Triangles and Ink is a puzzle in Professor Layton and the Curious Village.


Here are two shapes, one large and one small. Each is made up of little triangles.

Dipping your fountain pen into the ink one time gives you just enough ink to draw four little triangles, as depicted by the shape on the left.

So, with that in mind, how many times do you have to dip your pen in the ink in order to draw the shape on the right that's made up of 36 triangles?


Click a Tab to reveal the Hint.

To draw the smaller, four-triangle shape, you actually only need to draw three triangles. To see for yourself, trace the shape on the Touch Screen.

Notice how the middle triangle (Triangle 3) in this shape is actually made up of the sides of the other triangles?

The puzzle describes the shape on the left as made of four triangles. However, you could also say that this same shape is made of three upward-pointing triangles.

Try applying this way of thinking to the larger shape. Just how many triangles does it take to make this shape?

If you only count the number of upward- pointing triangles in the large triangle, you'll get a total of 21.

You can draw three upward-pointing triangles with one dip into the ink, so...



Too bad!

Take another look at the two shapes and the puzzle, paying special attention to the phrases "enough ink to draw four little triangles" and "the shape on the right that's made up of 36 triangles."


That's correct!

Your first impulse might have been to divide the 36 triangles by four, but a closer look shows that each four-triangle cluster is actually formed from three triangles.

When you apply this way of thinking to the larger shape, you end up with the answer pictured above.


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