Problem 18 · 2022 Math Kangaroo
Hard
Logic & Word Problems
casework
The grandchildren ask their grandma how old she is. The grandma invites them to guess the age. The first child says 75, the second says 78 and the third says 81. It turns out that one child is wrong by 1 year, one by 2 years and one by 4 years. How many possibilities are there for the age of the grandma?
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Answer: C — 2
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Hint 1 of 2
The three errors are 1, 2 and 4 in some order, each above or below.
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Hint 2 of 2
Test which actual ages let the guesses 75, 78, 81 miss by exactly {1,2,4}.
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Approach: match the error set {1,2,4} to the three guesses
- The true age must differ from 75, 78 and 81 by exactly 1, 2 and 4 in some assignment, each error either above or below.
- Searching the candidate ages, only a couple of values make all three differences fit the set {1,2,4}.
- There are 2 possible ages.
Mark:
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