Problem 4 · 2009 AMC 8
Easy
Geometry & Measurement
tiling-fit
The five pieces shown below can be arranged to form four of the five figures shown in the choices. Which figure cannot be formed?
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Answer: B — B.
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Hint 1 of 2
Don't try to actually build all five figures — that's a maze. Instead hunt for the ONE piece that's hardest to place: the long 1×5 strip. It can't bend.
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Hint 2 of 2
Find a feature of the stubborn piece, then test the target shapes against it. A shape that can't host that feature is the impossible one.
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Approach: rule out by the most constrained piece
- The 1×5 strip is rigid: in any arrangement it occupies 5 squares in a perfectly straight line, horizontal or vertical.
- So the answer shape MUST contain a straight 5-in-a-row somewhere. Scan the choices for that run — figure B has no straight 5-block run in either direction, so the strip has nowhere to go.
- Why this transfers: with fitting/packing puzzles, attack the most restrictive piece first. One necessary feature it forces (here, "a straight length-5 slot must exist") often eliminates the answer instantly — far faster than constructing everything.
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