5
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Divide the below figure into $5$ equal pieces (same shape, same size, possibly reflected).

$\qquad\quad\qquad$enter image description here

I believe this is one of Martin Gardner's, but I could not find the source.

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  • $\begingroup$ I think the dashed lines are misleading: if you consider them, we have a total area of 16 squares to divide into 5 parts $\endgroup$ – leoll2 Apr 13 '15 at 15:12
  • $\begingroup$ I actually find the dashed lines helpful, as they give me the relative sizes of each portion of the shape $\endgroup$ – Brian J Apr 13 '15 at 18:58
  • $\begingroup$ I think this might have been in one of the Aha! books? $\endgroup$ – zeb Apr 14 '15 at 0:43
  • $\begingroup$ @zeb, thank you, you are right! This appears in aha! Insight. $\endgroup$ – Mike Earnest Apr 14 '15 at 21:25
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The first observation we make is that

the left and right edges are identical
the top and bottom edges are identical

If we then

mark four equidistant points along each horizontal line,

we have constructed the basis for making 5 shapes that are basically

thinner versions of the original shape.

Connecting the dots vertically now subdivides the original shape into 5 equal pieces of the same shape and size.

x-x-x-x-x-x
 \ \ \ \ \ \
 / / / / / /
| | | | | |
x-x-x-x-x-x
 

Perhaps the most important observation to make is that

the lattice on which this shape is placed is a visual distraction. Once ignored and only the shape itself is considered, the solution is quite obvious.

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  • $\begingroup$ This means we could divide this into an infinite number of identical shapes, right? $\endgroup$ – VictorHenry Apr 13 '15 at 18:13
  • $\begingroup$ @VictorHenry You sure could. It's not what the puzzle was asking for, though. $\endgroup$ – Ian MacDonald Apr 13 '15 at 18:17

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