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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution | Comment 4 of 6 |

FOR yr = 1000 TO 9999
y1 = yr \ 100
y3 = yr MOD 100
y2 = (yr \ 10) MOD 100
IF y1 + y3 = y2 THEN
PRINT yr: ct = ct + 1
END IF
NEXT yr
PRINT ct

finds (plus my annotations):

1208 Part iiiA solution
1318
1428
1538
1648
1758
1868
1978
2307 Part iiA solution
2417
2527
2637
2747
2857
2967 Part iiB solution
3406
3516
3626
3736
3846
3956
4505
4615
4725
4835
4945
5604
5714
5824
5934
6703
6813
6923
7802
7912
8901 Part iiiB solution
36   Part i solution

 Posted by Charlie on 2012-08-08 12:38:33

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