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| Math Central | Quandaries & Queries |
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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
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