2. It is known that the sum of three different natural numbers is 15 1, where the sum of every two numbers is a complete square number, then these natural numbers are (,) respectively.
3. Grandpa is under 100 years old. Grandpa is five times as old as his grandson. A few years later, grandpa was four times as old as his grandson. In a few years, my grandfather is three times as old as my grandson, so my grandfather is now () years old.
4. The simplest true fraction with denominator of 2008 is (), and its sum is ().
5. After the surface of a large cube is painted red, it is divided into several cubes with side length of 1, of which only 20 cubes are painted red on both sides, so the volume of a large cuboid is at least () and at most ().
6. Write down the natural number starting from 1:1234567891kloc-0/2131415.
7. The escalator runs upward at a constant speed. A boy and a girl are walking up the escalator. Boys are twice as fast as girls. As we all know, the boy took 54 steps to reach the top, while the girl took 48 steps to reach the top. Then when the escalator is stationary, the part that the escalator can see has () level.
8.A and B walk back and forth between A and B, which are 200 meters apart. A leaves from both a and B. If the speed of A is 3/5 of that of B, then the place where two people meet for the first time 15 (including head-on and chasing) is () meters away from A.
9. Two grain depots, A and B, originally contained whole bags of grain. If 90 bags are transferred from warehouse A to warehouse B, the grain storage of warehouse B is twice that of warehouse A; If several bags are transferred from warehouse B to warehouse A, the storage capacity of warehouse A is six times that of warehouse B. Then warehouse A originally stored at least () bags of grain.
10. When a class is playing computer games in class, the teacher first writes an integer X between 2000 and 3000 on the blackboard. The first student adds 1 to the number written by the teacher, then multiplies it by 3/4, and writes the result on the blackboard. The second student adds 1 to the number written by the teacher, then multiplies it by 3/4, and writes the result on the blackboard. And so on.
(1) Try to explain that the number written on the blackboard by the nth student can always be written as: (3/4) times (x-k)+k to find the value of k.
(2) If the top five students all write integers, ask the teacher what the numbers are on the blackboard.
1 1. Known natural numbers 1, 2, 3, ..., n can be rearranged into a series starting from 1, so that the sum of any three consecutive terms can be divisible by the first of these three terms, and the last term of this series is odd.
(1) Q: Can two consecutive terms in this series be even numbers? Explain the reasons;
(2) Find the maximum value of n and write all the series that meet the conditions at this time.
12. Two cars, A and B, set off from A and B respectively at the same time and headed for the other side. Car A travels 45 kilometers per hour, while car B travels 36 kilometers per hour. After they met, they continued to move at the original speed, returned immediately after arriving at their destination, and kept driving back and forth. It is known that the location of the second meeting on the way is 60 kilometers away from the location of the third meeting. Then a and b are () kilometers apart.
13. Party A, Party B and Party C do a job, and everyone takes turns to do it for one day according to the original planned order, which happens to be an integer day. It was B who finished the work. If everyone takes turns to do one day in the order of B, C and A, it will take 1/2 days longer than planned; If everyone takes turns doing one day in the order of C, A and B, it will take 1/3 days longer than planned. It is understood that it takes 9 days for A to finish this work alone. If everyone does it one day in turn in the order of A, B and C, it will take () days to finish it.