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 Integer Count Illation (Posted on 2015-10-12)
Find the total number of 5-digit positive integers N such that:
The sum of the first digit and the third digit of N is equal to its second digit, and:
The sum of the third digit and the fifth digit of N is one more than its fourth digit.

*** Assume non leading zeroes for each of the values of N.

 No Solution Yet Submitted by K Sengupta No Rating

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 solution Comment 1 of 1
`Let abcde be the number.`
`a+c = b   <=  9c+e = d+1 <= 10`
`a > 0`
`b and d are determined by c, a and e.`
`c = 0: 9 choices for a * 9 choices for e  =  81 choices (1<=a<=9; 1<=e<=9)c = 1: 8 choices for a * 10 choices for e =  80 choices (1<=a<=8; 0<=e<=9)c = 2: 7 choices for a * 9 choices for e  =  63 choices (1<=a<=7; 0<=e<=8)   c = 3: 6 choices for a * 8 choices for e  =  48 choices        etc.c = 4: 5 choices for a * 7 choices for e  =  35 choicesc = 5: 4 choices for a * 6 choices for e  =  24 choicesc = 6: 3 choices for a * 5 choices for e  =  15 choicesc = 7: 2 choices for a * 4 choices for e  =   8 choicesc = 8: 1 choices for a * 3 choices for e  =   3 choicesc = 9: 0 choices for a * 2 choices for e  =   0 choices                                            ---                                            357 such numbers abcde.`

Edited on October 12, 2015, 3:30 pm
 Posted by Charlie on 2015-10-12 15:29:02

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