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**TORn 10th Anniversary Puzzle Post: A magical toy from the dwarves!

OhioHobbit
Gondor

Apr 25 2009, 4:02pm

Post #1 of 8 (924 views)
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**TORn 10th Anniversary Puzzle Post: A magical toy from the dwarves! Can't Post

I came across this puzzle in a magazine about thirty years ago. The original consists of rather odd looking leprechauns. I just took the rather odd looking leprechauns and replaced them with rather odd looking dwarves.

Right click on the image of the puzzle and save it to your hard drive as a graphics file. Insert the graphics file into a word processor document and print it out. Carefully cut out the puzzle along the dashed lines so that you have three sections Ė one long bottom section and two top sections (one long and one short). Line up the two top sections with the bottom section and count the number of dwarves. Now swap the two top sections, left and right, line them up with the bottom section and count the number of dwarves.



For those of you who donít want to go to all the trouble of copying, printing, and cutting, the image below shows the puzzle with the top sections swapped.



Notice that in the original arrangement there are 14 dwarves, in the second arrangement there are 15 dwarves. Where did the extra dwarf come from? When you switch it back, where does the extra dwarf go?

Have fun!

Movie Technical Discussion -- Index


squire
Half-elven


Apr 25 2009, 6:59pm

Post #2 of 8 (747 views)
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A very clever illusion! [In reply to] Can't Post

It's a clever optical illusion.

You can count 14 full dwarves in the upper drawing (see below). But note that there are only 13 who occupy the top half (which is what will switch around) and 14 in the bottom half.

One dwarf is entirely in the bottom half. I numbered him 14 and faded him out, even though he is in the middle of the sequence, because switching the top half segments can't possibly change him. So focus only on the 13 upper half dwarves, and see how they seem to become 14 dwarves after the switch.

Start by numbering the dwarves both in the upper half and the lower half. With #14 gone, we see that each of the 13 dwarves has an upper body and a lower body. The numbers are in parallel all the way across.

Okay, switch the left and right segments of the top half.


The body parts are rearranged in the bottom drawing, and you think you see 14 full dwarves, but you don't. You see 12 full dwarves, and one dwarf who is missing the top of his head (bottom #11), and one dwarf who is missing the bottom of his robe and boots (top #11)! Count the dwarves top or bottom, and only count bodies that have a part in the half that you are counting. The blue boxes highlight the missing parts, and show how the count has to skip to the next body. The two dwarves who are missing parts are both number 11 in the left-right sequence, but they are not the same dwarf!

To sum up, subtracting #14 in the bottom as not being part of the switcheroo, the misleading illusion is:

13 full dwarves become:
12 full dwarves + 1 part dwarf on top + 1 part dwarf on bottom = 14 apparent dwarves.



squire online:
RR Discussions: The Valaquenta, A Shortcut to Mushrooms, and Of Herbs and Stewed Rabbit
Lights! Action! Discuss on the Movie board!: 'A Journey in the Dark'. and 'Designing The Two Towers'.
Footeramas: The 3rd TORn Reading Room LotR Discussion; and "Tolkien would have LOVED it!"
squiretalk introduces the J.R.R. Tolkien Encyclopedia: A Reader's Diary


OhioHobbit
Gondor

Apr 26 2009, 12:22am

Post #3 of 8 (696 views)
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No, its magic! [In reply to] Can't Post

Excellent! A very good explanation. I did basically the same thing as you did. I labeled the top and the bottom and then checked to see how things matched up when rearranged. This is what I came up with.

T1_T2__T3__T4__T5__T6_T7_T8_T9_T10____T11_T12_T13
B1_B2__B3__B4__B5_B6_B7_B8_B9_B10____B11_B12_B13

T9_T10_T11_T12_T13_T1_T2_T3_T4_T5__T6_____T7__T8
B1_B2__B3__B4__B5_B6_B7_B8_B9_B10____B11_B12_B13

Before doing this I figured that the best way to solve this was to try it with actual people, but I could never talk my coworkers into being sliced in half.Evil

Movie Technical Discussion -- Index


dernwyn
Forum Admin / Moderator


Apr 26 2009, 12:28am

Post #4 of 8 (682 views)
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Bwahaha! [In reply to] Can't Post

Whatever, it's magical to me - I love these kinds of illusions!

Now, if Gandalf had been able to do this with Thorin & company, they would have been able to create 14 Dwarves out of 13, and they wouldn't have needed Bilbo...Angelic!


~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


"I desired dragons with a profound desire"

"It struck me last night that you might write a fearfully good romantic drama, with as much of the 'supernatural' as you cared to introduce. Have you ever thought of it?"
-Geoffrey B. Smith, letter to JRR Tolkien, 1915


weaver
Half-elven

Apr 26 2009, 2:27am

Post #5 of 8 (707 views)
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I have never spent so much time staring at dwarves in my life... [In reply to] Can't Post

 
I could not get it to print out right, so I just kept comparing the two images in your post.

I can't figure it out-- but I bet squire did!

Weaver







weaver
Half-elven

Apr 26 2009, 2:31am

Post #6 of 8 (669 views)
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Ah, it's all so apparent now! [In reply to] Can't Post

..maybe they can pull that same trick in the films, and cast only 6 actors but make them look like 12 dwarves....

Thanks for the illustrated reply -- now I get it!

Weaver







grammaboodawg
Immortal


Apr 26 2009, 12:54pm

Post #7 of 8 (664 views)
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I can't WAIT to show this to the gkiddies! [In reply to] Can't Post

Thirty years ago!? Ohhhhh boy... this is GREAT! *cuts, pastes* This is great! Cheers, OhioHobbit... and thanks!



sample

"Barney Snow was here." ~Hug like a hobbit!~ "In my heaven..."

I really need these new films to take me back to, and not re-introduce me to, that magical world.



TORn's Observations Lists


Ainu Laire
Tol Eressea


Apr 26 2009, 7:01pm

Post #8 of 8 (702 views)
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How neat! [In reply to] Can't Post

I had a puzzle book as a kid that had this optical illusion with people- it completely puzzled me. I figured that the cut off head and boots of the two dwarves had something to do with it, but I am glad that I had squire to figure it out for me ;)

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