Math Is Fun Forum

Hi wintersolstice,

I think I've worked out a formula for solving medium-level problems that commence with "1":

"generals"

Following on from soroban's good explanation of Jane's "12/13 people" illusion, here's an informative link I found today on the internet. It has some helpful illustrations:-
http://www.laurenceholbrook.com/main_00000e.htm

I also found these two illustrations.

The colour coding makes it a bit(!) clearer (I think ) to understand the illusion.

What's happening is that each person, in turn, gives an ever-increasing-height portion of their body to the next person, and after doing that with all 12 people you end up with a whole extra person.

They swap the body portion that they receive for that same portion from their own body, and give the rejected portion, combined with a further slice (about one 12th their height) from below that portion, to the next person.

The fractions are approximate, varying from person to person for best visual effect.

The process begins with the dark blue person (#1) at bottom left, who gives his hair to person #8, who gives his forehead and hair to #4, who gives the potion above the middle of his nose to #11, who gives his whole head to #6, who gives his shoulders and head to #2...and so on.

In the 13-person group you can see that all the donors have shrunk by about one 12th their original height, but the changes are subtle enough, and the figures are drawn roughly enough, for us not to notice what is really going on.   

The puzzle's creator cleverly mixed up the order of the people to hide what he did.

Oh...I see!!?! At least, I hope that my vision will return after I can uncross my eyes again!

Your explanation is quite in keeping with how that fella in your signature defines mathematics...and also seems to follow Berry's Paradox.

This Wikipedia article - http://en.wikipedia.org/wiki/Berry_paradox - begins by saying:

All too much for my little brain!

This is THE most baffling optical illusion I've ever seen!

My brain absolutely refuses to see this unaided...that the shading on squares A and B is identical!!

Try these simple proofs...you'll be amazed!! :-

Copy the image (the full one, not the thumbnail) and paste it into MS Paint.
1.
- Use either the "Select" or "Free-Form Select" tool to select a portion of square B, making sure your selection stays within the square's boundaries.
- Move the selection to the white area (holding down CTRL while you move it copies the selection instead of removing that area from the canvas).
- Do the same with square A and place it next to square B.
- Compare the two shades!

2.
- Paste the image into MS Paint again.
- Choose the "Pick Color" tool, left-click on square B to select the colour, select the "Fill With Color" tool and left-click somewhere in the white area...which then changes completely to square B's colour.
- Repeat 1...and squares A & B disappear into the filled area, leaving just the two dark letters visible there!

3.
- Instead of moving the squares off the checker board just select a portion of square B and move it onto square A.
- Watch B's shade appear to change along the way!! (works the other way round too...moving A onto B).

4.
- Select a portion of square B, delete it (which should leave a blank, white patch), use the "Pick Color" tool on square A and fill B's white patch...with the 'different' shade!

You left out "therapy", quittyqat.

I got the same answer as Bobby. Nice logic...took me a while to spot.

-evoking

youth's

Bobby, I think your word should have started with "d", which is the last letter of the last word.

I wonder if there's one such word that retains MathsIsFun's "wonderful".