Problem 29 · 2020 Math Kangaroo
Stretch
Spatial & Visual Reasoning
foldingpaper-cutting
Vania has a sheet of paper divided into nine equal squares. She folds it as shown — first the horizontal folds, then the vertical folds — until the coloured square is on top of the stack. She wants to write the numbers 1 to 9, one per square, so that after folding they read in order from top to bottom, starting with 1 on top. On the unfolded sheet shown, which numbers should she write in places a, b and c?
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Answer: C — a = 7, b = 5, c = 3
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Hint 1 of 2
Track where each unfolded square ends up in the stack after the horizontal then vertical folds.
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Hint 2 of 2
Reverse the folds to read which numbers land at positions a, b and c on the flat sheet.
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Approach: reverse the fold order to map stack layers to grid cells
- Folding horizontally then vertically stacks the nine squares; the coloured square is on top (number 1), and lower layers get 2,3,...
- Unfolding to the flat sheet, each layer returns to its cell, spreading the numbers in a fixed pattern.
- Reading positions a, b, c gives a = 7, b = 5, c = 3 - option C.
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