Problem 7 · 2016 Math Kangaroo
Medium
Algebra & Patterns
custom-operation
Lukas invents his own notation for negative numbers. When counting backwards he writes: … 3, 2, 1, 0, 00, 000, 0000, … What is the result of the calculation 000 + 0000 in his notation?
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Answer: C — 000000
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Hint 1 of 2
Match each string of zeros to the negative number it stands for.
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Hint 2 of 2
Counting backward: 0, 00, 000, 0000 mean 0, −1, −2, −3.
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Approach: decode the notation
- A run of k zeros stands for the value −(k−1): 000 = −2, 0000 = −3.
- Their sum is −2 + (−3) = −5.
- −5 is written with six zeros: 000000.
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