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A year is called an Additive year when the sum of the number formed by the first two digits and the number formed by the last two digits add up to the number formed by the middle two digits. For example, considering the year 1978 we observe that when 19 is added to 78, the result is 97 which is the number formed by the middle two digits.

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

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

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

 No Solution Yet Submitted by K Sengupta Rating: 5.0000 (1 votes)

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 Solution (cont.) | Comment 2 of 6 |
(ii)
The first additive year from 2000 to 2999 is
2307

The last is:

2967

(iii)

The first additive number is 1208 and the last is 8901.

 Posted by Chris, PhD on 2012-08-08 11:37:06

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