A year is called a Subtractive year when the absolute difference between the number formed by the first two digits and the number formed by the last two digits is equal to the number formed by the middle two digits.

For example, considering the year 3482, we observe that the absolute difference between 34 and 82 is 48, which is the number formed by the middle two digits, so that 3482 is a subtractive year. Likewise for the year 4220, the absolute difference between 42 and 20 is 22, so that 4220 is also a subtractive year.

(i) Determine the total number of subtractive years from years 1000 to 9999 inclusively.

(ii) What are the respective first and last subtractive years from years 2000 to 2999 inclusively?

(iii) What are the respective first and last subtractive years in the period covered under (i)?

(In reply to By calculator program by Jer)

It may be true that there are at least ten Subractive years in every millennium (with four or more and an even number of digits), at least one millennium has twenty Subractive years. Following are the twenty Subtractive years of the 101^st Millenium of the Common Era:

1. 100010
2. 100109
3. 100111
4. 100208
5. 100212
6. 100307
7. 100313
8. 100406
9. 100414
10. 100505
11. 100515
12. 100604
13. 100616
14. 100703
15. 100717
16. 100802
17. 100818
18. 100901
19. 100919
20. 101000

Posted by Dej Mar on 2012-12-14 04:12:01