A number is called a decreasing number if each digit is less than the preceding digit. How many three- digit decreasing numbers are less than 500.

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- Jan 10th 2009, 06:46 PMmath123456word problem
A number is called a decreasing number if each digit is less than the preceding digit. How many three- digit decreasing numbers are less than 500.

- Jan 10th 2009, 06:48 PMskeeter
- Jan 10th 2009, 06:54 PMJhevon
haha, nothing. just a case of recycling topics it seems

i suppose we are not considering numbers that begin with zero or two zeros

then you have 4 cases:

case 1: the number starts with 4

case 2: the number starts with 3

case 3: the number starts with 2

case 4: the number starts with 1

now, how many decreasing numbers are there in each case?

example: let me do the last one for you (:D)

if the first is 1, the the second digit has no choice but to be zero. but then the third digit would have to be negative. since we have to be less than the preceding digit (as opposed to less than or equal to the preceding digit) there are no decreasing numbers in this case.