Learning Notes Logical thinking Training topic set

1. In 257 bottles of water, 1 bottles are poisonous, poisonous hair time is 2 hours, how many mice to use in two hours to find poisonous water.

Answer: 9, 9 bits can represent 512 numbers. For each bottle of water number, so that 9 small white mice to represent 9 bits, if the bits 1 then drink the number of water, 0 do not drink.

2.25 Horses, 5 tracks, a horse a track, the game can only get 5 horses between the speed, rather than velocity, to win 1,2,3 name at least how many.

A. 6 B. 7 C. 8 D. 12

Answer: 7 games. 5 games to set the fastest horse in each group, 1 games to set the ranking of each group, this game can be set first and eliminated two groups of horses, respectively, with the first group of 2, 3 and 2nd Group of 1, 2 and 3rd Group 1 to carry out 1 games, set out 2, 3, this game is finished.

3. Group games, each group has 5 teams, each other to play a single round robin, win a 3 points, flat a 1 points, lose a score, the group's top three qualified. Divide the lottery. Ask a team at least take () the point of the theoretical outlet Hope ()

A.1 B.2 C.3 D.4

Answer:

The top two scored 4 wins and 3 wins respectively, after three were drawn, after three points were 2, the lottery decided to qualify.

4. The prevalence rate of one cancer in all populations is 0.008. For patients with cancer, 2% of the hospital tests may have been wrongly diagnosed as having no cancer. For cancer-free patients, 3% of them may be wrongly convicted of cancer. Q: A new patient has a test showing cancer, and the probability of a patient actually suffering from cancer. (The calculation process is rounded to keep 4 decimal digits)

Answer: Bayesian formula.

5. In an adventure game, you see a treasure box, the body has n keys, one can open the chest, if there is no hint, random try, ask:
(1) What is the probability of opening a chest (1=<k<=n) exactly the first K-time?
(2) The average number of times to try.

1.1/n

2. List the distribution law and calculate the mathematical expectation. (n+1)/2

Arithmetic progression sum formula:

Sn=n*a1+n (n-1) D/2 or Sn=n (A1+an)/2

Geometric progression sum formula: Promotion type: SN=N*A1 (q=1) sn=a1 (1-q^n)/(1-Q) = (a1-an*q)/(1-Q) (q≠1)



6. The figure below is an English equation. Each English letter represents a number in the 0~9. Now known: v=2,w=4,n=7.
F stands for () A.2 b.4 C.7 D.9
Answer: F can only move forward 1 digits, E is 1,i+t+o up to 27, so F is 8 or 9, select D. The deduction of the classmate: 9021+846+671=10538
e=1 o=6 i=0 t=8 f=9 First step, first, the e=1 reason, the 4-digit and 2 3-digit and 5-digit, 9999+999+999<20000, so, must be more than 10,000
Step two, look at the thousand and the Hundred
F if it is 8, then must enter 2, because it is impossible to enter 3, so, i=0, look at the hundred, there is a I, so it is impossible to enter 2 bits, so only into 1, so F is 9, meanwhile, I is 0
Step three, look at the digits.
E+e+o=t, it's 2+o=t.
0,1,2,4,7,9 has been used, so only 3, 5 and 6,8
So the bit is not carry, so the top ten H is 3, so the Single-digit O is 6,t is 8
The last step, G is 5.


7. Give you 8 small stones and a balance. The weight of 7 stones is the same, and the other one is slightly heavier than the 7. In the worst case, weigh at least a few times to find out the final stone.

Solution: 4 vs 4 weighing once, heavy over there 2 vs 2 weighing once, heavy over there 1 vs 1 weighing once, a total of 3 times.

8. The little squirrel picked up 100 nuts to be transported home. Home is 100 meters away from the place where the nuts are placed. The little squirrel transports up to 50 stars at a time. BUT. Little squirrel very greedy ... Every 2 meters to go to eat a nut ... Ask the little squirrel how many nuts can be transported home. A. 0 b.10 c.25 d.50 answer: C Set the location of the nuts for a, home for B, from A to B in the direction of the movement needs to consume nuts. The title asks the most how many nuts to go home, in order to maximize the results, so need to start every 50, so the title is to seek the least consumption of nuts, because the a->b direction of the movement has been to consume nuts, so is to seek this direction movement of the minimum distance. As long as 50, so there is a section of A->b direction must go two times, set this distance of X, the rest of the distance is Y, there are x+y=100. The total number of nuts consumed is (2x+y)/2. And in order for the last Y segment to be able to transport all the remaining nuts in the 2x segment, the 2* (50-X/2) <=50 must be met, so x>=50. Because to make (2x+y)/2= (x+100)/2 minimum, x should go to the minimum value of 50, so the number of nuts consumed (50+100)/2=75, so the remaining 25



9.

。 The graphic of the place is (a)

Answer: The 2 matches of the center connection rotate 45 degrees clockwise at a time.

10. A group of friends for dinner. When the first bottle of wine, everyone equally. A bottle of drink, a few friends have an emergency left. When the second bottle came up, the rest were equally divided, and a few of them left when the drink was finished. When the third bottle of wine is still the rest of the people equally. At the end of the time one of the humane: "Hey, I just had a bottle." How many people get together for a drink?

Answer:

A total of three bottles of wine, one of them drank three times, if each drink 1/3 can be drunk, but the number is changing, so there must be a drink more than 1/3 bottles; because it's an average, so the numerator is 1 and the denominator is an integer, so the last time is 2 people, and three times the number is not equal, so it can't be 1/ 2+1/4+1/4=1, so, can only be one greater than 1/4, one is less than 1/4, so only the 1/2+1/3+1/6 satisfies the condition, so the initial person is 6 people

11. Two people play games, put a number on the forehead (positive integer >=1), only see each other's, do not see their own, and the difference between the two figures is 1, the following is the dialogue between the two: a: I do not know B: I do not know a: I know B: I also know how to ask a head on the number of words, b Head of the number of words () A is 4,b is 3 A is 3,b is 2. A is 2,b is 1 A is 1,b is 2

Answer: B 1. A See B is 2, not sure A is 1 or 3, so don't know, 2 b see A is 3, not sure B is 2 or 4; 3 A hear B said B also don't know, excluding a is 1; so a is 3; 4 B Hear a say a know, excluding B to 4; so B is 2.

12. There is a sports competition with a total of M items, there are athletes a,b,c three participants, in each project, first, second, third, respectively, X,y,z, where x,y,z is a positive integer and x>y>z. Finally a gets 22 points, B and C get 9 points and B gets first in the hundred meter race. Find the value of M and who gets second place in the high jump.

A. 5, a B.    5,c C.   4,b D. 4,a

Answer: First calculate the total score of M project: 22+9+9=40 1. If 4 items, the score for each item is: X+Y+Z=10, the following 3 kinds of distribution can be obtained by x>y>z relationship: ①x=7,y=2,z=1;②x=5,y=4,z=1;③x=5,y =3,z=2. Then, a total score of 22, according to ② and ③ distribution, take a maximum of 5 points to calculate, even if a in these 4 projects all take the first also only 20 points, it can only be ① distribution. Or from a start, 22 points can be 3 times the first (that is, x=7) and 1 third (that is, z=1), because there are only 4 projects, so a third must be in the hundred meters project, so the ranking of hundred meters is: b>c>a. Then, in the remaining 3 projects, A is the first, the second may be B or C, take B, the total score of B 9 can be 1 times the first (hundred meters project, x=7) and 1 second (y=2), the rest of the position is filled by C, this is clearly contrary to the principle of ranking, because there will be 2 times a>c >c's strange logic. Similarly, take C, that is, C's total score of 9 points can be 4 times second (y=2) and 1 third (z=1) composition, and then the remaining position by C Fill, also appeared the above a>c>c strange logic, so 4 projects do not meet the requirements. 2. In 5 projects, the score for each item is: X+y+z=8, with the same kind of distribution as the following 2: ①x=5,y=2,z=1;②x=4,y=3,z=1. Then, a total score of 22, according to ② distribution, take the highest score of 4 points, assuming that 5 items A are first, but also only 20 points, so excluded. This is the ① principle of distribution. When you calculate it, you can know that C takes second in the high jump. So option B is correct.

13. There is a big watermelon, with fruit knife flat cut, a total of 9 knives, can be cut up to how many, at least how many parts can be cut?

14. Two rope, burning time is 1 hours (the burning speed is uneven), now give you a lighter, how to accurately measure 45 minutes time.

Answer: 1, the first root from both sides started at the same time burning, at the same time, the second rope from one side to burn. 2, the first rope after burning, is half an hour, at the same time, the second rope also just burn the general, and then the second end of the rope ignited, you can just use 15 minutes to burn out. 3, add down, just 45 minutes.