(In reply to
possible solution by Ady TZIDON)
For the numbers whose mod 28 representation is (4,8,16), the calculation of the number of choices is correct. 10^{3} = 1000. There are 10 different numbers mod 28 ≅ 4 × 10 different numbers mod 28 ≅ 8 × 10 different numbers mod 28 ≅ 16.
For the numbers whose mod 28 representation is (0,0,0), the calculation is in error. Though there are 5 numbers corresponding to mod 28 ≅0, the calculation is not 5^{3} = 125 for the number of combinations. As 3 of these numbers must be chosen from the set of 5, and as repetition is allowed, the number of combinations is given by (5 + 3  1)!/(3!×(5  3)!) = 35.
Thus, the total number of possible solutions is 1000 + 35 = 1035.
Nevertheless, I found your analysis of determining the number of different numbers mod 28 brilliant.
*Corrected, as the comparison operators also include equal in addition to the less than. (Thanks, Charlie).
Edited on December 21, 2014, 10:14 pm

Posted by Dej Mar
on 20141221 18:08:34 