perplexus.info :: Logic : Fill in the Squares II

Fill in the Squares II (Posted on 2005-05-17)

Place the numbers 1 through 9 in the grid below:

   1 2 3  
A |_|_|_|  
B |_|_|_|  
C |_|_|_|

The product of the numbers in row C is twice the sum of the numbers in row C.
The product of the numbers in column 3 is twice the sum of the numbers in column 3.
If you ignore column 1, all the columns have even products.
If you take the six-digit number C3 B3 B1 C1 A3 B2 and multiply it by 3, you get the six-digit number B3 B1 C1 A3 B2 C3.

Try to figure it out without using a computer program.

Submitted by Dustin

Rating: 2.6250 (8 votes)

Solution: (Hide)

965
274
831

The only sets of three digits whose product is twice their sum are: 138, and 145. Since one of these is Column 3, and the other is Row C, C3 must be a 1.
So clue 4 says "1ABCDE * 3 = ABCDE1".
Let X represent the number ABCDE.
(X + 100000)*3 = 10X + 1. 3X + 300000 = 10X + 1.
7X = 299999.
X = 42857.
So now we have:
__5
274
8_1
We know a 3 goes in the bottom blank from clue 1.
We know Column 2 has an even product. Since it has two odd numbers and a blank spot, the blank spot must be an even number. So it's 6, and A1 is 9.

Final grid:
965
274
831

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Huh?	Caleb	2019-03-09 13:49:30
Answer	K Sengupta	2009-02-06 01:59:17
Huh?	Tracy	2005-07-29 17:06:35
solution	josh	2005-06-28 23:58:37
re(2): x/7ths	john	2005-06-09 19:18:17
re: x/7ths	pcbouhid	2005-06-06 21:33:44
x/7ths	john	2005-06-06 20:59:12
Alternate Solution	Marc	2005-06-03 18:23:20
solution to "Fill in the squares 2"	svetislav	2005-05-27 02:55:19
re(3): Flaw in the problem	pcbouhid	2005-05-21 20:27:01
re(2): Flaw in the problem	Rupesh Khandelwal	2005-05-21 06:21:53
re: Flaw in the problem	pcbouhid	2005-05-19 17:14:00
Flaw in the problem	Rupesh Khandelwal	2005-05-19 10:35:30
re(2): Full Solution (Avin)	pcbouhid	2005-05-18 20:38:50
re: Full Solution (Avin)	Charley	2005-05-18 19:48:45
re: Got it	LifeTeach	2005-05-18 17:52:59
Got it	Richard	2005-05-18 16:35:32
another way...	pcbouhid	2005-05-18 01:08:13
re: solution - spoiler	pcbouhid	2005-05-17 19:02:07
re: Full Solution (to Avin)	pcbouhid	2005-05-17 18:53:31
Full Solution	Avin	2005-05-17 18:47:04
solution - spoiler	pcbouhid	2005-05-17 18:45:02

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