I've seen this with leprechauns in real life as well. I redrew the pictures with magicians in various poses and laminated it-
A VANISHING MAGICIAN!

http://www.dojopress.com/tvn.html

I have the vanishing leprechaun puzzle and I have never quiet understood how it works. I've also seen one that has a hen and eggs. Thanks for sharing.

Night_Crawler

Thanks for sharing that Shinobi. It is appreciated.

Best thoughts,
John Smetana

I like the puzzle itself, but "defied Western science for centuries"?!?

How does it "defy Western science"? Somebody needs to tell Ashida Kim that it does no such thing. I don't doubt that Kim doesn't understand it.

It's simple. The pieces are carefully drawn so that when they're rearranged, each ninja is 1/15 of a ninja longer than when there were 15. You're not losing 1 ninja, you're seeing 14 new ninjas.

You can do this yourself just using graph paper and straight lines, and the principle will become clear very quickly.

I tried to view this page but one out of the 3 pictures isn't showing up for me. Does anyone else have another page with the same idea on it?

Thanks
Shaun

Shaun, here is a link to the vanishing leprechaun puzzle that night crawler was referring to. Same principle, and they give an explanation of how it works.

There's a detailed write-up in Martin Gardner's Mathematics, Magic, and Mystery. In that book, he shows Sam Loyd's "Get Off the Earth" puzzle, which used the same principle in a circular format. I believe that Loyd was also responsible for Teddy and the Lion, another similar type puzzle with racist overtones.

Let me know if the Leprechaun thing doesn't work for you. I have examples of similar puzzles with varying themes that I can e-mail out to you if you wish. Even one with a rabbit that turns into an egg, from the Gardner book mentioned above.


http://www.physics.ohio-state.edu/~trey/lep/main.html



Scott, I believe that Kim's remarks about defying western science is akin to the hyperbole that we magicians often use. Just to add an air of mystery to the puzzle.

I once made a 3D version of this by gluing together red and blue pencils with erasers on one end. The good thing is that the top and bottom parts of each pen looks identical regardless if it's a red or blue pencil.

When I cut the glued pencils and exchanged two parts with each other, one pen seemed to change color. In other words I had 4 red pencils and 5 blue ones, but after the exchange there was 5 red and just 4 blue.

Been thinking about making similar 3D versions of the puzzle. It helps the illusion if the objects all are identical in top and bottom. Maybe thick-bottomed whisky glasses? Only four of them start out with whisky but after the exchange five of them now has whisky in them.

Or a gigantic 3D version using mannequins…

Any other ideas of objects that are identical in top and bottom but differ in the middle?

/Tomas

Could you share with us the arrangement of the pencils to make the effect possible? (Or PM me.) I'm puzzled by the fact that the total number of pencils remains constant while the number of each color changes. This is very clever, Tomas!

Yes, please do tell, Tomas. A 3D version with pencils is a very clever idea, indeed!

As the number of red and blue middles must remain the same, my guess is that one of the colored middles turn into a red or blue stick or other non-pencil entity when it's not paired with a pencil top or bottom.

For example, in the Martin Gardner example, the tail of one rabbit and the nose of another together turn into an egg when the pieces are shifted.

In another one I have, one person turns into a steaming pile of [something not nice.]

In most cases, however, one of the subjects disappears entirely.

I feel so foolish (smacks self on side of head)! Of course, the colors don't disappear. But they don't necessarily have to turn into something else either.

For example, in Phase 1, we could have a total of 14 inches of red pencil middles distributed over 4 pencils, and 16 inches of blue distributed over 5 pencils. In Phase 2, we'd still have the same 14 inches of red, redistributed (not evenly) over 5 pencils and the same 16 inches of blue distributed over 4 pencils. Laid out properly, you should have any pencils that are part-red, part-blue.

On average, each pencil would be shorter when there are 5 of that color, than when there are 4 of that same color. It's the law of conservation of matter.


That should read: you should NOT have any pencils that are part-red, part-blue.

As I gave away the 3D puzzle and didn't keep any diagrams of it I took some time last night to make another. I sense that it's not as good as the one I made before, but it'll illustrate the method. If you can’t view this correctly, cut and paste it to view with courier font.

"#" are eraser ends and are identical on all pencils. "V"s are the sharpened points and are identical on all pencils. You start out with 5 Blue pencils and 6 Red ones. After exchanging the top two pieces your end up with 6 Blue pencils and just 5 Red ones.

Before:
:___________
: |# #
: ## |R B
: RB |R# #B
:# RB|#RB RB
:B#RB#RRB RB
:BRRBBRRB#RB__
:BRRBBRVBRRB
:BRVBBR BRRV
:BR VBR BRV
:BR BV VR
:VV B R
: V V

After:

:___________
: # #|
: R B |##
: R# #B |RB
: #RB RB# RB
:#RRB RBB#RB
:BRRB#RBBRRB__
:BRRBBRVBRRB
:BRVBBR BRRV
:BR VBR BRV
:BR BV VR
:VV B R
: V V

You see that whichever color there is 6 of, the pens are 5 units long (exclusive rubber and point) and the colors there are 5 of are one unit longer. The more pens you use the less visible this difference will be of course.

During this I remembered another idea I had...to glue face up and face down cards onto cardboard. After moving pieces around one of the face down cards would appear to have turned face up when the cards are counted. Probably easiest to do this with blank faced cards but it'd be very cool if the faces would look all right in both assemblies of the puzzle.

/Tomas

Added: October 24, 2003
I believe the ASCII-art isn't working with this font at all. Spaces seem to have shifted too when I press "Submit Reply". I'll make a gif out of it and submit when I have the time.

Sorry,

/Tomas

Tomas,
Thank you for your effort!
Your idea for the playing cards reminds of one I tried to figure out shortly after reading Martin Gardner's Mathematics, Magic and Mystery. He illustrates a "Vanishing Card" that works on the same principle we are discussing on this thread. I thought it would be neat to have a group of cards sandwiched between transparent plastic and cut into three pieces, as in the Vanishing Ninja. After counting and examining these the plastic-imbedded card pieces would be turned face down, reversing the top two pieces in the process. Next you would have a small packet of duplicate cards, from which a spectator would remove one (forced). The three plastic pieces would then be turned over (without reversing the position of the two smaller pieces) to show that one card had vanished, the very same one that the spectator had selected. I was never able to work out the faces of the cards to prevent mismatched pips when the two pieces are rearranged. Maybe someone will be able to do this, if they are interested. I haven't worked on this for a number of years, but maybe I'll pick it up again.

Tomas -- thanks again for a stimulating contribution!

Dale Hoyt

While chatting with the amazing DME today I mentioned the effect of the card reversing itself. While writing, a very fun trick started to form in my mind:

You show a bunch of cards with strange things drawn on them. The spectator freely selects one of them and keeps that card.

You show a second set, which are the glued cards and ask him to count the number of face up cards and the number of face down cards. Let's say he counts 5 face up and 6 face down cards. You ask him if any of the face up cards holds his design. None of them does.

When you assemble the pieces differently all of a sudden there are 6 face up cards and the card he selected have turned face up.

The secret is that all 6 designs now visible are new and that when the spectator selected a card earlier he could chose freely from any of these designs. So it's like a Princess Card Trick in reverse.

Actually you could probably make this into a Princess Card Trick by having them think of any of the 6 designs and when you change the pieces around the thought of design have vanished.

Quite a challenge to design the faces of the cards though...

/Tomas

Today at the library I found a reference to the Vanishing Pencil that Tomas described. Mel Stover's geometrical vanishes are briefly discussed on p. 29 of "Puzzlers tribute: a feast for the mind" ed. by David Wolfe and Tom Rodgers, published 2002 by A. K. Peters (www.akpeters.com). This book is a compilation of material presented at the various "Gathering For Gardner"s that have been held to honor the contributions of Martin Gardner. The 1st plate in the book has 4 of Mel Stover's geometrical vanishes and includes one with red and blue pencils. Hope this helps!

Dlhoyt, thanks for that reference. Seems as if there is nothing new under the sun. I'll focus on the card version then. Hmmm, and maybe photos of whisky glasses.


Attached you'll find a miniature version of one attempt at the card that magically turns up. They should be cut along the thin horizontal line then the upper part should be divided in 5:8.

I have 13 cards there so it will be ok if all the cards are of the same suit. Quite a challenge to create the faces... I think I'd settle for strange symbols.

/Tomas

Click here to view attached image.

Found this on the S&R site. Check out the Tiger Toss.

http://www.siegfriedandroy.com/magic/interactive.php

Some of the tigers get terribly distorted after the transformation, but you'd get bent out of shape too if one of yours went missing.

I love Gardner's explanation of these.

"The Principle of Concealed Distribution"


Timothy

Now, imagine doing this with dollar bills.

/Tomas

Or socks. After each wash, I come out one sock short. However, each of the remaining socks is just a little bit longer.

Tomas, thanks for your little GIF of the cards. Probably can imagine them as short and fat little red and white pencils as well.

For entertainment purposes only --

There is a very time consuming con
that involves cutting a sliver off a dollar bill.
Spend the dollar - no one notices the bit missing.

Then cut a slightly larger section off another bill
and tape the first sliver on.

Spend that one.

Repeat , each time gaining a slightly larger piece
untill you have a new bill.

Bingo - Concealed Distribution

MagicCoach, to get identical serial numbers on both ends of the bills (if there are two serial numbers as I believe there are on American bills), begin with cutting each bill in half and do the procedure on each half individually. The serial numbers may look weird, but they are identical.

Mushu, you are welcome. But for using pens you can go with a version with fewer objects. I needed many objects with the cards so that the difference in length wasn't too great.

/Tomas