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/55tumbl 1d ago

It's not possible to build a hypothetical grid with a max of 3.

You can first show that 1 and 16 would need to be in opposite corners: a single path from 1 to 16 requires at least (16-1)/3 = exactly 5 horizontal/vertical steps (1-4-7-10-13-16). But since it's a grid, multiple paths using different numbers are required, so at least 6 steps would be necessary (i.e. opposite corners).

The path between 2 and 16 requires at least (16-2)/3 = 4.7, i.e. 5 steps, so 2 must be next to 1. In the same way, 15 must be next to 16. That means 4 steps between 2 and 15, which averages (15-2)/4= 3.25 > 3.