What are the deeper math Olympiad questions that can be answered and answered?

Assuming A gets x points on serve, he gets 54-x points on B's serve.

The two scored a total of 54 + 27 = 81 points, and the two served alternately, so one served 41 balls and the other served 40 balls.

If B serves first, B serves a total of 41 balls, of which 54-x points are grabbed by A, and B only scores 41 - 54-x) = x - 13 points.

Then since B has a score of 27, there is 27-(x-13)=40-x that is snatched from A's serve.

According to the title, the number of points snatched from the opponent's serve is (54-x) +40-x) = 41

So 94-2x = 41, because x is an integer, and the left is obviously an even number, and the right 41 is an odd number, so it doesn't hold.

That is, it is not B who serves first, but A who serves first.

Then A served a total of 41 balls, of which X scored by himself, and the other 41-x points were grabbed by B.

B gets 27-(41-x) = x-14 points in his own service round, and 40-(x-14)=54-x points are grabbed by A.

According to the title, there are (41-x) + (54-x) = 41

So 2x=54, the solution is x=27.

So the answer is that A serves first and gets 27 points in the round of his own serve.

Olympiad questions: One went to buy peaches, brought 10 yuan, 1 peach 1 yuan, the leftover three peach pits can be exchanged for a peach, how many peaches can there be?

Answer: 15. 10 yuan to buy 10 first, of which 9 peach pits can be exchanged for 3 peaches, these three peach pits can be exchanged for a peach, now it is 14 peaches and two peach pits, and then borrow one from passers-by or the boss, after changing a peach, return the peach pits left over from the peach to the person can be 15.

Olympiad question: If you are given a piece of 5, how to buy a pound of 3 salt and a 5 cents of ice cream?

Answer: Divide a pound of salt into 10 times to buy, each time it is 1 cent 3, and the salt is rounded off, so it is 1 cent, and it is 1 yuan to buy ten times, and you can buy ice cream for 5 cents.

Pure hand beating landlord to give some points.

There are two cases:

Because Qin Tong is known to be 1=5, according to the nature of the equation, it can be known that 5=1

Analyze a series of isotonic fierce formulas, and summarize the law: 5=12345, I hope you are satisfied.

This math problem is very profound. The carriage can only transport 1,000 catties at a time, and it has to travel 1,000 kilometers. But for every 1 kilometer walked, 1 pound of hay is consumed. So isn't the 1,000 hay already consumed after the 1,000 kilometers?

Then this person transported for the first time, and after reaching the end, the hay on the car has been consumed. And he can only stay at the finish line, and can't go back to the starting point.

Solution: Set up to unload the goods somewhere in the middle, and then return to pull the second car so back and forth five times, 5000 catties of hay is just finished, and the remaining hay is just enough for a truckload of goods, set the middle distance from the starting place is x kilometers, then the following formula is established.

1000-2x)×5=1000

400 (km).

The remaining 600 kilometers, 1,000 catties of hay were transported to the horses to eat 600 catties, just leftover.

1000-600 = 400 (catty).

400 catties of forage remaining.

5000 catties of hay to go back and forth 9 times, so (5000 - 4000) 9 is about equal to , walked a kilometer.

4000 catties of hay has to go back and forth 7 times, so (4000 - 3000) 7 is about equal to , and I walked another kilometer.

3000 catties of hay has to go back and forth 5 times, so (3000 - 2000) 5 = 200, and walked another 200 kilometers.

2000 catties of hay has to go back and forth 3 times, so (2000 - 1000) 3 is about the same, and another kilometer has been walked.

At this time, the remaining 1,000 catties of hay can be transported in one trip, and we have already walked kilometers, only from the end point.

The number of kilometers left -- that's the remaining hay is about equal to. ^

At the end of the line, not a pound of hay was gone, and it was all eaten up by the horses.

First of all, it needs to be carried to its maximum capacity, which is to carry 1,000 kilograms each time.

Second, try to minimize turnbacks, which means reduce the amount of walking.

Well, it can be planned like this:

1) Transported to a point in the middle in five times, so that the final pile is just over 1000 kg;

2) Then pull to the finish line in one go.

Then, we can set the distance that needs to be turned back for the first segment to be s, and the second segment is (1000-s).

Note that the first leg of the journey needs to be transported five times, and the total walking distance is 9s, and it satisfies 5000-9s=1000, which can be obtained, s=4000 9 km.

In the second section, the rest of the transportation to the end is:

1000-(1000-s)=s=4000 9 kg.

That is, at the end of the journey, there are up to 4000 9 kg of hay left.

If the yogurt weighs x grams, then (2*6)x+6x=2700 is solved to obtain x=150g; 900 grams for milk.

2700/(2+6/6)

900 (g)...1 carton of milk.

900 6 = 150 (grams).1 box of yogurt.

3 cartons of milk = 2700 grams.

1 carton of milk = 900 grams.

1 box of yogurt = 150 grams.

It's not esoteric, it's simple.

If the absolute value and square of any number are not equal to the negative number, then the first equation yields ab-2=0 and 1-b=0

Then a=2 and b=1

And so on, we get: 1 (n(n+1))=1 n+1 (n+1) then the original formula = 1-1 2+1 2-1 3+......1/2005-1/2006

The middle can be eliminated, and the original formula = 1-1 2006 = 2005 2006

Let the yogurt weigh x

Milk 6x then 2*6x+6x=2700

18x=2700

x = 150 milk 150 * 6 = 900

1) k is an arbitrary real number (k is an increasing function in a monotonic interval) 2) 16 (the sum of the squares of the two diagonals of the parallelogram = the sum of the squares of the 4 sides) The proof method is proved by vectors.

3) After 1,3 quadrants, the lecture point is brought in ==》k=24)10 inside:outside=4:1 so inside:flat angle = 4:5 and the sum of the inner angles is (n-2)*180, i.e. (n-2)*180=4 5*180*n

5) 7 times Since it takes hours to arrive, the trains from 6:00 have not yet arrived, and the trains that depart at 9:00 should arrive at 12:30, so there will be, and the trains that depart on the hour will meet at 11 and 12. 3

22-22=0, move the first 7 matchsticks horizontally, and place them in the middle of the bottom to become 0

Digital, refers to numbers.

For example: 13, there are two digits, 123, there are 3 digits with one digit: 1--9, the upper and lower volumes have a total of 9 2 = 18 digits with two digits:

10-99, the upper and lower volumes have a total of 90 2 2 = 360 numbers, and 777-18-360 = 399 numbers remaining.

The rest is the three-digit page number.

There are 7 more pages in the first volume, and (399 + 7 3) 2 = 210 numbers 210 3 = 70

It is the 70th three-digit number, which is 100 + 70-1 = 169 and there are (169) pages in the upper volume.

1 9 pages of 9.

10 99 pages of (99 10 1) 2 180 pages The total number of pages with three digits per page in the two volumes is: 777 (180 9) 2 399

Because the first volume has more pages than the second: 7 3 21.

The total number of pages with 3 digits per page in the next volume is: (399 21) 2 189.

Namely: 189 3 pages 63.

So the next volume is: 99 63 162 pages.

The first volume has 162 7 169 pages.

It's the page number.、Suppose the last book has x pages.,Then the next book is x-7 pages.、Two volumes are x+x-7=777.。。 x is 392 pages.

It's what we call a page number, a number that is marked at the bottom of a book.

Number of pages = (777 + 7) 2 = 392 pages.

If there is something you don't understand, ask again, I wish you to learn and make progress and go to the next level! (