Math CentralQuandaries & Queries


Question from John, a student:

Find a Six digit number containing no zeros in which the first digit is three less than the third,
the third digit is three less than the fifth,and the second digit equals the sum of the last three digits.

Hi John,

The fifth digit must be reasonably large since three less then it is the third digit and three less than that is still greater than zero. In fact if the fifth digit is 6 then the third digit is 3 and the first digit is 0 which is not allowed. Thus the fifth digit must be 7, 8 or 9. Hence the number is

?8?5?2 or

where the question marks are digits, all larger than 0.

Can you complete the problem? Write back if you need more help.


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