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1 (sanfan middle school exam)

Originally planned 18 people planted trees. After working for 2 hours as planned, three people were taken away, and the remaining people planted 1 tree every hour than originally planned, and the task was completed as scheduled. The original plan is to plant _ _ _ _ _ trees every hour.

2 (The examination questions are attached to the middle school attached to the first day of junior high school)

A project can be completed in 10, 20, 15 and 12 days. Now B will do it for four days first, but how many days will it take to finish it?

3 (National People's Congress High School Examination Questions)

For a manuscript, it takes 14 hours for A to type alone, and 20 hours for B to type alone. If Party A calls 1 hour first, then Party B takes over 1 hour, then Party A takes over 1 hour, and ... both work alternately. So, how many hours did it take Party A and Party B to finish this manuscript?

4 (Xicheng No.4 Middle School Examination Questions)

If an empty pool is filled with pipes A, B and C at the same time, 1 hour can be filled; If two tubes A and B are used, 1 hour can be filled in 20 minutes; If the two water pipes B and C can be filled in 1 hour and 15 minutes, it will take _ _ _ _ hours to fill this pool with the pipe B alone.

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There are as many piles of coal as there are piles of coal A and B. If only one pile of coal is transported, it will take 20 hours for car A, 24 hours for car B and 30 hours for car C.. Now car A is loading pile A, car B is loading pile B, and car C starts loading pile A first, and then turns to pile B halfway. Three cars start at the same time, and the two piles are loaded at the same time. How long did it take C train to load a pile of coal?

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It takes 24 days for A to complete a project alone, and 32 days for B.. If A did it for several days before B did it, it would take 26 days to ask: How many days did A do it alone?

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A pool has three discharge pipes, A, B and C. A can discharge 100 liter per hour and B can discharge 125 liter per hour. Now, drain the water with pipe A first, then use pipe B after 2 hours, and then open pipe C after a period of time, so that pipes A, B and C can drain water at the same time until the water is completely drained. Calculate the displacement of pipes A, B and C, and find out.

Children are completely equal. How much water is there in the swimming pool?

Number theory part one

1 (examination questions attached to the middle school of the National People's Congress)

There are _ _ _ _ four digits that meet the following conditions: its digits are all odd; Its digits are different from each other; Every number of it can be divisible by itself.

2( 10 1 middle school exam questions)

If you add a zero between two numbers of a two-digit number, then the three-digit number is nine times the original number. Ask this two-digit number.

It is _ _.

3 (National People's Congress High School Examination Questions)

A, B and C represent three different positive integers, which satisfy the following: A× A = B+B = C× 135. Then the minimum value of a is _ _ _ _.

4 (National People's Congress High School Examination Questions)

The following numbers that are not octal numbers are ()

a、 125B、 126C、 127D、 128

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1. What is the sum of all the natural numbers from 1 to 100 that are not divisible by 9?

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2. There are three websites, A, B and C. The website A is updated every three days, the website B is updated every five days and the website C is updated every seven days. On New Year's Day in 2004, three websites were updated at the same time. When will the next synchronization update take place in _ _ _ _ _?

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3. From left to right, students numbered 1 to 199 1 line up. From left to right, the student number is 1 to 1 1, and the student number is 1 1. Then the rest of the students count off from 1 to 1 1 from left to right, the students who count off from 1 1 stay and the rest leave the team; The students who stayed behind counted off for the third time from 1 to 10L from left to right. Those who reported to 1 1 stayed behind and the rest left the team. Then, among the last students left, the initial number of the first person from the left is _ _ _ _ _ _.

Number Theory Chapter 2

1 (Tsinghua High School Attached Test)

There are three lucky numbers 888,565,438+08,666. If you divide them by the same natural number and the remainder is a, a+7 and a+ 10, then this natural number is _ _ _ _.

2 (Three Sails Middle School Examination Questions)

1 40,225,293 is divided by a natural number greater than1and the remainder is the same. The remainder of 2002 divided by this natural number is.

3 (National People's Congress High School Examination Questions)

A two-digit number is divided by 3 after adding 3, and it is 1 after adding 4, 1 after adding 5, and 1 after dividing 5. This two-digit number is _ _ _ _ _.

4( 10 1 middle school exam questions)

An eight-digit number, divided by 3 to 1, divided by 4 to 2, is divisible by 1 1. It is known that the first six digits of this eight-digit number are 257633, so its last two digits are _ _ _ _ _ _ _.

5 (Experimental Middle School Examination Questions)

(1) How many of the 3998 natural numbers from 1 to 3998 are divisible by 4?

(2) Of the 3998 natural numbers from 1 to 3998, how many digits can be divisible by 4?

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If 1 = 1! , 1×2=2! , 1×2×3=3! …… 1×2×3×……×99× 100= 100! Then 1! +2! +3! +……+ 100! What is the unit number?

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2. (★★★★★) The number of the bus ticket is a six-digit number. If the sum of the first three digits of a ticket number is equal to the sum of the last three digits, the ticket is said to be lucky. Try to prove that the sum of all lucky banks can be divisible by 13.