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Zeros And Ones (Posted on 2003-04-08) Difficulty: 2 of 5
What is the smallest integer greater than 0 that can be written entirely with zeros and ones and is evenly divisible by 225?

See The Solution Submitted by Ravi Raja    
Rating: 3.0000 (4 votes)

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re(5): Idea | Comment 13 of 22 |
(In reply to re(4): Idea by Charlie)

The table of 1's and 0's numbers in other bases was correct in showing such numbers divisible by 225 in that base, but the ones for bases 16 and 18 were not the smallest. The correct table with the smallest for each base is:
6 11001 ( 1513 89 )
7 1011 ( 351 117 )
8 11101101101 ( 1225032257 149 )
9 11011011 ( 5321710 185 )
10 11111111100 ( 11111111100 225 )
11 1001010011 ( 2359733905 269 )
12 100011 ( 248845 317 )
13 1100001 ( 5198103 369 )
14 110101101 ( 1581743325 425 )
15 1101110 ( 12153615 485 )
16 10111000011 ( 1104091807761 549 )
17 100101011 ( 6977182229 617 )
18 10000101001 ( 3570469122025 689 )
19 11010101110101 ( 44272446480796725 765 )
20 1110010 ( 67360020 845 )
21 1011011011 ( 796167105007 929 )
  Posted by Charlie on 2003-04-09 16:27:10

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