Maximum product: the largest number is placed on one digit, the second largest number is placed on the hundredth digit of three digits, and the rest are arranged in descending order.

Such as: 432×8=3456

Minimum product: the smallest number is placed on one digit, the second smallest number is placed on the hundredth digit of three digits, and the rest are arranged in descending order.

Such as: 348×2=696

For example:

Let these two digits be ab and cd respectively.

( 10a+b)( 10c+d)= 100 a * c+ 10(a * d+b * c)+b * d

Obviously, on the premise that a*c is the largest, when a*d+b*c is the largest, the product is the largest;

On the premise that a*c is minimum, the minimum product of a*d+b*c is minimum;

So to maximize the product, a=4, c=3, d=2, b= 1, these two numbers are 4 1 and 32;

Minimize the product, a= 1, c=2, d=4, b=3, which are 13 and 24 respectively;

Maximum 41* 32 =1312;

Minimum13 * 24 = 322;

Extended data:

The concept of product depends on the definition of "multiplication". When people upgrade the set of multiplication objects to more general sets, such as groups, rings, fields, etc. The concept of the product will also change.

Let A be a set, we define the multiplication F:A ×A→A, that is, the mapping of A and its own cartesian product to A, and let (x, y)∈A×A, then we call the pixel F(x, y) the product of x and y, abbreviated as xy.

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