Problem 21 · 2010 Math Kangaroo
Stretch
Number Theory
casework
The teacher said, “In our school library there are roughly 2010 books.” The pupils then guessed exactly how many there are. Artur guessed 2010, Beate guessed 1998 and Carlos guessed 2015. Their guesses are off by 12, 7 and 5, but not in that order. How many books are in the library?
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Answer: A — 2003
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Hint 1 of 2
The real number differs from the three guesses by 12, 7 and 5 in some order.
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Hint 2 of 2
Try a value near 2010 and check that its distances to 2010, 1998 and 2015 are exactly 12, 7 and 5.
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Approach: find the value whose distances to the guesses are 12, 7, 5
- Test 2003: |2003 − 2010| = 7, |2003 − 1998| = 5, |2003 − 2015| = 12.
- Those are exactly 7, 5 and 12 — the required errors.
- So the library has 2003 books.
Mark:
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