Which Whole Do the Parts Make?

Two odd-looking pieces can hide a perfectly familiar shape. The trick is not guessing the outline. It is finding the edges that fit... then letting the whole appear!

First, inspect every edge. Look for equal lengths, matching angles, and notches that complement bumps. Here, the amber piece rotates until its long straight edge meets the same-length edge on the blue piece. The edges touch exactly. Keep each piece rigid. You may turn it or slide it, but never stretch it, squash it, or place it over another piece unless the question says so. When the join is correct, the shared edge disappears inside the new outline. Now trace only the outside boundary. Ignore the join line inside. And remember: pieces separated on a flat net are not automatically opposite after folding. Their final positions depend on which edges actually meet.

Let's work through an example. Two pieces must join without gaps or overlap. Piece one is a blue rectangle four squares long and two squares high, with its right edge marked red. Piece two is an amber rectangle two squares long and one square high, with one long edge marked red. The red edges must meet. Which finished outline is correct? Option A is a ten-by-one strip. Option B is a five-by-two rectangle. Option C is an L-shape with a four-by-two base and two squares above the left end. Option D is a four-by-three block with its two top corner squares missing. Which option is correct? Turn the amber piece a quarter-turn clockwise. Its marked two-square edge becomes vertical, exactly like the blue edge. Slide the amber piece to the blue piece's right. The red edges meet completely. The amber piece fills one new column. The join line is now inside. Trace the outside: five squares across and two squares high. That is a five-by-two rectangle, so Option B is correct. The pieces stayed rigid. Nothing overlapped.

Find compatible edges, rotate or slide rigid pieces, then trace the OUTSIDE boundary. Trust the completed outline, not the starting gaps. You can connect the parts!