Current location - Training Enrollment Network - Mathematics courses - From 0000 to 9999, a total of 10000 numbers are arranged from small to large. How many kinds of math problems are there? Four numbers at a time can start from 0.
From 0000 to 9999, a total of 10000 numbers are arranged from small to large. How many kinds of math problems are there? Four numbers at a time can start from 0.
I figured it was 2 10, which was a bit troublesome.

The general process is as follows

On the other hand, from big to small.

0 1 2 does not start.

There are 32 10 1 species at the beginning of 3.

There are four kinds at the beginning of 4: 432 1 4320 43 10 (the first three kinds are 43)+42 10 (n3).

5 starts with 54 # # 6 species (54-32,31,30,21,20, 10) plus 53,52. And the ones starting with 53 and 52 are equal to all the cases starting with 4, so N5=6+N4= 10.

And so on, as long as the numbers 65, 76, 87, 98 at the beginning of several cases.

N3= 1

N4=4

N5= 10

n6 = 10+N5 =( 1+2+3+4)+N5 = 20

n7 = 15+N6 =( 1+2+3+4+5)+N5 = 35

N8 = 2 1+N7 =( 1+2+3+4+5+6)+N5 = 56

n9 = 28+N8 =( 1+2+3+4+5+6+7)+N5 = 84

N (1+2+3+4+5+6+7+8+9) = 210 species.

Attachment: 76 # # Starting numbering method

76 54 43 32 265 438+0 65 438+00 * * 65 438+0+2+3+4+5 species.

53 42 3 1 20

52 4 1 30

5 1 40

50

Finally finished. . .