Find some Olympiad questions, and help with an Olympiad problem

It's very complete, and it should help you somewhat.

Here are a few others**.

There are also many nets available.

In fact, this is a basic physical kinematic acceleration problem, and you will be able to learn physics!! What Olympiad math problems, (the book is really engaged now!)

Solution: If the uphill and downhill roads are long x,y, then x 28+y 35+(142-x-y) 30=9 2y 28+x 35++(142-x-y) 30=47 10 multiply 420 on both sides and simplify x-2y=-98y-2x=-14, and solve the equation x=42,y=70

The flat road is 140-42-70=28 km.

1.There are 3 left after the elder brother gives the younger brother's apples, 6 after the younger brother gets the elder brother's apples, 3 left after eating 3, and the elder sister has 3, so there are the same amounts.

Years later, they are both 2 years older, so Xiao Ming is always stronger than Xiao 2 years old) Xiao Ming is also in the team, so it is 9.

4.Read 2 pages on the first day, 2+2=4 pages on the second day, 2+2+2=6 pages on the third day, 2+2+2+2=8 pages on the first day, 2+4+6+8=20 pages.

5.The calculation is repeated 1 time, so subtract 1,4+5-1=8 (person) 6Boys: (8-2) 1=6 (people).

Girls: (8+2) 1=10 (person).

Duo) ) this person).

block) branch) 13Female classmates: 8 people.

Total: 8+8=16 (people).

14.Dahua gave Xiaogang 2 and there were 8 left, and Xiaogang got 2 and there were 12 cards, 12-8 = 4 (cards).

Article only) 17White balls: 5 + 10 = 15 (pcs).

Flower balls: 5 + 5 = 10 (pcs).

Duo) only).

Solution: Let this field be x acres.

85x+85x+ (This is convenient for calculation, and it is easier to move the unknown aside) x=6Answer: This field is 6 acres.

Analysis: The overall idea of this question is that the sum of the respective yields of the two fields is equal to the total yield of the two fields (the average yield is multiplied by the total number of acres), and the equations on the left and right sides can be found very simply.

Let's talk about finite decimal numbers first, the finite decimal number with the denominator of prime numbers within 2005 is only 5, and these two numbers are multiplied by each other any number of times until the denominator is less than or equal to 2005, and in 2005, there are 10 multiples of 2, 4 multiples of 5, 19 multiples of 2 and 5, adding up to 33 finite decimals.

Then calculate the pure cyclic decimal, the denominator within 2005 is formed by the prime number in addition to 1 2 and 1 5, and the rest of the fractions are pure cyclic decimals, that is, the number of prime numbers less than 2005, which is actually beyond the scope of the Olympiad, this is dizzy, there are roughly more than 200.

Subtract the three numbers from each other to subtract the remainder, and you get an integer multiple of the number.

That is: 2001-1000 = 1001 = 11 91 (91 is the integer quotient of this number divided by 2001 - the integer quotient of this number divided by 1000, and so on), 2001-967 = 132 = 11 12, 1000-967 = 33 = 11 3

One of the factors they have in common is 11, so this number is 11 validation: 2001 11 = 181....10；1000÷11=90...10；967÷11=87...10

So 11 is the answer.