Problem 22 · 2013 Math Kangaroo
Stretch
Logic & Word Problems
careful-countingcasework
Baris has a few dominoes, shown in the picture. He wants to lay them in a line following the rules of dominoes: two dominoes can be placed next to each other only if the touching squares have the same number of dots. What is the greatest number of these dominoes that he can lay in a single line?
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Answer: C — 5
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Hint 1 of 3
Two dominoes may touch only when the halves that meet show the same number of dots.
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Hint 2 of 3
Treat it like a chain: the right end of one domino must equal the left end of the next.
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Hint 3 of 3
Try building the longest single chain you can, joining matching ends, and you may flip a domino around.
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Approach: build the longest chain where touching halves match
- Pick a starting domino, then add a domino whose end matches its end.
- Keep linking matching ends, flipping a domino around when that helps the numbers meet.
- The longest single line you can make uses 5 dominoes, which is answer C.
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