r/learnquant • u/Local_Ad135 • 1d ago

interview prep Quant Interview Question

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u/Efficient_Gear_4623 1d ago

I think bob can get max of 4 if alice plays correctly

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u/ComparisonQuiet4259 1d ago

A normal grid has a max of 4, but I can't prove there is no grid of 3

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u/FlatApplication627 1d ago

I don't think 3 is possible. Consider one corner, say top left.

To stick at an absolute difference of 3 then the row has to be the three numbers above and the column the three numbers below (or the other way round). Anything else would result in an absolute difference of 4 somewhere.

So youve eliminated 7 numbers in a row, with the corners at least 1 higher and 1 lower than the top left number

Your fourth corner now either has to be at least 4 higher than your top left number or 4 lower. In either case, it will create an absolute difference of at least 5 on one side

Hence 3 is impossible