There is a basket of duck eggs in large wooden cases, 12 in each case, 1 left, 9 in small wooden cases, 8 less. How many duck eggs are there in all?

There is a basket of duck eggs in large wooden cases, 12 in each case, 1 left, 9 in small wooden cases, 8 less. How many duck eggs are there in all?

There are 8 less than 9 in each box and 1 more than 9 in each box, which means the same, so the problem becomes a congruence problem
The minimum number of duck eggs is the least common multiple of 12 and 9 plus 1
The least common multiple of 12 and 9 is 36
36 + 1 = 37

--------- Congcong asked Mingming to write four numbers at will, such as 2006. Then he subtracted the sum of the four numbers from this number, that is, 2006 - (2 + 0 + 0 + 6) = 1998. Then he removed any number, such as 8. After telling congcongcong 1, 9 and 9, Congcong soon told him that the number was 8. Mingming didn't know why he wrote four more numbers. After subtracting, the number was 3, 6 and 7, What is the number and why

Suppose four digits are ABCD, then four digits are: 1000A + 100b + 10C + d1000a + 100b + 10C + D - (a + B + C + D) = 999a + 99b + 9C. No matter what a, B and C are worth, the number can be divided by 9. The characteristic of the number divided by 9 is that the sum of all numbers can be divided by 9

1. A row of poles. The original distance between each two poles is 30 meters, but now it is 45 meters. If one pole at the starting point does not move, at least how far apart does another pole not move? 2. A room is 900 cm long and 480 cm wide. Now we plan to use square tiles to pave the floor. How many square tiles (whole bricks) are needed to pave the floor of the room?

1. Another 90 meters away. Don't move
2. 120 bricks for a brick with a side length of 60 cm