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MathNet 2006 — Part 05 Question 54

Math Olympiad Vault · MathNet 2006 — Part 05

Question 54

Suppose we have an octagon with all angles of $135^{\circ}$, and consecutive sides of alternating length $1$ and $\sqrt{2}$. We draw all its sides and diagonals. Into how many regions do the segments divide the octagon? (No proof is necessary.)