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Title: Sloppy arithmetic
Xiao Ming was a hothead and often copied the teacher’s formulas wrong when he was at school.
Once, the teacher’s topic is: 36 * 495 =?
Instead, he wrote: 396 * 45 =?
But it turned out dramatically that he was right!
Because of the 36 * 495 = 396 * 45 = 17820
There are many similar coincidences, such as 27*594=297*54
Suppose a, B, C, D, and e represent five different numbers from 1 to 9.
How many types of ab * cde = adb * ce?
Please take advantage of the computer to look for all the possibilities and answer the number of types of different formulas.
There are different kinds of equations that satisfy the commutative law of multiplication, so the answer must be an even number
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Answer:
What is the main content of the passage?
Suppose a, B, C, D, and e represent five different numbers from 1 to 9.
How many types of ab * cde = adb * ce?
So we can use enumeration to find all the possible combinations and determine,
At the same time, the number of formulas that meet the requirements can be counted.
Answer source:
Package 2013 Provincial competition Public class Year2013_t3 {/ * * * if a b c d e representative 1 ~ 9 different 5 Numbers (pay attention to the Numbers are different, and do not contain 0) can satisfy the form such as: ab * * ce cde = the adb formula how many kind of like this? * */ public static void main(String[] args) { int count = 0; for (int a = 1; a < 10; a++) { for (int b = 1; b < 10; b++) { if (a! =b) { for (int c = 1; c < 10; c++) { if (c! =a&&c! =b) { for (int d = 1; d < 10; d++) { if (d! =a&&d! =b&&d! =c) { for (int e = 1; e < 10; e++) { if (e! =a&&e! =b&&e! =c&&e! =d) { int x = (a*10+b)*(c*100+d*10+e); int y = (a*100+d*10+b)*(c*10+e); if (x==y) { count++; System.out.printf("(%d*10+%d)*(%d*100+%d*10+%d)==(%d*100+%d*10+%d)*(%d*10+%d)==%d\n",a,b,c,d,e,a,d,b,c,e,x); } } } } } } } } } } System.out.println(count); }}Copy the code
Example output:
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