What are the number of total four digit number formed by using non zero integers (1 to 9) greater than 1745 ?

Question

A four digit positive number having all non-zero distinct digits is such that the product of all the digits is least. If the difference of hundreds digit and tens digit is 1.
How many possibilities are there of such number?

Answer 1

Lets break the problem into following four part
[1][7][4][6-9] = 1*1*1*4 = 4 --- Numbers between 1746 to 1749
[1][7][5-9][1-9] = 1*1*5*9 = 45 --- Numbers between 1750 to 1799
[1][8-9][1-9][1-9] = 1*2*9*9 = 162 --- Numbers between 1800 to 1999
[2-9][1-9][1-9][1-9] = 8*9*9*9 = 5832 --- Numbers between 2000 to 9999

Total
4+45+162+5832 = 6043