Problem 8 · 2016 Math Kangaroo
Easy
Spatial & Visual Reasoning
spatial-reasoning
Four girls are sleeping in a room with their heads on the grey pillows. Bea and Pia are sleeping on the left-hand side of the room with their faces towards each other; Mary and Karen are on the right-hand side with their backs towards each other. How many girls sleep with their right ear on the pillow?
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Answer: C — 2
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Hint 1 of 3
For each girl, picture which cheek is pressed into the pillow and so which ear is underneath.
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Hint 2 of 3
When two girls lie side by side facing opposite ways, they rest on opposite ears.
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Hint 3 of 3
So in a face-to-face pair (and in a back-to-back pair) exactly one girl is on her right ear.
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Approach: pair up the girls and use mirror directions
- Bea and Pia lie facing each other: since they point opposite ways, one rests on her left ear and the other on her right ear, so that pair gives 1 right-ear girl.
- Mary and Karen lie back to back, again pointing opposite ways, so that pair also gives exactly 1 right-ear girl.
- Adding the two pairs, \(1 + 1 = 2\) girls sleep on their right ear, choice (C).
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