Maths Olympiad Prep

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Number theory Difficulty 5.7 AIME, harder Find the answer

3. As an odometer check, a special counter measures the miles a car travels modulo 7. Explain how this counter can be used to determine whether the car has been driven 49335,149335 , or 249335 miles when the odometer reads 49335 and works modulo 100000 .

A number or a short expression. Spacing and $ signs are ignored.

Solutions — 2

Solution 1

None

Solution 2

None

Translate the text above into English, please retain the original text's line breaks and format, and output the translation result directly.

Note: The provided instruction is a meta-instruction and not part of the text to be translated. Since the text to be translated is "None", the translation is also "None". Here is the formatted output as requested:

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.