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
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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) (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
...
the pattern should be clear
...
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
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