The Infinite Chocolate Bar
Previous puzzle in this series
A chocolate bar is cut into five pieces: a small square, a rectangle, two diagonal slope pieces, and a large base piece. We rearrange the pieces, reforming the original chocolate bar with an addition square piece. Can you explain what’s really happening here?
Hint
You can step through the animation below. See if you can spot the trick!
Solution
Answer: What the animation cleverly hides is a subtle increase in the height of both slanted pieces.
The trick lies in the gradual expansion of the diagonal pieces during the rearrangement:
- Narrow slope piece: Originally 2.3 units tall at its left edge, it quietly expands to 2.5 units during the animation
- Wide slope piece: Originally 2.5 units tall at its left edge, it quietly expands to 2.7 units during the animation
Each of these two slanted pieces increases by exactly 0.2 units in height. Since the chocolate bar is 5 units wide, this expansion accounts for precisely 0.2 × 5 = 1 square unit—the exact area of the “vanished” square.
Watch the animation below without the trick—the pieces maintain their original dimensions, and a grid overlay reveals what’s really happening:
You can see that without the subtle expansion, the chocolate bar ends up with an actual gap where the removed square used to be.
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