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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(4): Idea | Comment 8 of 22 |
(In reply to re(3): Idea by Charlie)

In fact, interpreting the question in various bases gives the following table. Each line has the base, written in decimal, followed by the 1's and 0's number in that base, and in parentheses, the decimal interpretation of that number and the decimal interpretation of the 225 in that base that divides the number evenly:
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 11000010111 ( 1168231170321 549 )
17 100101011 ( 6977182229 617 )
18 11011010001 ( 3769472854225 689 )
19 11010101110101 ( 44272446480796725 765 )
20 1110010 ( 67360020 845 )
21 1011011011 ( 796167105007 929 )

  Posted by Charlie on 2003-04-08 19:38:57

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