"Lattice multiplication" is a calculation method of multiplying two numbers introduced by Italian mathematician pacioli in his book "An Overview of Arithmetic, Geometry and Proportional Properties" in the middle of15th century. Lattice algorithm is between drawing lines and calculating formulas. After this method was introduced into China, it was called "bedding" by Cheng Dawei, a mathematician in Ming Dynasty, in his book "Algorithm Unification".

Write the factors on the top and the right respectively, then calculate 6*7=42, write it on the grid in the upper right corner, 4 on the left and 2 on the right, and so on, and fill in the grid; Finally, add the numbers on the same diagonal: 0 falls; 2+3+0=5, and write 5 at the bottom left; 4+8+2= 14, move forward one place, and write 4 at the bottom left; 2+ 1=3, and 3 is written at the top left, so it is: 46*75=3450.

Extended data:

Calculation method:

1. First draw a rectangle and divide it into m×n squares (m and n are the digits of two multipliers respectively), and write down two factors on the upper and right sides of the squares respectively.

2. Divide the square into two diagonal lines and record the ten digits and the single digits of the product corresponding to the above numbers respectively.

3. Then, from the bottom right to the top left, add these products diagonally, and when the sum is full, move forward by one.

4. Finally get the result (the numbers on the left and bottom of the square are arranged in turn).

Extended data source: Baidu encyclopedia square multiplication