Find some interesting logical reasoning questions with answers.

For example, let's assume that there are three beautiful women, namely angels (who often tell the truth) and demons (who never tell the truth) and people (who tell the truth and lie). If 1 says "I am a demon", then who is this woman? Do you know?

First of all, suppose the devil said "I am the devil", that is, the devil told the truth. Therefore, this person can't be a demon. If an angel says "I am a demon", it becomes a lying angel. So it can't be an angel. Then, this person can only be human.

The so-called "what can I know from that speech" speech refers to such a speech. Searching whether there is such a statement is the first step to answer the "lying question".

Next, let's look at an example.

Example 2

There are angels, demons and people. Angels always tell the truth, demons always tell lies, and people sometimes tell lies when they tell the truth.

The woman in black said, "I'm not an angel",

The woman in blue said, "I'm not human",

The woman in white said, "I'm not a demon",

So, who are they?

People can only say "I am not an angel". Why? If it is said by an angel, it becomes that the angel is lying; if it is said by the devil, it becomes that the devil is telling the truth (that is, in this case, people are telling the truth).

Only angels and people can say "I'm not human". Why? Suppose the devil speaks, it is the devil who tells the truth (that is, in this case, angels tell the truth and people tell lies)

Perhaps it can be said that "I am not a demon" can be an angel, a demon or a human (that is, in this case, the angel and the human are telling the truth, and the devil is telling a lie).

Based on the above, the following table can be obtained.

Angel demon man

The woman in black ××× χ

A woman in blue ×××

A woman in white.

Therefore, the woman in blue is an angel, and the other women in white are demons.

Angel demon man

The woman in black ××× χ

A woman in blue.

A woman in white.

To answer the question of lying, the second important thing is to examine whether there are contradictions between multiple speeches.

For example, there are three people, A, B and C. Suppose only one person can lie. And A said "C is a doll" and B said "C is not a doll", which means that one of A or B lied, because it is conditional that only one person lied, so we can know that C's words are true.

At this time, you may disdain to think, "I understand these." However, when you answer questions, especially when your eyes are fixed on the topic, you may often really ignore these things. Therefore, it is important to take these so-called natural things into consideration calmly.

Then, if the above two experiences still can't be answered, we should assume an argument first and then advance it step by step. If you encounter contradictions in the process of reasoning, it shows that this argument is wrong, which becomes a new clue to solve the problem. For example, if "A is not a unicorn", there is a contradiction in inference and the conclusion that "A is a unicorn" is obtained.

By the way, this method is very effective even if it is not lying, so try to apply it.

Generally speaking, beginners need so much knowledge.

Please take some time to try it at once. Only by answering with your own thinking, will you feel that kind of special happiness more.

The first article. [Monotypic question article]

I can't put it down.

Logical reasoning intelligence test questions

The role of [single question]

First of all, there is a "combination decision problem", which is a beginner of puzzles.

A favorite topic, which is also the first to help you become a master of logicism.

A clever move.

Although it is called a "single type" problem, it is only based on these simple questions.

Questions can make you feel that your logical thinking has improved. Answering every question in a down-to-earth manner will make you progress.

[Warning]! Pay attention to such a question in the process of answering this question. Why can't we use the method of "random combination and getting the answer by chance"? Because then, your logical reasoning ability can't be improved at all.

Moreover, not only this one, but all chapters of this book have such requirements.

1. [Elegance 3 Goddess]

Q: This happened in 182 1 year. In order to carve a group of goddess statues, three women (of different ages) made models of three elegant goddesses.

Excuse me, who is in which position, who is the model of which goddess, and how old?

(1) Catherine is not 2 1 year-old, and a woman of 2 1 year-old is not in the position of C. C is not Catherine.

②B is Apotheuna, but not 19 years old.

(3) The model of Tarea is Moling.

(4) Jones (not 19 years old) is not a female.

⑤A is less than 20 years old.

Goddess: Agura Ye, Apotona, Talaia.

◎ Female: Mo Ling, Jones, Catherine

◎ Age:19,20,21.

Location A B C

goddess

female

age

Solution: [Elegance 3 Goddess]

Comments: Catherine, a woman of 2 1 year-old, as mentioned in ①, the position of C has a series of conditions, so it is easier to answer by paying attention to these conditions. And think, "Katherine is B …" so it's easy to consider.

The following two groups of conclusions can be drawn from ① and ②.

(i) If Catherine is B; (II) If Catherine is.

(i) The condition of (4) cannot be met (Jones is not 19 years old, nor is he a position). So it should be the conclusion of (Ⅱ).

Next, we can know from ⑤ that A is 19 years old and C is 20 years old. From ③, we can know that C is the model Moling of Tarea, so we can get the following table.

Answer:

B.C.

Agura Ayye Ploxiu Nataleia

Catherine Jones Maureen

19 years old 2 1 20 years old

1. A group of people held a dance, each wearing a hat. There are at least two kinds of hats, black and white.

There is one. Everyone can see the color of other people's hats, but not their own. The host will show you first.

Look at what hats others are wearing, and then turn off the lights. If someone thinks he is wearing a black hat, call himself.

Got a slap. The first time I turned off the lights, there was no sound. Then turn on the light and watch it again. The light is off, and it's still a crow.

The birds are silent. I didn't get a slap in the face until I turned off the light for the third time. Ask how many people wear black.

Hat? The answer is three.

The key to reasoning lies in this sentence: there is at least one black one!

1. If there is only one black hat, when the light is turned on for the first time, the person wearing the black hat will see that everyone else is wearing white hats. According to the condition of "having at least one black hat", he will know that he is the only one who wears a black hat.

But no one slapped after turning off the lights, indicating that there is more than one black hat, at least two;

2. The point is that if there are only two black hats, then when the light is turned on for the second time, a person wearing a black hat will see one person wearing a black hat and others wearing white hats. According to the reasoning of 1, he will know that he is another person wearing a black hat (so does the other person wearing a black hat).

But no one slapped after turning off the lights, indicating that there are more than two black hats, at least three;

If there are only three black hats, then when turning on the light for the third time, a person wearing a black hat will see two people wearing black hats and the others wearing white hats. According to the second reasoning, he will know that he is the third person wearing a black hat (so do the other two people wearing black hats).

So after turning off the lights this time, three people slapped at the same time, indicating that there were only three black hats;

One day, the Chinese teacher died in a narrow street, clutching his mobile phone before he died. The mobile phone shows the number 98 4364 98. There is no broadcast. I'm still on the phone, but I hung up.

Finally, our FBI identified five suspects and determined that one of them was the murderer.

1 Suspect: Tian Tel: 98436498. She had a conflict with Dali. Six months ago, she and Dali had a conflict because of their work. But now she is going abroad to study in Europe. She has always held a grudge against Dali.

Suspect No.2: Lei Long, Dali's neighbor. She lives in No.9, Unit 8-4-3, da li Community, and she has a bad temper, while da li lives in No.6, Unit 4-9-8. Zeng and Dali elected representatives of the main Committee. As a result, she was eliminated and won with great success. She spent a lot of money this time, so she always wanted revenge!

Suspect number three: Wen owes Dali a lot of money. I remember borrowing 10000 for 9843, and borrowing 10000 for 6498, but I never paid it back. Maybe Dali pushed her hard and then killed Dali.

Suspect No.4: Wu is an energetic student. In the final exam, 98 people in the class scored 43 points. He severely criticized him. Strongly hate him, often insult him, insult his personality. If possible, kill him.

Suspect number five: Amy, the last person who spoke to Dali on the phone, had a very good relationship with Dali and had no motive to kill.

The answer is: Chinese teachers should be very clear about pinyin, so it is the number 4.

Mr. 2Q plays games with Mr. S and Mr. P. Mr. Q wrote a number on two pieces of paper. These two numbers are both

Is a positive integer, and the difference is 1. He put a piece of paper on Mr. S's forehead and another on Mr. P's forehead. So,

Two people can only see the numbers on each other's foreheads.

Mr. Q kept asking: Can any of you guess the number on your head?

Mr. S said, "I can't guess."

Mr. P said, "I can't guess either."

Mr. S added, "I still can't guess."

Mr. P added, "I can't guess either."

Mr. s still can't guess; Mr. P can't guess either.

Mr. S and Mr. P guessed three times, but they didn't get it right.

However, by the fourth time, Mr. S shouted, "I know!" " "

Mr. P also shouted, "I know!" "

Q: What are the numbers on the heads of Mr. S and Mr. P?

There is a cell with three prisoners. Because the glass is thick, three people can only see each other, but can't hear.

The voice of the other party. "

One day, the king thought of a way to put a hat on each of them and let them know the hat.

The children are either white or black, so they don't know what color their hats are. in?that?case

Next, the king announced the following two items:

1. Whoever can see the other two prisoners wearing white hats will be released;

Whoever knows that he is wearing a black hat will be released.

In fact, the king wears black hats for them. They can't see themselves because they are tied up. So the three of them

People stare at each other and don't talk. Soon, however, A, a conscientious man, decided by reasoning that he was wearing a black hat. you want

, how did he infer?

There is a very old village. There are two kinds of people in this village, red eyes and blue eyes. There is nothing wrong with both kinds of people.

Yao is different. No one knew what color his eyes were before the baby was born. There is a wide village in the middle.

Tian is a place where villagers gather. Now there are only three people in this village.

Live in three places. In this village, there is a rule that if a person can know the color of his eyes, at night,

If he kills himself, he will go to heaven. These three people can't tell each other the color of their eyes in words, nor can they use them.

How to tell each other what color their eyes are, and you can't use a mirror.

Water and other reflective substances can see the color of their eyes. Of course, they are not blind. They can see each other.

Eyes, but just can't tell him! They can only think with their minds, so they come to the square early every morning.

In fact, sitting face to face, thinking about the color of your eyes, day by day passed.

There was no progress until one day, a foreigner came and said a word in the square, which changed him.

Our destiny, he said, at least one of you has red eyes. Say that finish and left. Listen, these three people.

After that, they sat face to face in the evening and went back to sleep. The next day, they came again.

I came to the square and sat for another day. That night, the two committed suicide successfully! On the third day, when the last person

When I came to the square, I saw that the two men didn't come, and I knew that they had succeeded in committing suicide, so he also went back, and so did that night.

Successful suicide!

According to the above, please tell the colors of three people's eyes and tell the reasoning process!

5. There are nine points, arranged as follows:

. . .

. . .

. . .

How to connect these nine points with four straight lines (these four straight lines are required to be continuous)

Answer:

I can't guess this number. ..

Hat color problem

A, B and C are all wearing black hats. The protagonist A can see the black hats of B and C..

So he thought, "What if I wear a white hat?

Then of course B will see a white hat and a black hat.

So he (b) will think, if I (b) have a white hat,

C saw two white hats,

He (c) can already pat his ass and leave.

But c didn't do it,

So I (b) must be wearing a black hat.

The above shows that if I (a) wear a white hat, then B has already left.

However, now B doesn't think he wears a black hat like above.

That's because he (b) lacks a condition,

That is-I (a) wear a white hat.

So obviously-I'm wearing a black hat!

By the way: this damn king ... "

Red and blue eyes problem

Because people with red eyes have at least 1, there are only three possibilities:

There are 1 person, 2 or 3 people with red eyes.

Obviously it can't be 1.

If there is only 1, then this 1 can commit suicide on the spot after hearing the sound of two other pairs of blue eyes. ..

Not three.

If it's three pairs of red eyes, then no matter how you reason,

Because they have exactly the same conditions,

So they have no reason to commit suicide in batches. ..

Moreover, they look at two pairs of red eyes every day.

To them, what the foreigner said was all nonsense. ..

The fact is: people with two red eyes.

The process is as follows.

The first day:

Outsiders came to talk, and then three people went home.

Waiting to see if anyone committed suicide that day.

Among them, people with red eyes see red and blue eyes.

So they think:

If another red-eyed man committed suicide that night,

Then he must have seen two pairs of blue eyes and believed that he was red.

So I killed myself.

People with blue eyes see two pairs of red eyes,

So what he thinks in his mind is: that foreigner is really talking nonsense. ...

The next day:

The three returned to the square and found that no one committed suicide.

So the red-eyed person thought,

People with red eyes must have seen red eyes and blue eyes.

So I'm not sure about my color.

It seems that my eyes must be red. I can't be wrong.

So that night, two people with red eyes committed suicide with this idea. ..

That night, the blue-eyed man still thought:

That foreigner is really full of nonsense. ...

The third day:

The man with blue eyes came to the square and found himself alone.

Then he suddenly realized that what outsiders said was not nonsense!

So that night, he also committed suicide. ...

That's what happened.

That's right: this damn foreigner ...

The last connection problem, I remember, is the title in the comic book "The Adventures of the Sloppy King" ...

Because you can't draw here. ...

So I'll tell you by coordinate method. ..

In Cartesian coordinates (I think you should have learned it? ) Take 9 points, namely:

(0,0),( 1,0),(2,0),

(0, 1),( 1, 1),(2, 1),

(0,2),( 1,2),(2,2).

Next is the stroke:

Starting point: (2,0) → (3,2 )→ (0,-1) → (2,0) → (3,1)

Since the strokes are drawn outside the 9 o'clock range,

So it is generally difficult to think of the answer.

However, the fact is that the title does not limit the scope of strokes. ...

That's right: this damn questioner ...

This is a purely logical question. People and slaps are just for convenience. Reasoning problems cannot be mixed with irrational factors. All this is nonsense.

1. One summer day, Detective Jane Doe went for an outing. In the grass by the river, she suddenly found a body with an empty juice bottle next to it.

The female detective immediately called the police. When the police arrived, they found that the residual liquid on the wall of the juice bottle was highly toxic. When the police were moving the body, the female detective found an evening primrose and a small yellow flower just below the body. The female detective looked thoughtfully at the beautiful and lovely little flower.

After an autopsy, the police concluded: "The time of death was about 24 hours ago, and it is likely that he committed suicide by taking poison here yesterday afternoon."

The female detective disagreed and retorted: "Even if it is suicide, this is not the first scene." Which means someone put the body here. The police listened carefully to the analysis of the female detective and agreed with her. What is the basis of female detective?

The archaeologist excavated a rare bronze mirror somewhere in the northwest. There are some decorative patterns on the back of the bronze mirror, and a monkey and a cow are cast in the center. Strangely, monkeys and cows only have bodies and no heads.

After repeated research, archaeologists believe that this pattern probably hides the manufacturing age of bronze mirrors. Professor Wang knows a lot about solve riddles on the lanterns. He analyzed that these two patterns represent two characters, which together conform to the chronology of heavenly stems and earthly branches in ancient China, and indeed indicate the age of the maker. So, do you know when this bronze mirror was made?

In a hot summer, the outdoor temperature is as high as 37 degrees Celsius. On the platform of the railway station, an air-conditioned express train just arrived at the station, and the crowd was crowded, which made the platform seem a little chaotic.

Female detective Maggie was standing in the crowd when she suddenly heard someone calling her from behind: "Miss Maggie, are you going on a trip?" Maggie turned to call her Melissa, a suspect in the case he was investigating. "No, I'm here to see someone." Maggie replied. "Just right, I'm here to see someone, too." Melissa said, taking a piece of chocolate out of her handbag, dividing it in half and handing it to Maggie. "Haven't you had lunch? Here, have a chocolate. " Maggie likes chocolate. Of course, you are welcome to bring it to her mouth. Chewed for a long time. Maggie suddenly thought of something and said sharply to Melissa, "Why did you lie? You obviously just got off the train, why did you lie to me and say that you are here to pick up people? " Melissa's face changed when she asked, but she still wanted to deny it and asked, "How do you know that you saw me as soon as I got off the train?" "No, I didn't see it, but I know you are lying!" Maggie said firmly. Why did Maggie say that? Can you guess?

4.a and B traveled to the desert together, and they felt very thirsty. Suddenly, A saw a spring in the distance, but he was not sure whether he could drink it or not. At this moment, an aboriginal living in the desert came along. Only he knows that water can't be drunk, but A and B don't know the indigenous language. Suddenly, B had an idea. He stepped forward and said, "The sun is really fierce today!" "The natives replied with a smile," #% RMB! " "He can understand us, but we don't understand him. "A person who knows the local situation took over and said," Is the water here drinkable? " B asked. The aborigines still smiled and replied: "#% RMB! "So, is the water here drinkable?

5. [Simple] riddle: There is a sea, a river and no water, and there are towns where no one lives. There are roads, no cars, mountains and no trees.

6. "Ah, my diamond necklace is gone!" A scream came from the guest room of a five-star hotel. A lady angrily told the security guard that her diamond jewelry had been stolen and demanded compensation from the hotel. The sheriff rushed to the scene after receiving the report and asked your wife for details. Your wife said, "As soon as I opened the bathroom door, I saw a man in black about 180cm running out of my room from the bathroom mirror." The sheriff looked in the bathroom mirror and asked, "Are you sure you saw it from this mirror?" The lady must have nodded. The sheriff smiled: "put away your disguise, you are only doing this to get the insurance money." Do you know the sheriff's basis?

answer

1. Evening primrose blooms at night and withers in the morning, just like epiphyllum. Cordate telosma blooms under the corpse, so the corpse should have been moved.

The headless cow is noon, the headless monkey is armor, and the bronze mirror is made in Wu Jia.

3. Chocolate will soften above 28 degrees, but on the platform with outdoor temperature as high as 37 degrees, the chocolate Melissa gave Maggie was hard [chewed for a long time. ] only means that she just got off the air-conditioned car)

can

5. Map

6. The mirror blurred after taking a shower.

People work for you for seven days, and the worker's reward is a gold bar. Gold bars are divided into seven consecutive parts. At the end of each day, you must give them some gold bars. If you are only allowed to break the gold bars twice, how can you pay the workers?

Xiao Pu (now working in minimally invasive surgery, I met this question last year): This question is relatively simple compared with other minimally invasive questions, but it still makes my head bigger. That's how I did the problem. If it is broken twice, it will be divided into three parts. I divided the gold bars into three parts: 1/7, 2/7 and 4/7. In this way, I can give it to him on 1 that day1/7; The next day, I gave him 2/7 to get back1/7; On the third day, I will give him 1/7, plus the original 2/7 is 3/7; On the fourth day, I gave him 4/7 gold bars and asked him to find out 1/7 and 2/7 gold bars. On the fifth day, give him1/7; The sixth day is the same as the second day; 1/7 restored him on the 7th day.

Example 2: Now Xiaoming's family has crossed a bridge. It's dark when crossing the bridge, so there must be a light. Now it takes 1 second for Xiaoming to cross the bridge, 3 seconds for Xiaoming's brother, 6 seconds for Xiaoming's father, 8 seconds for Xiaoming's mother and 12 seconds for Xiaoming's grandfather. At most two people can cross the bridge at a time. The speed of crossing the bridge depends on the slowest one. The light turns on for 30 seconds and then goes out. Ask Xiaoming how to cross the bridge.

Reference answer: This puzzle is actually to examine the ability of candidates to solve problems under restricted conditions. Specific to this topic, many people often think that Xiao Ming should go into battle lightly and save the most time, but in the end he can't find a solution. But in another way of thinking, we can decide who will come and go according to the specific situation, as long as we make some slight changes: the first step, Xiaoming crosses the bridge with his brother and Xiaoming comes back, which takes 4 seconds; In the second step, Xiaoming crossed the river with his father and his younger brother came back, which took 9 seconds. The third step, mom and grandpa cross the river, and Xiaoming comes back, which takes 13 seconds; Finally, Xiao Ming and his younger brother crossed the river in 4 seconds, with a total time of 30 seconds. How thrilling!

Expert opinion: This kind of topic often appears in the recruitment interview of multinational enterprises, which plays an extremely obvious role in examining a person's way of thinking and his ability to change his way of thinking. According to some studies, this ability is often closely related to the tension and innovation at work. Therefore, when answering these questions, we must break through the mindset, try our best to consider the problem from different angles, constantly think backwards and empathize, and connect the question with the familiar scene to avoid confusion.

Puzzle: Guess the card.

Introduction: This is a classic and interesting logical question.

Mr. S, Mr. P and Mr. Q know that there are 16 playing cards in the desk drawer: hearts A and Q, 4 spades J, 8, 4, 2, 7, 3 flowers K, Q, 5, 4 and 6 diamonds A and 5. Professor John chooses a card from 16 card, tells Mr. P the number of points in this card, and tells Mr. Q the color of this card. At this time, Professor John asked Mr. P and Mr. Q: Can you infer what this card is from the known points or colors? So, Mr. S heard the following conversation: Mr. P: I don't know this card.

Mr q: I know you don't know this card.

Sir: Now I know this card.

Mr. Q: I know that, too.

After listening to the above conversation, Mr. S thought about it and correctly deduced what this card was.

Excuse me: What kind of card is this?

Classic puzzle set

1. A manager has three daughters, and their ages add up to 13. The ages of the three daughters add up to the manager's own age. A subordinate already knows the manager's age, but still can't determine the age of the manager's three daughters. At this time, the manager said that only one daughter's hair was black, and then the subordinates knew the age of the manager's three daughters. What are the ages of the three daughters? Why?

3 people went to a hotel and stayed in 3 rooms. The price of each room is $65,438+00, so they pay the boss $30. The next day, the boss thought that $25 was only enough for three rooms, so he asked my brother to return $5 to three guests. Unexpectedly, my brother was insatiable, and only returned 1 USD each, and secretly took it away by himself. But at the beginning, the three of them paid 30 dollars, so 1 dollar?

There are two blind people. They all bought two pairs of black socks and two pairs of white socks. Eight pairs of socks are made of the same cloth, the same size, and each pair of socks is connected with trademark paper. Two blind people accidentally mixed up eight pairs of socks. How can each of them get back two pairs of black socks and two pairs of white socks?

4. One train leaves Los Angeles for new york at the speed of 15km per hour, and another train leaves new york for Los Angeles at the speed of 20km per hour. If a bird starts from two trains at a speed of 30 kilometers per hour, starts from Los Angeles, meets another train and returns, and flies back and forth in turn until the two trains meet, how long does the bird fly?

You have two jars, 50 red marbles and 50 blue marbles. Choose a jar at random and put a marble in the jar at random. How can you give red marbles the best chance? What is the exact probability of getting the red ball in your plan?

Classic Interview Questions: Interesting Intelligence Questions of Foreign Enterprises

6. You have four jars containing pills. Each pill has a certain weight. The contaminated pill is the uncontaminated weight+1. You only weigh it once. How do you know which jar is polluted?

7. For a batch of lights numbered 1 ~ 100, all the switches are turned up (turned on), and the following operations are done: always turn the switches in the opposite direction once in multiples of 1; A multiple of 2 toggles the switch in the opposite direction again; A multiple of 3 turns the switch in the opposite direction again ... Q: Finally, the number of lights in the off state.

8. Imagine yourself in front of a mirror. Excuse me, why can the image in the mirror be upside down, but not upside down?

9. A group of people have a dance, each wearing a hat. There are only two kinds of hats, black and white, and there is at least one kind of black. Everyone can see the color of other people's hats, but not their own. The host first shows you what hats others are wearing, and then turns off the lights. If someone thinks he is wearing a black hat, he will slap himself in the face. The first time I turned off the lights, there was no sound. So I turned on the light again and everyone watched it again. When I turned off the light, it was still silent. I didn't get a slap in the face until I turned off the light for the third time. How many people are wearing black hats?

10, two rings with radii of 1 and 2 respectively. The small circle goes around the big circle. How many times does the small circle turn by itself? If it is outside the big circle, how many times does the small circle turn by itself?

1 1, 1 Yuan for a bottle of soda. After drinking two empty bottles, change one bottle of soda. Q: You have 20 yuan money. How many bottles of soda can you drink at most?

Determination of hat color problem

Introduction: This is a classic and interesting logical question.

There are three red hats, four black hats and five white hats. Let 10 people stand in a row from short to high, each wearing a hat. Everyone can't see the color of his hat, but he can only see the color of the hat of the person standing in front. So the last person can see the color of the hats on the heads of the nine people in front, while the first person can't see anyone's hats. Now, start with the last person and ask him if he knows the color of the hat he is wearing. If he says no, keep asking the person in front. Suppose the person in front must know that he is wearing a black hat. Why?

Call it the apple problem

Introduction: Not a brain teaser. Let's think about it.

10 box, with 10 apples per box, including 9 apples per box and the rest 1 kg. A box containing 9 pairs/piece can be found only by using the balance once.

The survival of prisoners

Introduction: A puzzle that really stumbles hundreds of millions of people is an interview question of Microsoft.

Five prisoners, according to 1-5, caught mung beans in sacks containing 100 mung beans. It is stipulated that everyone should catch at least one, and those who catch at most and at least should be put to death. And they can't communicate with each other, but when they catch, they can find out the remaining number of beans. Ask them who has the best chance of survival. Tip:

1, are very smart people.

Their principle is to save people first, and then kill more people.

3, 100 don't have to finish it all.

4. If there is any duplication, it will be regarded as the largest or smallest and executed together.