2022-2023年Bebras挑战练习题-Flower Garden(花园)

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-Flower Garden(花园)

A new game has been started below. The player thinks that there is a flower in one of the squares marked A, B, C, or D, but has not decided which to click with button B yet.下面开始了一个新游戏。玩家认为在标有 A、B、C 或 D 的方格中有一朵花,但还没决定用按钮 B 点击哪一个。
Task: 任务:

In which square marked A, B, C, or D is there another hidden flower?在标有 A、B、C 或 D 的哪个方格里还藏着一朵花?

(Click on the square to select it and then press 'Save.')(点击方框将其选中,然后按“保存”。)

Explanation 解释

Answer: 答案:

B

Explanation: 解释:

In the square below square A, we have a "1". We assume there is a flower below that. So "1" indicates that assumed flower and thus, square A cannot contain a flower.在正方形 A 下方的那个正方形里有一个“1”。我们假定那里有一朵花。所以“1”表示那个假定存在的花,因此正方形 A 里不能有花。

In the square to the left of square C, and above square D we have a "1". To the left of that "1" is the assumed flower. So this "1" indicates that assumed flower and, thus, square C and square D cannot contain a flower.在 C 方格左侧且 D 方格上方的位置有一个“1”。在那个“1”的左侧是假定的花。所以这个“1”表明假定的花所在的位置,因此 C 方格和 D 方格不能有花。

Square B has two neighbors with a "1". These "1"s could be referring to square B, but only the "2" on the square on the bottom left of square B, shows that a flower needs to be in square B. This "2" only has 2 neighbors which don't contain numbers and if we have the assumed flower, another flower needs to be in square B.方格 B 有两个相邻的方格标有“1”。这些“1”可能指的是方格 B,但只有方格 B 左下角的那个标有“2”的方格表明方格 B 需要种一朵花。这个“2”只有两个相邻的方格没有数字,如果按照假设种了一朵花,那么方格 B 还需要再种一朵花。

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2022-2023年Bebras挑战练习题-Benjamins (10-12岁) 集合

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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2022-2023年Bebras挑战练习题-Cipher 8(密码8)

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。

2022-2023年Bebras挑战练习题-Cipher 8(密码8)

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

Answer: 答案:

72-11-62-32-43

Explanation: 解释:

We get the correct answer by gradually creating an encrypted text for the message WATER.我们通过逐步为信息“WATER”创建加密文本而得出正确答案。

The encrypted text will contain 5 codes:加密文本将包含 5 个代码:

  • At the start of the encryption, the arrow points to the letter group ABC. The letter W is located within the letter group, which the arrow will point to after rotating 7 vertices. The letter W is the second letter in the letter group VWX, so the first code is 72.加密开始时,箭头指向字母组 ABC。字母 W 位于该字母组内,箭头旋转 7 个顶点后将指向它。字母 W 是字母组 VWX 中的第二个字母,所以第一个代码是 72。
  • The second letter of the encrypted message is A. This letter is in the letter group ABC, which the arrow will point to after rotating once from its current position at letter group VWX. A is in the first position, so the second code is 11.加密信息中的第二个字母是 A。这个字母位于字母组 ABC 中,而箭头从当前指向的字母组 VWX 旋转一次后会指向该字母组。A 处于第一个位置,所以第二个密码是 11。
  • We get to the letter group containing T by rotating 6 vertices and the letter T is the second letter, so the third code is 62.我们通过旋转 6 个顶点到达包含字母 T 的字母组,而字母 T 是第二个字母,所以第三个密码是 62。
  • The letter E is in the letter group that the arrow will point to after the arrow is rotated 3 vertices and E is the second letter in the group, so the code is 32.字母 E 在箭头旋转 3 个顶点后所指向的字母组中,且 E 是该组中的第二个字母,所以密码是 32。
  • The last letter is R, in the letter group, which can be reached after rotating 4 vertices. R is the third letter, so the last code is 43.最后一个字母是 R,在字母组中,旋转 4 个顶点后可以到达。R 是第三个字母,所以最后一个代码是 43。

The whole encrypted text is 72-11-62-32-43.整个加密文本是 72 - 11 - 62 - 32 - 43 。

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2022-2023年Bebras挑战练习题-Nuts and Bolts(螺母和螺栓)

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。

2022-2023年Bebras挑战练习题-Nuts and Bolts(螺母和螺栓)

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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2022-2023年Bebras挑战练习题-Rug Weaving(地毯纺织)

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。

2022-2023年Bebras挑战练习题-Rug Weaving(地毯纺织)

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

Answer: 答案:

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: 2022-2023年Bebras挑战练习题-Rug Weaving(地毯纺织)

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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2022-2023年Bebras挑战练习题-Lights On(亮着灯)

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”。)

2022-2023年Bebras挑战练习题-Lights On(亮着灯)

 

 

 

 

 

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:

2022-2023年Bebras挑战练习题-Lights On(亮着灯)

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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2022-2023年Bebras挑战练习题-Mary's Neighbors(玛丽的邻居)

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? 

2022-2023年Bebras挑战练习题-Mary's Neighbors(玛丽的邻居)

 

 

 

 

 

 

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。

2022-2023年Bebras挑战练习题-Mary's Neighbors(玛丽的邻居)

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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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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