告诉我一下初中数学智力题 说50个初中数学智力题,50语文智力题,50个英语智力题.....

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1\u3001\u4f60\u8ba9\u5de5\u4eba\u4e3a\u4f60\u5de5\u4f5c15\u5929\uff0c\u7ed9\u5de5\u4eba\u7684\u56de\u62a5\u662f\u4e00\u6839\u91d1\u6761\u3002\u91d1\u6761\u5e73\u5206\u6210\u76f8\u8fde\u768415\u6bb5\uff0c\u4f60\u5fc5\u987b\u5728\u6bcf\u5929\u7ed3\u675f\u65f6\u7ed9\u4ed6\u4eec\u4e00\u6bb5\u91d1\u6761\uff0c\u5982\u679c\u53ea\u8bb8\u4f60\u4e09\u6b21\u628a\u91d1\u6761\u5f04\u65ad\uff0c\u4f60\u5982\u4f55\u7ed9\u4f60\u7684\u5de5\u4eba\u4ed8\u8d39\uff1f\uff081/15\uff0c2/15\uff0c4/15\uff0c8/15\uff092\u3001\u4f60\u8ba9\u5de5\u4eba\u4e3a\u4f60\u5de5\u4f5c31\u5929\uff0c\u7ed9\u5de5\u4eba\u7684\u56de\u62a5\u662f\u4e00\u6839\u91d1\u6761\u3002\u91d1\u6761\u5e73\u5206\u6210\u76f8\u8fde\u768431\u6bb5\uff0c\u4f60\u5fc5\u987b\u5728\u6bcf\u5929\u7ed3\u675f\u65f6\u7ed9\u4ed6\u4eec\u4e00\u6bb5\u91d1\u6761\uff0c\u5982\u679c\u53ea\u8bb8\u4f60\u56db\u6b21\u628a\u91d1\u6761\u5f04\u65ad\uff0c\u4f60\u5982\u4f55\u7ed9\u4f60\u7684\u5de5\u4eba\u4ed8\u8d39\uff1f\uff081/31\uff0c2/31\uff0c4/31\uff0c8/31\uff0c16/31\uff093\u3001\u4f60\u8ba9\u5de5\u4eba\u4e3a\u4f60\u5de5\u4f5c\uff082^n\uff09-1\u5929\uff0c\u7ed9\u5de5\u4eba\u7684\u56de\u62a5\u662f\u4e00\u6839\u91d1\u6761\u3002\u91d1\u6761\u5e73\u5206\u6210\u76f8\u8fde\u7684\uff082^n\uff09-1\u6bb5\uff0c\u4f60\u5fc5\u987b\u5728\u6bcf\u5929\u7ed3\u675f\u65f6\u7ed9\u4ed6\u4eec\u4e00\u6bb5\u91d1\u6761\uff0c\u5982\u679c\u53ea\u8bb8\u4f60n-1\u6b21\u628a\u91d1\u6761\u5f04\u65ad\uff0c\u4f60\u5982\u4f55\u7ed9\u4f60\u7684\u5de5\u4eba\u4ed8\u8d39\uff1f\uff081/\uff08\uff082^n\uff09-1\uff09\uff0c2/\uff08\uff082^n\uff09-1\uff09\uff0c4/\uff08\uff082^n\uff09-1\uff09\uff0c...\uff094.\u4eba\u6c11\u5e01\u4e3a\u4ec0\u4e48\u53ea\u67091\u30012\u30015\u300110\u7684\u9762\u503c\uff1f\uff08\u4fbf\u4e8e\u627e\u96f6\u94b1\u3002\u7406\u60f3\u72b6\u6001\u4e0b\u5e94\u662f1\u30012\u30014\u30018\uff0c\u5728\u73b0\u5b9e\u751f\u6d3b\u4e2d\u5e38\u752810\u8fdb\u5236\uff0c\u6545\u5c064\u30018\u53d8\u4e3a5\u300110\u3002\u53ea\u89812\u6709\u4e24\u4e2a\uff0c1\u30012\u30012\u30015\u300110\u4e94\u4e2a\u6570\u5b57\u53ef\u8868\u793a1-20\u3002\uff09
\u667a\u529b\u98987(\u79f0\u91cf\u836f\u4e38)
\u79f0\u91cf\u836f\u4e38
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\u89e3\u9898\u601d\u8def\uff1a
1\u3001\u5148\u7ed9\u56db\u4e2a\u7f50\u5b50\u7f16\u53f71\u30012\u30013\u30014\u3002 2\u3001\u5982\u679c\u5df2\u77e5\u53ea\u6709\u4e00\u4e2a\u7f50\u5b50\u88ab\u6c61\u67d3\uff1a\u52191\u53f71\u4e2a\uff0c2\u53f7\u62ff2\u4e2a\uff0c3\u53f7\u62ff3\u4e2a\uff0c4\u53f7\u62ff4\u4e2a\uff0c\u79f0\u4e00\u4e0b\uff0c\u518d\u51cf\u53bb15\u4e2a\u836f\u4e38\u7684\u6807\u51c6\u91cd\u91cf\u3002\u7ed3\u679c\u53ef\u80fd\u4e3a1,2,3,4\u3002 \u82e5\u662f1\uff0c\u5c31\u662f1\u53f7\u7f50\uff1b\u82e5\u662f2\uff0c\u5c31\u662f2\u53f7\u7f50\uff1b\u82e5\u662f3\uff0c\u5c31\u662f3\u53f7\u7f50\uff1b \u82e5\u662f4\uff0c\u5c31\u662f4\u53f7\u7f50\uff1b 3\u3001\u5982\u679c\u56db\u4e2a\u7f50\u5b50\u90fd\u53ef\u80fd\u88ab\u6c61\u67d3\uff0c\u4e5f\u53ef\u80fd\u4e0d\u88ab\u6c61\u67d3\uff1a\u52191\u53f7\u62ff1\u4e2a\uff0c2\u53f7\u62ff2\u4e2a\uff0c3\u53f7\u62ff4\u4e2a\uff0c4\u53f7\u62ff8\u4e2a\uff0c\u79f0\u4e00\u4e0b\uff0c\u518d\u51cf\u53bb15\u4e2a\u836f\u4e38\u7684\u6807\u51c6\u91cd\u91cf\u3002\u7ed3\u679c\u53ef\u80fd\u4e3a0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15\u3002\u82e5\u662f0\uff0c\u56db\u4e2a\u7f50\u5b50\u90fd\u6ca1\u88ab\u6c61\u67d3\uff1b\u82e5\u662f1\uff0c\u5c31\u662f1\u53f7\u7f50\uff1b<br \u82e5\u662f2\uff0c\u5c31\u662f2\u53f7\u7f50\uff1b \u82e5\u662f3\uff0c\u5c31\u662f1\u30012\u53f7\u7f50\uff1b \u82e5\u662f4\uff0c\u5c31\u662f3\u53f7\u7f50\uff1b\u82e5\u662f5\uff0c\u5c31\u662f1\u30014\u53f7\u7f50\uff1b\u82e5\u662f6\uff0c\u5c31\u662f2\u30013\u53f7\u7f50\uff1b \u82e5\u662f7\uff0c\u5c31\u662f1\u30012\u30013\u53f7\u7f50\uff1b \u82e5\u662f8\uff0c\u5c31\u662f4\u53f7\u7f50\uff1b \u82e5\u662f9\uff0c\u5c31\u662f1\u30014\u53f7\u7f50\uff1b\u82e5\u662f10\uff0c\u5c31\u662f2\u30014\u53f7\u7f50\uff1b\u82e5\u662f11\uff0c\u5c31\u662f1\u30012\u30014\u53f7\u7f50\uff1b \u82e5\u662f12\uff0c\u5c31\u662f2\u30014\u53f7\u7f50\uff1b \u82e5\u662f13\uff0c\u5c31\u662f1\u30013\u30014\u53f7\u7f50\uff1b \u82e5\u662f14\uff0c\u5c31\u662f2\u30013\u30014\u53f7\u7f50\uff1b \u82e5\u662f15\uff0c\u56db\u4e2a\u7f50\u5b50\u5168\u88ab\u6c61\u67d3\u3002 \uff08\u6b65\u9aa43\u5b9e\u9645\u4e0a\u5df2\u7ecf\u5305\u542b\u6b65\u9aa42\u3002\uff09
\u53c2\u8003\u7b54\u6848\uff1a \u540c\u4e0a\u3002

\u8bd5\u9898\u62d3\u5c55\uff1a
1\u3001\u670910\u74f6\u836f\u4e38\uff0c\u5176\u4e2d\u82e5\u5e72\u74f6\u5185\u4e3a\u8d85\u91cd\u836f\u4e38\u3002\u666e\u901a\u836f\u4e385g/\u6bcf\u7c92\uff0c\u8d85\u91cd\u836f\u4e386g/\u6bcf\u7c92\uff0c\u6bcf\u74f6\u836f\u4e38\u7684\u6570\u91cf\u76f8\u540c\u3002\u6c42\uff1a\u53ea\u7528\u4e00\u67b6\u5929\u5e73\uff0c\u53ea\u79f0\u4e00\u6b21\uff0c\u627e\u51fa\u54ea\u51e0\u74f6\u88c5\u6709\u8d85\u91cd\u836f\u4e38\u3002\uff08\u7b54\u6848\uff1a\u5206\u522b\u53d6\u51fa1\u30012\u30014\u30018\u300116\u300132\u300164\u3001128\u3001256\u3001512\u7c92\uff09 2\u3001\u6709N\u74f6\u836f\u4e38\uff0c\u5176\u4e2d\u82e5\u5e72\u74f6\u5185\u4e3a\u8d85\u91cd\u836f\u4e38\u3002\u666e\u901a\u836f\u4e385g/\u6bcf\u7c92\uff0c\u8d85\u91cd\u836f\u4e386g/\u6bcf\u7c92\uff0c\u6bcf\u74f6\u836f\u4e38\u7684\u6570\u91cf\u76f8\u540c\u3002\u6c42\uff1a\u53ea\u7528\u4e00\u67b6\u5929\u5e73\uff0c\u53ea\u79f0\u4e00\u6b21\uff0c\u627e\u51fa\u54ea\u51e0\u74f6\u88c5\u6709\u8d85\u91cd\u836f\u4e38\u3002\uff08\u7b54\u6848\uff1a\u5206\u522b\u53d6\u51fa1\u30012\u30014\u3001...\u30012^n\u7c92\uff093\u300110\u4e2a\u7bb1\u5b50\uff0c\u6bcf\u4e2a\u7bb1\u5b5010\u4e2a\u82f9\u679c\uff0c\u5176\u4e2d\u4e00\u4e2a\u7bb1\u5b50\u7684\u82f9\u679c\u662f9\u4e24/\u4e2a\uff0c\u5176\u4ed6\u7684\u90fd\u662f1\u65a4/\u4e2a\u3002 \u8981\u6c42\u5229\u7528\u4e00\u4e2a\u79e4\uff0c\u53ea\u79e4\u4e00\u6b21\uff0c\u627e\u51fa\u90a3\u4e2a\u88c59\u4e24/\u4e2a\u7684\u7bb1\u5b50\u3002\uff08\u7b54\u6848\uff1a\u7f16\u53f7\uff0c\u5206\u522b\u53d6\u51fa1\u30012\u30014\u3001...\u300110\u4e2a\uff0c\u79e4\uff0c\u51cf\uff0c\u5c11n\u4e24\u5c31\u662fn\u53f7\uff09

1. What room has no walls, no doors, no windows, and no floors?

A mushroom.(\u8611\u83c7)

2. What is smaller than an insect's mouth?

Anything it eats.

3. What large instrument do you carry in your ears?

Drums, that is eardrums.(\u9f13\u819c)

4. What's too much for one, just right for two, but nothing at all for three?

A secret.

5. What person tried to make you smile most of the time?

A photographer.

6. What animal has a head like a cat, eyes like a cat, a tail like a cat, but isn't a cat?

A kitten.(\u5c0f\u732b)

7. What surprising things happen every 24 hours?

Day breaks, but doesn't fall; night falls, but doesn't break.

8. What can hear you without ears and can answer you without a mouth?

An echo.(\u56de\u58f0)

9. What do you know about the kings of France?

They are all dead.

10. What question can you never answer 'yes" to"

Are you asleep?

11. Why do some old people never use glasses?

They must prefer bottles to glasses.

12. Why is the person wearing two coats while painting the house?

Because the instructions on the paint can say "Put on two coats for best results."

13. What two words have thousands of letters in them?

Post office.

14. What do workers do in a clock factory?

They make faces all day.

15. What 5-letter word has 6 left when you take 2 letters away?

Sixty.

16. When do you go as fast as a racing car?

When you are in it.

17. How many sides does a house have?

Two - inside and outside.

18. What never asks any questions but always gets answers?

A doorbell.

19. Where did Columbus stand when he discovered America?

On his feet.

20. When the boy fell into the water, what's the first thing he did?

He got wet first of all.

21. Who isn't your sister and isn't your brother, but is still a child of your mother and father?

I myself.

22. What has teeth but cannot eat?

A comb.

23. What kind of man can raise things without lifting them?

A farmer.

24. Why does time fly?

To get away from all the people who are trying to kill it.


25. Name five days of the week without saying: Monday, Tuesday, Wednesday, Thursday, Friday.

The day before yesterday, yesterday, today, tomorrow, and the day after tomorrow.

26. What animal eats and drinks with its tail?

All do. No animal takes off its tail when eating and drinking.

27. What has a soft bed but never sleeps, a big mouth but never speaks?

A river.

28. What kind of dog never bite?

A hot dog.

29. Why does the Statue of Liberty stand in New York Harbor?

Because it can't sit down.

30. What did one invisible man say to the other invisible man?

It's nice not to see you again.

1. What room has no walls, no doors, no windows, and no floors?

A mushroom.(\u8611\u83c7)

2. What is smaller than an insect's mouth?

Anything it eats.

3. What large instrument do you carry in your ears?

Drums, that is eardrums.(\u9f13\u819c)

4. What's too much for one, just right for two, but nothing at all for three?

A secret.

5. What person tried to make you smile most of the time?

A photographer.

6. What animal has a head like a cat, eyes like a cat, a tail like a cat, but isn't a cat?

A kitten.(\u5c0f\u732b)

7. What surprising things happen every 24 hours?

Day breaks, but doesn't fall; night falls, but doesn't break.

8. What can hear you without ears and can answer you without a mouth?

An echo.(\u56de\u58f0)

9. What do you know about the kings of France?

They are all dead.

10. What question can you never answer 'yes" to"

Are you asleep?

11. Why do some old people never use glasses?

They must prefer bottles to glasses.

12. Why is the person wearing two coats while painting the house?

Because the instructions on the paint can say "Put on two coats for best results."

13. What two words have thousands of letters in them?

Post office.

14. What do workers do in a clock factory?

They make faces all day.

15. What 5-letter word has 6 left when you take 2 letters away?

Sixty.

16. When do you go as fast as a racing car?

When you are in it.

17. How many sides does a house have?

Two - inside and outside.

18. What never asks any questions but always gets answers?

A doorbell.

19. Where did Columbus stand when he discovered America?

On his feet.

20. When the boy fell into the water, what's the first thing he did?

He got wet first of all.

21. Who isn't your sister and isn't your brother, but is still a child of your mother and father?

I myself.

22. What has teeth but cannot eat?

A comb.

23. What kind of man can raise things without lifting them?

A farmer.

24. Why does time fly?

To get away from all the people who are trying to kill it.


25. Name five days of the week without saying: Monday, Tuesday, Wednesday, Thursday, Friday.

The day before yesterday, yesterday, today, tomorrow, and the day after tomorrow.

26. What animal eats and drinks with its tail?

All do. No animal takes off its tail when eating and drinking.

27. What has a soft bed but never sleeps, a big mouth but never speaks?

A river.

28. What kind of dog never bite?

A hot dog.

29. Why does the Statue of Liberty stand in New York Harbor?

Because it can't sit down.

30. What did one invisible man say to the other invisible man?

It's nice not to see you again.

1. What room has no walls, no doors, no windows, and no floors?

A mushroom.(\u8611\u83c7)

2. What is smaller than an insect's mouth?

Anything it eats.

3. What large instrument do you carry in your ears?

Drums, that is eardrums.(\u9f13\u819c)

4. What's too much for one, just right for two, but nothing at all for three?

A secret.

5. What person tried to make you smile most of the time?

A photographer.

6. What animal has a head like a cat, eyes like a cat, a tail like a cat, but isn't a cat?

A kitten.(\u5c0f\u732b)

7. What surprising things happen every 24 hours?

Day breaks, but doesn't fall; night falls, but doesn't break.

8. What can hear you without ears and can answer you without a mouth?

An echo.(\u56de\u58f0)

9. What do you know about the kings of France?

They are all dead.

10. What question can you never answer 'yes" to"

Are you asleep?

11. Why do some old people never use glasses?

They must prefer bottles to glasses.

12. Why is the person wearing two coats while painting the house?

Because the instructions on the paint can say "Put on two coats for best results."

13. What two words have thousands of letters in them?

Post office.

14. What do workers do in a clock factory?

They make faces all day.

15. What 5-letter word has 6 left when you take 2 letters away?

Sixty.

16. When do you go as fast as a racing car?

When you are in it.

17. How many sides does a house have?

Two - inside and outside.

18. What never asks any questions but always gets answers?

A doorbell.

19. Where did Columbus stand when he discovered America?

On his feet.

20. When the boy fell into the water, what's the first thing he did?

He got wet first of all.

21. Who isn't your sister and isn't your brother, but is still a child of your mother and father?

I myself.

22. What has teeth but cannot eat?

A comb.

23. What kind of man can raise things without lifting them?

A farmer.

24. Why does time fly?

To get away from all the people who are trying to kill it.


25. Name five days of the week without saying: Monday, Tuesday, Wednesday, Thursday, Friday.

The day before yesterday, yesterday, today, tomorrow, and the day after tomorrow.

26. What animal eats and drinks with its tail?

All do. No animal takes off its tail when eating and drinking.

27. What has a soft bed but never sleeps, a big mouth but never speaks?

A river.

28. What kind of dog never bite?

A hot dog.

29. Why does the Statue of Liberty stand in New York Harbor?

Because it can't sit down.

30. What did one invisible man say to the other invisible man?

It's nice not to see you again.

31. What wears a cap but has no head?

A bottle.

32. What rises in the morning and waves all day?

A flag.

33. What is an astronomer?(\u5929\u6587\u5b66\u5bb6)?

A night watchman with a college education.

34. How can you tell clocks and watches are shy?

Because they always have their hands in front of their faces.

35. What is wind?

Air in a hurry.

36. What comes after the letter "A"?

All the other letters.

37. What starts with a T, ends with a T, and is full of T?

Teapot.

38. What word can you make shorter by adding to it?

Short.

39. What person does every man take his hat off to?

A barber.

40. Why does the boy carry a ladder to the school?

Because he wants to go to high school.

41. What can you swallow that can also swallow you?

Water.

42. What's the difference between a hill and a pill?

A hill is hard to get up and a pill is hard to get down.

43. Why is it useless to send a letter to Washington?

Because he's dead.

44. A doctor and a lawyer loved the same girl. The lawyer went away for a week and gave the girl seven apples before he left. Why?


Because an apple a day keeps the doctor away.

45. What will you do if a man-eating tiger is running after you?

Nothing. Because I'm a woman.

46. What always travels on foot?

A shoe.

47. Where can happiness always be found?

In the dictionary.

48. What is higher without a head than with a head?

A pillow.(\u6795\u5934)


49. Why don't you advertise for your lost dog?

He can't read.

50. On which side does a bird have the most feathers?

The outside.

5个海盗抢得100枚金币后,讨论如何进行公正分配。他们商定的分配原则是: (1)抽签确定各人的分配顺序号码(1,2,3,4,5);(2)由抽到1号签的海盗提出分配方案,然后5人进行表决,如果方案得到超过半数的人同意,就按照他的方案进行分配,否则就将1号扔进大海喂鲨鱼(3)如果1号被扔进大海,则由2号提出分配方案,然后由剩余的4人进行表决,当且仅当超过半数的人同意时,才会按照他的提案进行分配,否则也将被扔入大海; (4)依此类推。这里假设每一个海盗都是绝顶聪明而理性,他们都能够进行严密的逻辑推理,并能很理智的判断自身的得失,即能够在保住性命的前提下得到最多的金币。同时还假设每一轮表决后的结果都能顺利得到执行,那么抽到1号的海盗应该提出怎样的分配方案才能使自己既不被扔进海里,又可以得到更多的金币呢?
解题思路1:
首先从5号海盗开始,因为他是最安全的,没有被扔下大海的风险,因此他的策略也最为简单,即最好前面的人全都死光光,那么他就可以独得这100枚金币了。接下来看4号,他的生存机会完全取决于前面还有人存活着,因为如果1号到3号的海盗全都喂了鲨鱼,那么在只剩4号与5号的情况下,不管4号提出怎样的分配方案,5号一定都会投反对票来让4号去喂鲨鱼,以独吞全部的金币。哪怕4号为了保命而讨好5号,提出(0,100)这样的方案让5号独占金币,但是5号还有可能觉得留着4号有危险,而投票反对以让其喂鲨鱼。因此理性的4号是不应该冒这样的风险,把存活的希望寄托在5号的随机选择上的,他惟有支持3号才能绝对保证自身的性命。 再来看3号,他经过上述的逻辑推理之后,就会提出(100,0,0)这样的分配方案,因为他知道4号哪怕一无所获,也还是会无条件的支持他而投赞成票的,那么再加上自己的1票就可以使他稳获这100金币了。 但是,2号也经过推理得知了3号的分配方案,那么他就会提出(98,0,1,1)的方案。因为这个方案相对于3号的分配方案,4号和5号至少可以获得1枚金币,理性的4号和5号自然会觉得此方案对他们来说更有利而支持2号,不希望2号出局而由3号来进行分配。这样,2号就可以屁颠屁颠的拿走98枚金币了。 不幸的是,1号海盗更不是省油的灯,经过一番推理之后也洞悉了2号的分配方案。他将采取的策略是放弃2号,而给3号1枚金币,同时给4号或5号2枚金币,即提出(97,0,1,2,0)或(97,0,1,0,2)的分配方案。由于1号的分配方案对于3号与4号或5号来说,相比2号的方案可以获得更多的利益,那么他们将会投票支持1号,再加上1号自身的1票,97枚金币就可轻松落入1号的腰包了
智力题2(猜牌问题)猜牌问题
S先生、P先生、Q先生他们知道桌子的抽屉里有16张扑克牌:红桃A、Q、4 黑桃J、8、4、2、7、3 草花K、Q、5、4、6 方块A、5。约翰教授从这16张牌中挑出一张牌来,并把这张牌的点数告诉 P先生,把这张牌的花色告诉Q先生。这时,约翰教授问P先生和Q 先生:你们能从已知的点数或花色中推知这张牌是什么牌吗? 于是,S先生听到如下的对话: P先生:我不知道这张牌。Q先生:我知道你不知道这张牌。 P先生:现在我知道这张牌了。 Q先生:我也知道了。 听罢以上的对话,S先生想了一想之后,就正确地推出这张牌是什么牌。 请问:这张牌是什么牌?
解题思路:
由第一句话“P先生:我不知道这张牌。”可知,此牌必有两种或两种以上花色,即可能是A、Q、4、5。如果此牌只有一种花色,P先生知道这张牌的点数,P先生肯定知道这张牌。由第二句话“Q先生:我知道你不知道这张牌。”可知,此花色牌的点数只能包括A、Q、4、5,符合此条件的只有红桃和方块。Q先生知道此牌花色,只有红桃和方块花色包括A、Q、4、5,Q先生才能作此断言。 由第三句话“P先生:现在我知道这张牌了。”可知,P先生通过“Q先生:我知道你不知道这张牌。”判断出花色为红桃和方块,P先生又知道这张牌的点数,P先生便知道这张牌。据此,排除A,此牌可能是Q、4、5。如果此牌点数为A,P先生还是无法判断。 由第四句话“Q先生:我也知道了。”可知,花色只能是方块。如果是红桃,Q先生排除A后,还是无法判断是Q还是4。综上所述,这张牌是方块5。
参考答案:
这张牌是方块5。

智力题3(燃绳问题) 燃绳问题
烧一根不均匀的绳,从头烧到尾总共需要1个小时。现在有若干条材质相同的绳子,问如何用烧绳的方法来计时一个小时十五分钟呢?
解题思路:
烧一根这样的绳,从头烧到尾1个小时。由此可知,头尾同时烧共需半小时。同时烧两根这样的绳,一个烧一头,一个烧两头;当烧两头的绳燃尽时,共要半小时,烧一头的绳继续烧还需半小时;如果此时将烧一头的绳的另一头也点燃,那么只需十五分钟。
参考答案:
同时燃两根这样的绳,一个烧一头,一个烧两头;等一根燃尽,将另一根掐灭备用。标记为绳2。再找一根这样的绳,标记为绳1。一头燃绳1需要1个小时,再两头燃绳2需十五分钟,用此法可计时一个小时十五分钟。

智力题4 乒乓球问题
假设排列着100个乒乓球,由两个人轮流拿球装入口袋,能拿到第100个乒乓球的人为胜利者。条件是:每次拿球者至少要拿1个,但最多不能超过5个,问:如果你是最先拿球的人,你该拿几个?以后怎么拿就能保证你能得到第100个乒乓球?
解题思路:
1、我们不妨逆向推理,如果只剩6个乒乓球,让对方先拿球,你一定能拿到第6个乒乓球。理由是:如果他拿1个,你拿5个;如果他拿2个,你拿4个;如果他拿3个,你拿3个;如果他拿4个,你拿2个;如果他拿5个,你拿1个。2、我们再把100个乒乓球从后向前按组分开,6个乒乓球一组。100不能被6整除,这样就分成17组;第1组4个,后16组每组6个。3、这样先把第1组4个拿完,后16组每组都让对方先拿球,自己拿完剩下的。这样你就能拿到第16组的最后一个,即第100个乒乓球。
参考答案:
先拿4个,他拿n个,你拿6-n,依此类推,保证你能得到第100个乒乓球。
试题扩展:
1、假设排列着100个乒乓球,由两个人轮流拿球装入口袋,能拿到第100个乒乓球的人为胜利者。条件是:每次拿球者至少要拿2个,但最多不能超过7个,问:如果你是最先拿球的人,你该拿几个?以后怎么拿就能保证你能得到第100个乒乓球?(先拿1个,他拿n个,你拿9-n,依此类推)2、假设排列着X个乒乓球,由两个人轮流拿球装入口袋,能拿到第X个乒乓球的人为胜利者。条件是:每次拿球者至少要拿Y个,但最多不能超过Z个,问:如果你是最先拿球的人,你该拿几个?以后怎么拿就能保证你能得到第X个乒乓球?(先拿X/(Y+Z)的余数个,他拿n个,你拿(Y+Z)-n,依此类推。当然必须保证X/(Y+Z)的余数不等于0)

智力题5(喝汽水问题)
喝汽水问题
1元钱一瓶汽水,喝完后两个空瓶换一瓶汽水,问:你有20元钱,最多可以喝到几瓶汽水?
解题思路1:
一开始20瓶没有问题,随后的10瓶和5瓶也都没有问题,接着把5瓶分成4瓶和1瓶,前4个空瓶再换2瓶,喝完后2瓶再换1瓶,此时喝完后手头上剩余的空瓶数为2个,把这2个瓶换1瓶继续喝,喝完后把这1个空瓶换1瓶汽水,喝完换来的那瓶再把瓶子还给人家即可,所以最多可以喝的汽水数为:20+10+5+2+1+1+1=40
解题思路2:
先看1元钱最多能喝几瓶汽水。喝1瓶余1个空瓶,借商家1个空瓶,2个瓶换1瓶继续喝,喝完后把这1个空瓶还给商家。即1元钱最多能喝2瓶汽水。20元钱当然最多能喝40瓶汽水。
解题思路3:
两个空瓶换一瓶汽水,可知纯汽水只值5角钱。20元钱当然最多能喝40瓶的纯汽水。N元钱当然最多能喝2N瓶汽水。
参考答案:
40瓶

试题拓展:
1、1元钱一瓶汽水,喝完后两个空瓶换一瓶汽水,问:你有N元钱,最多可以喝到几瓶汽水?(答案2N) 2、9角钱一瓶汽水,喝完后三个空瓶换一瓶汽水,问:你有18元钱,最多可以喝到几瓶汽水?(答案30) 3、1元钱一瓶汽水,喝完后四个空瓶换一瓶汽水,问:你有15元钱,最多可以喝到几瓶汽水?(答案20)
智力题6(分割金条) 分割金条
你让工人为你工作7天,给工人的回报是一根金条。金条平分成相连的7段,你必须在每天结束时给他们一段金条,如果只许你两次把金条弄断,你如何给你的工人付费?
解题思路:
本题实质问题是数字表示问题。由1、2两个数字可表示1-3三个数字。由1、2、4三个数字可表示1-7七个数字(即1,2,1+2,4,4+1,4+2,4+2+1)。由1、2、4、8四个数字可表示1-15十五个数字。依此类推。
参考答案:
把金条分成1/7、2/7和4/7三份。这样,第1天我就可以给他1/7;第2天我给他2/7,让他找回我1/7;第3天我就再给他1/7,加上原先的2/7就是3/7;第4天我给他那块4/7,让他找回那两块1/7和2/7的金条;第5天,再给他1/7;第6天和第2天一样;第7天给他找回的那个1/7。

试题拓展:
1、你让工人为你工作15天,给工人的回报是一根金条。金条平分成相连的15段,你必须在每天结束时给他们一段金条,如果只许你三次把金条弄断,你如何给你的工人付费?(1/15,2/15,4/15,8/15)2、你让工人为你工作31天,给工人的回报是一根金条。金条平分成相连的31段,你必须在每天结束时给他们一段金条,如果只许你四次把金条弄断,你如何给你的工人付费?(1/31,2/31,4/31,8/31,16/31)3、你让工人为你工作(2^n)-1天,给工人的回报是一根金条。金条平分成相连的(2^n)-1段,你必须在每天结束时给他们一段金条,如果只许你n-1次把金条弄断,你如何给你的工人付费?(1/((2^n)-1),2/((2^n)-1),4/((2^n)-1),...)4.人民币为什么只有1、2、5、10的面值?(便于找零钱。理想状态下应是1、2、4、8,在现实生活中常用10进制,故将4、8变为5、10。只要2有两个,1、2、2、5、10五个数字可表示1-20。)
智力题7(称量药丸)
称量药丸
你有四个装药丸的罐子,每个药丸都有一定的重量,被污染的药丸是没被污染的重量+1。只称量一次,如何判断哪个罐子的药被污染了?
解题思路:
1、先给四个罐子编号1、2、3、4。 2、如果已知只有一个罐子被污染:则1号1个,2号拿2个,3号拿3个,4号拿4个,称一下,再减去15个药丸的标准重量。结果可能为1,2,3,4。 若是1,就是1号罐;若是2,就是2号罐;若是3,就是3号罐; 若是4,就是4号罐; 3、如果四个罐子都可能被污染,也可能不被污染:则1号拿1个,2号拿2个,3号拿4个,4号拿8个,称一下,再减去15个药丸的标准重量。结果可能为0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15。若是0,四个罐子都没被污染;若是1,就是1号罐;<br 若是2,就是2号罐; 若是3,就是1、2号罐; 若是4,就是3号罐;若是5,就是1、4号罐;若是6,就是2、3号罐; 若是7,就是1、2、3号罐; 若是8,就是4号罐; 若是9,就是1、4号罐;若是10,就是2、4号罐;若是11,就是1、2、4号罐; 若是12,就是2、4号罐; 若是13,就是1、3、4号罐; 若是14,就是2、3、4号罐; 若是15,四个罐子全被污染。 (步骤3实际上已经包含步骤2。)
参考答案: 同上。

试题拓展:
1、有10瓶药丸,其中若干瓶内为超重药丸。普通药丸5g/每粒,超重药丸6g/每粒,每瓶药丸的数量相同。求:只用一架天平,只称一次,找出哪几瓶装有超重药丸。(答案:分别取出1、2、4、8、16、32、64、128、256、512粒) 2、有N瓶药丸,其中若干瓶内为超重药丸。普通药丸5g/每粒,超重药丸6g/每粒,每瓶药丸的数量相同。求:只用一架天平,只称一次,找出哪几瓶装有超重药丸。(答案:分别取出1、2、4、...、2^n粒)3、10个箱子,每个箱子10个苹果,其中一个箱子的苹果是9两/个,其他的都是1斤/个。 要求利用一个秤,只秤一次,找出那个装9两/个的箱子。(答案:编号,分别取出1、2、4、...、10个,秤,减,少n两就是n号)

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