Results fill in the blanks carelessly (violent solution)

Xiao Ming is an acute child , When I was in primary school, I often copied the questions that the teacher wrote on the blackboard wrong .

There is a , The teacher's question is ：36 x 495 = ?

He was copied as ：396 x 45 = ?

But it turned out to be dramatic , His answer turned out to be right ！！

because 36 * 495 = 396 * 45 = 17820

There may be many such coincidences , such as ：27 * 594 = 297 * 54

hypothesis a b c d e representative 1~9 Different 5 A digital （ Note that there are different numbers , And it doesn't include 0）

Can satisfy the shape as ： ab * cde = adb * ce How many kinds of formulas are there in all ？

Please use the advantages of computer to find all the possibilities , And answer the kinds of numbers of different formulas .

There are different kinds of formulas satisfying the commutative law of multiplication , So the answer must be an even number .

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answer

142

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The problem solving process

To be honest, the choice of the blue bridge cup can be passed by the general violent solution , But it sometimes plays tricks （ Get some accuracy or something , Far away ）. Here, the direct five fold cycle of violence is solved ！

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Attach code

#include<iostream>
using namespace std;
int main()
{
	int counts=0;
	for(int a=1;a<=9;a++)
	{
		for(int b=1;b<=9;b++)
		{
			for(int c=1;c<=9;c++)
			{
				for(int d=1;d<=9;d++)
				{
					for(int e=1;e<=9;e++)
					{
						if(a!=b&&a!=c&&a!=d&&a!=e&&b!=c&&b!=d&&b!=e
						&&c!=d&&c!=e&&d!=e)
						{
							int num1=(a*10+b)*(c*100+d*10+e);
							int num2=(a*100+d*10+b)*(c*10+e);
							if(num1==num2)
								counts++;
						}
					}
				}
			}
		}
	}
	cout<<counts<<endl;
	return 0;
}