箭头总是指向字母 ABC。

• The first number indicates how many vertices of the octagon the arrow should be rotated, starting at its current position.第一个数字表示箭头应绕八边形的顶点旋转的次数，从其当前位置开始。
• The second number indicates the position of the encrypted letter in the letter group to which the arrow points.第二个数字表示箭头所指字母组中加密字母的位置。

Example:例子:

TREE is encrypted with the sequence 62-73-42-02.“TREE”用序列 62 - 73 - 42 - 02 进行了加密。

Question:问题:

What is the encrypted message for WATER?WATER 的加密信息是什么？

A. 72-11-26-32-53

B. 62-11-62-22-43

C. 62-11-26-22-53

D. 72-11-62-32-43

 

 

 

 

 

Explanation 解释

At the Beaver Construction factory, Benoit works at the nut and bolt  assembly line.在比弗建筑工厂，贝努瓦在螺母和螺栓装配线上工作。

His job description is as follows:他的工作职责如下：

• Stand at one end of a conveyor belt, which brings a line of nuts and bolts.站在传送带的一端，传送带上有一排螺母和螺栓。
• Take each element, either a nut or a bolt, off the conveyor belt.把传送带上的每个零件，不管是螺母还是螺栓，都取下来。
• Put the nuts from the conveyor belt in the red bucket.把传送带上的坚果放进红色的桶里。
• Attach any bolt, taken from the conveyor belt, to a nut from the red bucket and place the assembled part onto the table behind you.从传送带上取下任意一个螺栓，与红色桶里的一个螺母拧在一起，然后把拧好的部件放到你身后的桌子上。

However, things can go wrong for Benoit in two different ways:然而，对于贝努瓦来说，事情可能会以两种不同的方式出错：

1. When Benoit takes a bolt from the conveyor belt there may not be a nut in the bucket.当贝努瓦从传送带上取下一颗螺栓时，桶里可能没有螺母。
2. There may be no more nuts or bolts on the conveyor belt but there are still nuts in the bucket.传送带上可能已经没有螺母或螺栓了，但桶里还有螺母。

Question: 问题:

Which sequence of nuts and bolts, when processed from left-to-right, will not cause things to go wrong for Benoit?从左至右依次加工哪一组螺母和螺栓，才不会让贝努瓦出错？

A.

B.

C.

D.

   

 

 

 

 

Explanation 解释

Answer: 答案:

C.

Explanation: 解释:

We can keep track of the state of the bucket and conveyor belt from left-to-right:我们可以从左到右跟踪料斗和传送带的状态：

• N =
• B =

Bucket	Conveyor Belt
empty	N B N N B N N B B B
N	B N N B N N B B B
empty	N N B N N B B B
N	N B N N B B B
N N	B N N B B B
N	N N B B B
N N	N B B B
N N N	B B B
N N	B B
N	B
empty	empty

Looking at the other answers:看看其他答案：

will go wrong after N B B, since there will be no nut in the bucket when the second B is encountered.在执行了 N 次 B B 操作之后将会出错，因为在遇到第二个 B 时桶里将没有坚果了。

will go wrong after N N B N N B B B B, since there will be no nut in the bucket when the fifth B is encountered: notice there are only 4 N's before this B.在遇到第 5 个 B 时将会出错，因为此时桶里已没有坚果了：请注意，在这个 B 之前只有 4 个 N。

will go wrong after the entire sequence is processed, since there will be two nuts in the bucket, since there are 6 N's and 4 B's.在整个序列处理完毕后会出现错误，因为桶里会有两个螺母，因为有 6 个 N 和 4 个 B。

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（Bebras每日一练部分展示）

Hale is a Turkish weaving artist. She is making a square rug with 6 rows (left to right) and 6 columns (up and down).黑尔是一位土耳其的织布艺术家。她正在制作一块 6 行（从左到右）6 列（从上到下）的方形地毯。

Hale puts a symbol in each square on the grid of the rug, using the following questions:黑尔在地毯网格的每个方格中都放上一个符号，他依据以下问题进行操作：

Question: 问题:

Using this method, what would the resulting rug look like?用这种方法，最终的地毯会是什么样子？

A.

B.

C.

D.

 

 

 

 

 

Explanation 解释

The rug Hale weaves is:黑尔编织的地毯是：

B.

The first question that Hale asks indicates that the 1st and 6th rows, as well as the 1st and 6th columns, should have purple shapes.

黑尔提出的第一个问题表明，第 1 行和第 6 行，以及第 1 列和第 6 列，应当有紫色的图形。

The second question leads to all squares on the diagonal of the rug having a red symbol, because on the diagonal the row and column numbers are the same:第二个问题导致地毯对角线上的所有方格都有红色符号，因为在对角线上行号和列号相同：

On the next layer of questions, we find that the row number is larger than the column number in all the squares to the left of the diagonal. In these places, a blue symbol is placed:在接下来一层的问题中，我们发现对角线左侧所有方格中的行号都大于列号。在这些位置，放置一个蓝色符号：

Finally, the remaining squares to the right of the diagonal all have row numbers that are NOT larger than the column numbers, hence they are filled in with the yellow symbol, giving the answer seen in option B.最后，对角线右侧剩余的所有方格其行号都不大于列号，因此都用黄色符号填充，从而得到选项 B 中所示的答案。

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（Bebras每日一练部分展示）

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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（Bebras每日一练部分展示）