perplexus.info :: General : Nine square pieces

Nine square pieces (Posted on 2005-12-11)

You are given 9 square pieces (A - I), each one having in each side a number from 1 to 4, positive or negative, as shown:

        +------------+   +------------+   +------------+
        |     +1     |   |     +2     |   |     +1     |
        |            |   |            |   |            |
        |-3   (A)  +4|   |+3   (B)  -1|   |+3   (C)  -2|
        |            |   |            |   |            |
        |     -2     |   |     -4     |   |     -4     |
        +------------+   +------------+   +------------+
        +------------+   +------------+   +------------+
        |     -1     |   |     -2     |   |     +2     |
        |            |   |            |   |            |
        |+2   (D)  -4|   |-4   (E)  +1|   |+1   (F)  -3|
        |            |   |            |   |            |
        |     +1     |   |     +3     |   |     -4     |
        +------------+   +------------+   +------------+
        +------------+   +------------+   +------------+
        |     +3     |   |     -3     |   |     +3     |
        |            |   |            |   |            |
        |-2   (G)  +4|   |+2   (H)  -4|   |-2   (I)  +4|
        |            |   |            |   |            |
        |     -1     |   |     +1     |   |     -3     |
        +------------+   +------------+   +------------+

Your task is to juxtapose them forming a 3x3 grid so that "touching numbers" of each pair of touching pieces (horizontally or vertically) adds to zero.

Note: You are free to rotate the pieces.

Submitted by pcbouhid

Rating: 3.0000 (1 votes)

Solution: (Hide)

One solution (of others found by Charlie): the position of each piece is indicated below, and some of them must be rotated 90º (CW or CCW) or 180º:
+------------++------------++------------+ | -2 || -2 || -4 | | || || | |+1 (C) -4||+4 (A) -3||+3 (E) -2| | || || | | +3 || +1 || +1 | +------------++------------++------------+ +------------++------------++------------+ | -3 || -1 || -1 | | || || | |+2 (F) -4||+4 (G) -2||+2 (B) -4| | || || | | +1 || +3 || +3 | +------------++------------++------------+ +------------++------------++------------+ | -1 || -3 || -3 | | || || | |+2 (D) -4||+4 (I) -2||+2 (H) -4| | || || | | +1 || +3 || +1 | +------------++------------++------------+

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

Subject	Author	Date
re(3): For those who wanna try... random sampling ... computer used	Charlie	2005-12-12 16:17:23
re(2): For those who wanna try... random sampling ... computer used	pcbouhid	2005-12-12 15:45:38
re: For those who can try... random sampling ... computer used	Charlie	2005-12-12 15:35:36
For those who can try...	pcbouhid	2005-12-12 10:25:44
Both (all) solutions -- computer used -- spoiler	Charlie	2005-12-11 19:25:20
re(2): question	pcbouhid	2005-12-11 18:31:24
re: question	Larry	2005-12-11 17:23:59
question	James	2005-12-11 15:00:03
One solution by hand (spoiler)	Larry	2005-12-11 12:08:23

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