"T" Puzzle - Plan

Plans to make your own:

There are a number of variations of the T puzzle around. In making your own, you will have some of the key decisions to make such as the width and height of the puzzle. We chose the width to be 3a (where "a" is the length of the unit square). The next question is how to select "x" and "y" for a satisfying puzzle (see figure on the right). In this plan the central shape was made with the same width "a" as the unit square uses. This fixes the size of "y". For "x" an appropriate size was selected such that the "Teezer" shape in the figure below can be made (same as published in [4]). But you will also often find "x" to be selected as "a" which allows the building of the "Fat Arrow" (see figure below) and many other shapes [5]&[6]. Finally, a good to play with size uses a side length of about 25 to 30mm or 1 to 1¼ inch for the side "a".

From the T figure above we can see that:
z = 2a - a√2 = a(2 - √2)
y = a - z = a - 2a + a√2 = a (√2 - 1)

And, from Teezer figure on the right follows:
a + z = a + x + y
z = x + y
x = z - y
x = 2a - a√2 - a√2 + a
x = 3a - 2a√2
x = a(3-2√2) ~ a * 0.172

For the second set of pieces we can see from the "Fat Arrow" figure that only one piece changes by having a larger x:
a + z + a√2 = 2a + x
x = z + a√2 - a
x = 2a - a√2 + a√2 - a
x = a

Laser Files:

To laser-cut your own very nice pieces with rounded over corners and a hole to string up all the pieces (figure on the right), Corel Draw files are provided here:
Corel Draw V8:
Corel Draw V13:

References: