There are some tutorials on the web for a puzzle ball or clutch ball but very few explain the 'puzzle' part of the ball and many actually sew all the pieces together discarding the puzzle component altogether.
This is how I learned to make an Amish puzzle ball from the women in the Mennonite community near my hometown in Missouri.
The puzzle ball is intended as an educational toy. It can be grasped by babies and taken apart and reassembled by older children. It fosters small motor skills which stimulate brain development and abstract thinking abilities.
A puzzle ball can be made with fabric scraps of all types, preferably woven materials. You can use satins, velvets, calicos, denim, wool suiting, corduroy, whatever you have on hand. You can use felted wool, old blankets, sweaters. Stuff with wool, cotton, or other natural stuffing if you can. Not only do I detest the idea of a baby chewing on plastic fibers such as fiberfill, that stuffing tends to be too insubstantial for a puzzle ball. A good puzzle ball is solidly made.
Use the tutorial here or scroll down for the link to a downloadable PDF.
Find a circular bowl or plate that is the desired size of your finished ball. Trace 6 of these circles on the wrong side of the fabric. Cut out the circles. Cut the circles in half and then in half again to make 4 wedges from each circle. You have 24 wedges. I'm using a 5" embroidery hoop here.
Cut 12 of these ellipses.
With right sides together, match the round edge of the ellipse with one round edge of a wedge. Sew together using a 3/8 inch seam allowance. If you are making a smaller ball or not very good at sewing curves on a sewing machine, hand sewing is your best bet. A larger ball can be machine sewn easily.
Repeat on the other side of the ellipse, sewing the other rounded edge to a second wedge. Sew one side of the wedge together and halfway down the other side. Turn this piece right side out.
Now you can see the wedge shapes you'll be sewing, sew 11 more. Turn all right side out. Stuff solidly and whipstitch or ladder stitch your wedges closed.
Use button thread, quilting thread, or embroidery floss to join the top corners of your wedges together. You want to sew three circles together made of 4 wedges. Sew tightly enough to keep pieces touching but loosely enough that the wedges are not smashed together.
Now here's what makes the puzzle a puzzle! Leave one of the wedge circles as is with only the outer tops joined. Take the second circle and imagining the inner points numbered 1 through 4, sew points 1 and 2 together and sew points 3 and 4 together. That circle now looks like a mouth opening. Take the third circle and sew all the inner points together closing the circle.
To put the puzzle ball together, work the 'mouth' circle over the fully closed circle, like a rubber band. Point all the inner points to the inside center of the ball. Next work the open circle of wedges over the combined circles. Point all the inner points to the inside center of the ball.