   SEARCH HOME Math Central Quandaries & Queries  Question from john, a student: my thousands digit is 2 times my ones digit.my hundreds digit is my ones digit plus 2. my tens digit is the difference between my thousands and hundreds digit what numbers can i be? Hi John,

The problem doesn't mention anything larger than a thousands digit so I assume you are looking for a four digit number.

Since the "thousands digit is 2 times my ones digit" the thousands digit must be even, so it must be 0, 2, 4, 6 or 8. The corresponding ones digit is then 0, 1, 2, 3 or 4 so the possible numbers are

0??0
2??1
4??2
6??3
8??4

where the question marks are yet to be determined.

Now look at the statement "my hundreds digit is my ones digit plus 2" and for each of the five possibilities above fill in the hundreds digit. Finally I think that "my tens digit is the difference between my thousands and hundreds digit" means that the tens digit is the thousands digit minus the hundreds digit so, for the five possibilities you have so far what is this difference. This difference must be a digit so it must be positive. Does this rule out any of the five possibilities?

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.