Determine 55891

Determine the number of nine-digit numbers in which each of the digits 0 through 9 occurs at most once and in which the sums of the digits 1 through 3, 3 through 5, 5 through 7, and 7 to the 9th place are always equal to 10. Find the smallest and largest of these numbers.

Correct answer:

n =  16
a =  280736145
b =  820736154

Step-by-step explanation:

$n=16$

$a=280736145$

$$\begin{gathered} b=820736154 \\ 1:280736145 \\ 2:280736154 \\ 3:352719046 \\ 4:352719064 \\ 5:451637028 \\ 6:451637082 \\ 7:460917235 \\ 8:460917253 \\ 9:532719046 \\ 10:532719064 \\ 11:541637028 \\ 12:541637082 \\ 13:640917235 \\ 14:640917253 \\ 15:820736145 \\ 16:820736154 \end{gathered}$$

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