My thousands digit is three times my hundreds digit. the sum of my tens digit and one digit is one less than my thousandsdigit. my hundreds digit is two less than my tens digit. what 4-digit number am i?

6241 is one answer, but see below.

Step-by-step explanation:

If the number is vwxy we have:

v = 3w

x + y = v - 1

w = x - 2

From equations 1 and 2:

v = 3 (x - 2).

The only possible values of v are 3, 6 or 9.

If v = 3: - 3 = 3 (3 - 2) so x = 3 also.

If v = 6: - 6 = 3 (4 - 2) so x = 4.

If v = 9: - 9 = 3 (5 - 2) so x = 5.

Now consider the first equation x + y = v - 1:-

If v = 3 then 3 + y = 3 - 1 giving y = - 1 so v = 3 is not possible.

If v = 6 then 4 + y = 6 - 1 giving y = 1 which is a possible value.

If v = 9 then 5 + y = 9 - 1 giving y = 3 which is also possible.

If x = 4 w = 4 - 2 = 2

If x = 5 w = 5-2 = 3.

Thus the possible values are 6241 or 9353.

If all digits must be different the answer is 6241.