Problem 3 · 2010 Math Kangaroo
Easy
Counting & Probability
careful-countingcasework
Kangi goes directly from the zoo (Zoo) to school (Schule) and counts the flowers along the way. Which of the following numbers can he not obtain this way?
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Answer: C — 11
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Hint 1 of 2
At each fork in the path Kangi can take either the top branch or the bottom branch.
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Hint 2 of 2
Write down every total he can make by mixing the branch choices, then see which listed number never appears.
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Approach: list the reachable totals
- Each of the two loops offers two flower counts, and the middle stretch is always counted.
- Combine a choice from the first loop with a choice from the second (plus the middle) to get the possible totals.
- Listing them shows 9, 10, 12 and 13 are reachable but 11 is not.
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