SOLUTION: The number 2013 has the property that its units digit is the sum of its other digits, that is 2 + 0 + 1 = 3. How many integers less than 2013 but greater than 1000 share this prope

Algebra ->  Finance -> SOLUTION: The number 2013 has the property that its units digit is the sum of its other digits, that is 2 + 0 + 1 = 3. How many integers less than 2013 but greater than 1000 share this prope      Log On


   

Question 1148540: The number 2013 has the property that its units digit is the sum of its other digits, that is 2 + 0 + 1 = 3. How many integers less than 2013 but greater than 1000 share this property?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


1xx1: the two middle digits must sum to 0; clearly only 1 number that satisfies the condition: 1001

1xx2: the two middle numbers must sum to 1; they can only be 01 or 10. So 2 numbers: 1012 and 1102

1xx3: the two middle numbers must sum to 2; they can only be 02 , 11, or 20. So 3 numbers: 1023, 1113, and 1203

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the pattern should be clear

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1xx9: 9 numbers

Then with leading digit 2 and less than 2013 there is only 1 number that satisfies the condition: 2002

ANSWER: (1+2+3+...+9) + 1 = 45+1 = 46