5 Digit Number (Posted on 2003-08-20)

	Submitted by Gamer
Rating: 3.0000 (6 votes)
Solution:	(Hide)
The numbers must be split into a 3 digit number and a 2 digit number. Since the 3 digit number is double the 2 digit number, it must be divisible by 201 (for example 13869 = 69 x 201). This can be easier seen doing multiplaction by hand. Since 201 = 67 x 3, and the two digit number times 201 or (67 x 3) times 3 is a perfect square, the following equation is true: ((? x (67 x 3)) x 3) = perfect square. Since 67 needs to be accounted for, it must be some perfect square times 67 for the two digit number. The only one that works here is 67 itself. So the 5 digit number is 13467. 134 = 67 x 2, and 13467 x 3 = 201^2

	Subject	Author	Date
	re(2): Assuming Leading Zeroes	K Sengupta	2011-07-02 01:25:17
	re: Assuming Leading Zeroes	Dej Mar	2011-07-01 07:23:43
	Assuming Leading Zeroes	K Sengupta	2008-05-19 04:54:07
	Puzzle Solution	K Sengupta	2008-05-19 04:42:20
	Answer	K Sengupta	2008-05-18 02:48:15
	Solution	Lawrence	2003-08-24 11:35:15
	Solution	Daniel Gordon	2003-08-21 11:35:50
	Five Digit Numbers	Gordon Steel	2003-08-20 19:09:35
	re: Full Solution	DJ	2003-08-20 17:21:04
	Full Solution	DJ	2003-08-20 16:31:07
	Trial and error?	Gamer	2003-08-20 15:54:17
	Solution	Ender	2003-08-20 14:49:53
	SOLUTION	Not Applicable	2003-08-20 14:41:51