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Sandy Wood
Brain Game: L-ementary
by Sandy Wood - October 9, 2009 - 7:30 AM

bloghead_braingames.jpg

Here’s today’s Brain Game; enjoy!

bluebox

Find a way to divide the above blue shape
into FOUR identically-shaped parts. 

Here is the SOLUTION.
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Comments (14)

  1. You could also trace one line from LU corner to RD corner and another between the other two points, resulting in four identical triangles

    posted by Blog Mallmal on 10-9-2009 at 8:15 am

  2. What if you just drew 3 lines outward from the inside (center of whole pic) corner of the “L”? One out to the top left corner, one to the bottom left corner, and one to the bottom right? It would make two larger and two smaller triangles, but the puzzle just said make the same shape, which they would be. I think…

    posted by MoronicPlague on 10-9-2009 at 8:22 am

  3. I have done enough puzzles to see this one fairly quickly, however, my freind divided it into four isoceles right triangles, two small and two large. Since the puzzle specified \identically-shaped\ I would have to say he was technically correct in his solution.

    posted by Richard on 10-9-2009 at 8:25 am

  4. You folks are absolutely right. Even though I intended to mean “same size AND shape,” your answer does indeed work based on the way I phrased the instructions. Nice job!

    posted by Sandy Wood on 10-9-2009 at 8:36 am

  5. What about drawing 3 “L”’s inside the shape, facing the same way as the blue “L”? Again, they all would be the different sizes, but it would work.

    posted by Tdl on 10-9-2009 at 9:42 am

  6. I also came to the triagle conclusion. In order to make the triangles the same size, you could take the two larger triangles and split them in two in order to make 6 triangles of identical size.

    posted by CH on 10-9-2009 at 9:44 am

  7. @Tdl – I don’t think you could manage that and actually keep them the same shape. To be the same shape, the proportions between the sides would have to remain constant.

    posted by Lugh on 10-9-2009 at 10:35 am

  8. Four right triangles, TL to BR then BL to inner vertex of the ‘l’

    posted by EAS on 10-9-2009 at 10:39 am

  9. @Tdl … I liked the idea so I worked it out. If the height of the figure is X, than the width of the largest “L” would be 0.1591(X), the next 0.1338(X), the next 0.1125(X) and the last and smallest 0.0946(X). Of course I rounded to the fourth decimal.

    posted by Richard on 10-9-2009 at 12:04 pm

  10. I also came up with the triangle solution. Demonstrates the difference between “similar” and “congruent” quite well.

    posted by Marc in UT on 10-9-2009 at 1:23 pm

  11. @Richard… If they’re not similar anyway, is there any reason there couldn’t just be, for instance, three skinny ones and a fat one?

    posted by Betsy on 10-9-2009 at 1:57 pm

  12. @Betsy, Similar polygons are polygons for which all corresponding angles are congruent and all corresponding sides are proportional. Keeping the sides proportional would be a crucial.

    posted by Richard on 10-9-2009 at 2:41 pm

  13. I’m glad to see so many others came up with 4 triangles and it wasn’t just me.

    posted by Nerak on 10-9-2009 at 6:36 pm

  14. I think the instructions could have been a bit vaguer.

    No indication whether or not the whole shape is a square. Also, what kind of description is “identically-shaped parts?” Doesn’t a 2 x 6 rectangle and a 4 x 12 identically shaped rectangles, just not the same measurements…maybe I just don’t get the lingo. Odd wording I guess.

    posted by Olympia on 1-6-2010 at 8:36 pm

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