Problem 18 · 1990 AJHSME
Stretch
Geometry & Measurement
truncationedge-counting
Show answer
Answer: C — 36.
Show hints
Hint 1 of 2
Don't try to draw the whole chopped shape and count edges off the picture. Instead account for edges in two separate groups: the ones that were already there, and the brand-new ones each cut creates.
Still stuck? Show hint 2 →
Hint 2 of 2
Track what a single slice does, then multiply by how many slices. Each corner cut slices off a little corner triangle — how many fresh edges does that one triangle add, and how many original edges get destroyed?
Show solution
Approach: count edges as 'survivors' + 'new ones per cut'
- A box (rectangular prism) starts with 12 edges and 8 corners. Cutting a corner just *shortens* the three edges meeting there — it doesn't remove any, so all 12 original edges survive.
- Each cut exposes a new little triangular face, and a triangle has 3 sides — so every corner adds 3 brand-new edges. Eight corners (the cuts don't touch each other) add 8 × 3 = 24 new edges.
- Total edges = 12 survivors + 24 new = 36.
- *Why this transfers:* for 'slice the corners' (truncation) problems, count by category — old edges that survive plus (new edges per cut) × (number of cuts). The same bookkeeping handles faces and vertices too.
Mark:
· log in to save