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M Is For Miracle

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Tuition given in the topic of A-Maths Tuition Questions from the desk of Miss Loi at 8:45 pm (Singapore time)

Continuing from last week’s episode

Night has fallen when the Maths Tutor reached her car.

Just as she was about to start the engine and drive away, the street lamps began to flicker wildly.

A great sense of foreboding filled the air, as a strange vision suddenly flashed before her eyes …

In an imaginary grid, a man walks along a straight street defined by the equation: mx + (m − 1)y = 10

At the same time, a black car zooms furiously along a straight road defined by the equation: (m − 2)x + 3my = 20

The car will hit the man if their paths meet …

A scream snapped her out of her trance before her vision was complete, and she blinked her eyes in time to see a frightened woman pushed a man away under the glare of the bright street lamps.

The man (who happens to be our young henchman if you’ve been following the previous episodes) then turned around and walked away with his head bowed, looking dejected.

In a shocking realization of her déjà vu experience, she recognized the man as the walking man in her vision just moments ago.

And in that very moment, the silence of the night was broken by the unmistakable roar of a speeding car’s engine, while the Maths Tutor could only cover her eyes and pray for a miracle …

find the ‘miracle’ value of m where the paths of the car and the man would never meet.
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