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A Quicky III (Posted on 2014-04-09) Difficulty: 1 of 5
If each of the a,b,c,d is a decimal digit - for how many ordered quadruplets (a,b,c,d) is the sum S= a+b+6c+d divisible by 3 ?

Answer: within 20 sec.

No Solution Yet Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

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Solution re: Thoughts - justifying "20 sec""...SPOILER | Comment 7 of 9 |
(In reply to Thoughts by tomarken)

6*c is divisible by 3, so it will only cause multiplication  by 10 of the "abd" result.

if a+b+d is divisible by 3 , so is the decimal string abd.

The number of "qualifying" strings from 000 to 999 is  999/3+1=334.

Hence the answer 3340.


  Posted by Ady TZIDON on 2014-04-09 15:35:05
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