Zeros And Ones (Posted on 2003-04-08)

	Submitted by Ravi Raja
Rating: 3.0000 (4 votes)
Solution:	(Hide)
The prime factorization of 225 is 5*5*3*3. So the answer will be both a factor of 25 and of 9. All factors of 25 end in either 00, 25, 50, or 75. The only one of these composed of 0's and 1's is obviously 00, so the answer must end in 00. Now, we know that if the sum of digits of a number is divisible by 9 then the number itself is also divisible by 9. Note that this is true for 3 also. Since we are to find a series of zeros and ones which will be divisible by 9, we get the following: The smallest number consisting of all 1's and divisible by 9 is thus 111,111,111. Adding the two zeros at the end results in the answer to the problem: 11,111,111,100.

	Subject	Author	Date
	Solution	K Sengupta	2021-12-16 00:23:45
	re: Smaller positive integers	Charlie	2008-02-16 11:37:24
	Smaller positive integers	Dej Mar	2008-02-16 06:46:38
	answer	K Sengupta	2008-02-15 10:59:50
	re: Wrong Official Solution	Tristan	2004-09-23 18:36:34
	Wrong Official Solution	Syzygy	2004-09-23 11:57:13
	Not looking at the solution	Dan Porter	2004-01-21 14:34:58
	re(2): I think i got it!!!!	Andrew	2003-04-12 02:48:09
	re: I think i got it!!!!	Gamer	2003-04-11 13:35:57
	I think i got it!!!!	Andrew	2003-04-10 17:23:39
	re(5): Idea	Charlie	2003-04-09 16:27:10
	re: Decimal Representation ( Base 10 )	Gamer	2003-04-09 15:46:24
	re: Zeros and Ones	Charlie	2003-04-09 04:31:40
	Decimal Representation ( Base 10 )	Ravi Raja	2003-04-09 00:08:00
	re(2): Idea	Ravi Raja	2003-04-08 23:57:23
	re(4): Idea	Charlie	2003-04-08 19:38:57
	re(3): Idea	Charlie	2003-04-08 10:24:15
	re(2): Idea	Charlie	2003-04-08 09:59:53
	re: Idea	Lyman Hurd	2003-04-08 08:22:21
	Zeros and Ones	John	2003-04-08 06:00:18
	Zeros and Ones	John	2003-04-08 05:51:52
	re: Idea	Charlie	2003-04-08 03:50:39
	Idea	Gamer	2003-04-08 01:48:11