The Vanishing Ninja puzzle stumps a lot of people. With a simple shift of two out of three parts of the image, it appears that fifteen ninjas suddenly become fourteen ninjas. The question posed by the puzzle: what happens to the fifteenth ninja?

The puzzle works in part because they are ninjas. That is, we expect the figures in the image to assume strange positions and stances, and we're not surprised if the shapes look a little odd. Ninjas are, after all, trained contortionists.

But there's nothing mysterious about this puzzle, and the claim that this is some sort of "mathematical Puzzle that has defied Western science for centuries" is just hyperbole.

Let us reverse the process. We'll pretend we started with the 14 ninja view, and changed the image by switching the top two sections to create fifteen ninjas. Why? Because that's the way the puzzle was actually created.

All the ninjas look fairly normal and complete in the 14 ninja view.

Now closely examine the ninjas in the 15 ninja image. Something rather strange happened during the shift...

Notice, for example, this fellow (number six from the left in both images, above) loses the top of his head in the 15 ninja view:

And this guy (number seven, moving to thirteen in the 15 ninja image) loses his foot when there are fifteen in the image:

Another fellow seems to have lost some curves-- look at the square shoulders on ninja number eleven:

Here is what is really happening. The shift of the tops of all the ninjas makes many of the ninjas shorter, and the parts of fourteen ninjas are cleverly gathered together to create the fifteenth. This process isn't obvious in the ninja puzzle because the ninjas have been carefully positioned to make the change difficult to see.

Suppose we simplify. Here are the same fourteen ninjas, arranged in a nice simple pattern.

Now, we'll shift the top of each ninja to a different position-- one place to the left:

Surprise! We now have fifteen ninjas! But many of them are a little shorter, because each is missing a part that was contributed to make number 15!

In essence, moving the tops of 14 ninjas creates fifteen ninjas, and because they're carefully positioned and each one matches up with another, the viewer may not notice that each has had a little piece chopped out and contributed to the new guy. And we can easily see how the fellow on the left loses his foot, and the "new" guy on the right no longer has all of his head.

Hat tip to The Vanishing Leprechaun.

This page created by richard myers.