Problem 12 · 2009 Math Kangaroo
Medium
Counting & Probability
careful-countingcasework
What is the minimum number of dots that must be taken away from the picture so that no three of the remaining dots lie on a straight line?
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Answer: C — 3
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Hint 1 of 2
List every line of three dots: 3 rows, 3 columns, 2 diagonals.
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Hint 2 of 2
Find the most dots you can keep with no three in a line; the rest are removed.
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Approach: maximise the dots kept, then subtract
- The 3x3 grid has 8 lines of three dots (3 rows, 3 columns, 2 diagonals).
- You can keep at most 6 dots with no three collinear.
- So you must remove 9 - 6 = 3 dots.
Mark:
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