   SEARCH HOME Math Central Quandaries & Queries  Question from Anya, a parent: I need help with my daughter's math problem. It is a 4-digit number The tens are double the ones. The thousands are double the tens. The sum of the digits is 19. What number is it? Anya,

Since the tens digit is double the ones digit and the thousands digit is double the tens digit, the thousands digit is 4 times the ones digit. Thus the ones digit can't be very large since 4 times the ones digit is a one digit number. The ones digit could be 1 since 4 times 1 is 4. The ones digit could be 2 since 4 times 2 is 8. The ones digit can't be 3 since 4 times 3 is 12 and 12 is not a digit. Likewise the ones digit can't be 4, 5, 6, 7, 8 or 9.

Can you find a 4 digit number that has 1 as the ones digit and satisfies your conditions?
No! It would have to look like 4  21 and the missing digit can't be large enough to make
the sum of the digits 19.
Can you find a 4 digit number that has 2 as the ones digit and satisfies your conditions?
Can you find a 4 digit number that has 0 as the ones digit and satisfies your conditions?

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.