Latest Others Aptitude Question SOLUTION: A four digit number numbered from 0000 to 9999 is said to be lucky, if the sum of the first two digits is equal to the sum of the last two digits. Find how many such numbers are po

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A four digit number numbered from 0000 to 9999 is said to be lucky, if the sum of the first two digits is equal to the sum of the last two digits. Find how many such numbers are possible ?

Asked In Others Bankim (12 years ago)

Solved Aman Read Solution (2)

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Vignesh  (12 years ago)

670 such numbers are possible.

Minimum Sum for first two and last two digits = 0 (0000)
Maximum Sum for first two and last two digits = 18(9999)

Sum of first two = 0 --> 1 Case (0000)
Sum of first two = 1 --> 2 Cases (10. 01)
.....
.....
Sum of first two = 9 --> 10 Cases(09,18,27,36,54,45,63,72,18,90)
Sum of first two = 10 --> 9 Cases(19,28,37,46,55,64,73,82,91)
Sum of first two = 11 => 8 Cases (38,47,56,65,74,83,92,29)
.....
.....
Sum of first two = 18 => 1 Case (99)

Thus, Total will be = 2(1^2 + 2^2 + .... + 9^2) + 10^2 = 670 such numbers,

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Aman  (12 years ago)

670 such numbers are possible.

Sum of the first two digit = Sum of the last two digit
when
Sum of first two digits = 0... 1 possible Case
Sum of first two digits = 1 .. 2 Cases possible
.....
.....
Sum of first two = 10 .. 9 Cases
Sum of first two = 11 .. 8 Cases
.....

Sum of first two digits = 18 .... 1 Case

Thus, Total will be = 2(1^2 + 2^2 + .... + 9^2) + 10^2 = 670

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