Smudge Sludge (Posted on 2004-04-28)

   ??7
 x 3??
  ?0?3
  ?1?
 ?5?
 ?7??3

	Submitted by Gamer
Rating: 3.6667 (3 votes)
Solution:	(Hide)
Since the only digit that can end in 3 when multiplied by 7 is 9, that must be the first digit of the bottom multiplicand. Also, since 3 times 7 is 21, the last digit on the row second from the bottom must have a 1 in the ones place. Since the only way ?7 times 3 will give 51 is 17, that must be the next number. ?17 x 3?9 ?0?3 ?1? ?51 ?7??3 Now we can fill in the ?0?3 with 9 times 17 or 53. Also, since 9 times ?17 needs to have an extra 900, the only ?00 times 9 to end in 900 is 1. This means the top multiplicand is 117 and the third line down is 1013 and the fifth line down is 351. 117 x 3?9 1013 ?1? 351 ?7??3 The second column adds up to 7 with no carrying possibility, so the ? in that column must be 1. This means the tens digit in the lower multiplicand must be 1 because it's the only thing that can result in 11? when multiplied by 117, and the ? must also be 7. The bottom three numbers can be added together to get the final solution. 117 x 319 1013 117 351 37283

	Subject	Author	Date
	Puzzle Solution With Explanation	K Sengupta	2009-01-22 06:02:48
	re: Solution incorrect. FK is correct.	K Sengupta	2009-01-22 06:00:51
	re: Answer	JayDeeKay	2009-01-21 13:37:16
	Solution incorrect. FK is correct.	jduval	2007-09-16 19:57:16
	Answer	K Sengupta	2007-08-17 12:30:19
	No Subject	varadarajan	2005-03-03 12:08:38
	solution	Steve Royer	2004-04-28 21:53:13
	Reasoned solution	Federico Kereki	2004-04-28 17:58:06
	No Subject	Saka Devi	2004-04-28 14:11:31