Math Olympiad Puzzles! High score bounty!

Poof, it's just a simple calculation problem.

The score is expressed as 1 2

Here's how it works.

Original = (1 2 + 1 3) - (1 3 + 1 4) + (1 4 + 1 5) - (1 5 + 1 6) + (1 6 + 1 7) -...1/20+1/21）-（1/21+1/22）

Ideas. First of all, this kind of problem that seems to be troublesome must be a simple calculation, so you have to find a pattern.

As for finding patterns......In fact, the rules of the primary school exam are nothing more than a few, generally adding and subtracting, eliminating things, so that otherwise it is something about the end of the appointment.

Looking at the questions intuitively, it looks messy, but it is easy to find that 5 6 = 1 2 + 1 3 As for why it is ...... at a glanceOkay, that's it. When I was in elementary school and junior high school, I did a lot of this kind of problem-solving. In fact, after doing one or two of each type, you will have this kind of thinking, and you will be able to basically grasp this simple calculation.

That's it.

6=2 3 and so on, this kind of law is easy to see, and it is more familiar.

5/6 minus 7/12 plus 9/20 minus 11/30 plus 13/42 minus 15/56... Add 420/41 minus 462/43.

1. (3 baskets of 24 kg) bai (3 8) = 8 baskets of 64 kg, a total of 3 + 6 = 9 baskets, so each basket is 64 kg 2, set the dao foot return ball, basketball into the price of a and b respectively

50a+40b=3000

Solution: a=32, b=35

3. There are A and B respectively.

a+b=126

a/6=2b/9 -7

The solution is a=54 and b=72

4. Set up a and b tons respectively.

a+30=4b/5

a+10=(b-10)x3/4

a=170，b=250

1. Set all tomatoes as A, and B in each basket

The meaning of the title is: 3 8*a=3b+24

5/8*a=6b

The simultaneous solution of the equation obtains: b=40 (a=384)2, set the basket ball into the price a, soccer b

The meaning of the title is: 50b+40a=3000

50b(1+9%)+40a(1+11%)-3000=298 The simultaneous solution of the equation yields: a=35 b=32

3. There are a book of literature and art, ***b

The meaning of the title is: a+b=126

1/6*a=2/9*b-7

The simultaneous solution of the equation yields: a=54 b=72

4. Set A to store a ton, B B

The meaning of the title is: a=4 5*b-30

a+10=3/4*(b-10)

The simultaneous solution of the equation yields: a=170 b=250

1 Let each frame hold x kg 3x+24=(3x+6x+24) multiplied by three-eighths.

1 38 4 4 dm)

2 4 * 3 * 2 24 (cubic decimeters).

24 3 2 4 (decimeter).

4<5 so the water depth is 4 decimeters.

The time is measured in hours, 40 minutes = 2 3 hours, 20 minutes = 1 3 hours If the water speed is V, then the speed of the ship is 7V, then the speed is 8V when the water is downstream, and 6V when the water is against the water; Let the speed of the cruise ship be V0, the departure interval of the cargo ship be T, the ship will be shipped from port A at time T, and the cruise ship will be chased by the cruise ship at time T0, and the cruise ship will have traveled S kilometers at this time, then 8V(T0 - T)=S

Then the second ship is sent out at t+t, and t0+2 3 catches the cruise ship, then 8v(t0+2 3-t-t)=s+2 3 * v0

The two formulas are arranged to obtain that 8V(2 3-t)=2 3 * V0 adopts the same idea for the ship in port B, and there are 6V(1 3-t)=-1 3*V0 compared with the two formulas, there are [8(2 3-t)] [6(1 3-t)] = (2 3) (-1 3), and the solution is t=7 15 (hours) = 28 minutes.

Solution: Let the separation distance of the freighter be sent out as the unit length "1", then the speed difference between the freighter and the cruise ship: 1 40

The speed of the freighter and the cruise ship: 1 20

Freighter speed: (1 40 + 1 20) 2 = 3 80 cruise ship speed: 1 20-3 80 = 1 80

The interval between the issuance of freighters is:

1 (3 80) = 80 3 = minutes = 26 minutes and 40 seconds.