Problem 14 · 2022 Math Kangaroo
Medium
Spatial & Visual Reasoning
foldingsymmetry
Johanna takes a paper with the numbers 1 to 36 and folds it in half twice (see diagrams). Then she pokes a hole through all four layers at once (see the diagram on the right). Which four numbers does she pierce?
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Answer: C — 14, 17, 20, 23
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Hint 1 of 2
Each fold lays one half exactly onto the other, so the hole goes through matching squares.
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Hint 2 of 2
Track which four numbers stack on top of each other at the hole's position.
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Approach: undo the folds to find the stacked numbers
- The horizontal fold pairs each top-half square with the bottom-half square it lands on.
- The vertical fold then pairs left columns with right columns.
- The hole's spot stacks the squares 14, 17, 20 and 23.
- So she pierces 14, 17, 20, 23.
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