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easy
infer the vector field
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A hidden vector field F(x,y) = (ax+by,\ cx+dy) is waiting to be found. You have 10 probes — pick a point (x,y), see F(x,y). Spend them wisely, then guess a, b, c, d.
of probes left.
Guess the rule: F(x,y) = (ax + by,\ cx + dy)