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2011 Math Kangaroo

Problem 10

Problem 10 · 2011 Math Kangaroo Medium
Spatial & Visual Reasoning symmetryreflection

The picture shows an L-shaped object made up of four squares. We would like to add another equally big square so that the new object has a line of symmetry. How many ways are there to achieve this?

Figure for Math Kangaroo 2011 Problem 10
Show answer
Answer: C — 3
Show hints
Hint 1 of 2
A line of symmetry means one half is the mirror image of the other.
Still stuck? Show hint 2 →
Hint 2 of 2
Try adding the extra square in each open position and test for a mirror line.
Show solution
Approach: add a square so the figure gains a line of symmetry
  1. The L of four squares can be completed in different ways by adding one equal square.
  2. Check each spot where a new square can sit and see if the result has a mirror line.
  3. Exactly 3 placements give a figure with a line of symmetry.
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