Problem 20 · 2013 Math Kangaroo
Stretch
Logic & Word Problems
casework
Two buttons showing smiling faces and two showing sad faces are in a row, as shown. Pressing a button changes its face and also the faces of its neighbours. What is the least number of button presses needed so that only smiling faces are showing?
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Answer: B — 3
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Hint 1 of 3
Pressing a button flips that face and the faces right next to it (sad becomes happy and happy becomes sad).
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Hint 2 of 3
Try pressing one button and watch which faces change, then plan the next press from the new picture.
Still stuck? Show hint 3 →
Hint 3 of 3
Check whether 1 or 2 presses can ever work before settling on a small number.
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Approach: try short sequences and watch the faces flip
- Each press flips the button you push and its direct neighbours.
- One or two presses always leave at least one sad face showing, so they are not enough.
- Pressing the right three buttons in turn flips all the sad faces happy, so the fewest presses is 3, choice B.
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