Problem 1 · 2024 Math Kangaroo
Medium
Spatial & Visual Reasoning
sequence-of-figuressymmetry
Which of the squares shown is split into two parts that do not have the same shape?
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Answer: E
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Hint 1 of 2
For each square, check whether the two pieces could be slid or rotated to lie exactly on top of each other.
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Hint 2 of 2
Four of the cuts split the square into two congruent (matching) halves; look for the odd one out.
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Approach: test each cut for two congruent pieces
- A cut gives two pieces of the same shape exactly when one piece can be slid, turned, or flipped onto the other.
- In four of the squares the cut has a centre of symmetry, so the two halves match.
- In one square the cut is not centrally symmetric, so its two pieces are different shapes.
- That odd one out is option E.
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