-4
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enter image description here

How can you move 3 matchsticks in order to make the above figure balance symmetrically?

Note: Cutting through the center of gravity of the new figure must make 2 equal halves or sets (i.e. we seek reflectional symmetry of the figure).

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    $\begingroup$ What kind of symmetry are we aiming for? Left/right? Top/bottom? Rotational? EDIT: Also, do the heads of the matches count as part of the symmetry? $\endgroup$ – Leafy Greens Oct 15 '16 at 20:49
  • $\begingroup$ @LeafyGreens 360degrees-Yes $\endgroup$ – TSLF Oct 15 '16 at 20:58
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    $\begingroup$ The match heads have to be symmetrical? $\endgroup$ – Leafy Greens Oct 15 '16 at 21:03
  • $\begingroup$ Need to balance $\endgroup$ – TSLF Oct 15 '16 at 21:05
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This answer should work.

ans
This has 180 degree rotation symmetry. Any line drawn through the center would create two congruent halves, with matchstick heads taken into account.

[old answer]

Like this? Seems pretty symmetrical to me.

enter image description here

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  • $\begingroup$ Gah, you beat me while I was trying to format my post DX $\endgroup$ – Leafy Greens Oct 15 '16 at 21:01
  • $\begingroup$ If by symmetrical the OP means "mirrored", then no, it's not (he said the match heads count, although the statement was pretty vague about it). $\endgroup$ – Alenanno Oct 15 '16 at 21:30
  • $\begingroup$ Given what OP said, I now believe the real problem is constructing a figure such that any line drawn through the center divides it into congruent halves i.e. it should have 180 degree rotational symmetry. I update my answer. $\endgroup$ – greenturtle3141 Oct 15 '16 at 21:35
  • $\begingroup$ The snail figure is correct! $\endgroup$ – TSLF Oct 15 '16 at 21:41
2
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Before:

       _ 
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|_| |_|

After:

     _ _  
|_|_|
|_|_|

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  • $\begingroup$ The "window" figure will tilt like the plus sigh $\endgroup$ – TSLF Oct 15 '16 at 21:04
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    $\begingroup$ @TSLF I don't understand what you mean. What do you mean by "tilt"? $\endgroup$ – Leafy Greens Oct 15 '16 at 21:05
  • $\begingroup$ I cant see the heads but mostly that figure isn't symmetrically balanced. Cutting through c,g. gives equal rotational or mirrored halves $\endgroup$ – TSLF Oct 15 '16 at 21:10
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    $\begingroup$ You absolutely need to specify that the heads count. $\endgroup$ – greenturtle3141 Oct 15 '16 at 21:20
  • $\begingroup$ "center of gravity" includes everything in this lateral thinking-puzzle $\endgroup$ – TSLF Oct 16 '16 at 4:55

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