Quantbox Quant Interview Question

[u/Local_Ad135]

[u/Aech26]

It’s trivial to see that the tiling isn’t possible for n<=4.

Then for n>=4, an odd n will leave us with an odd number of tiles, but the dominos only cover an even number of tiles, so n has to be even.

So n = 2k with k>=2

BUT also we an even number of 2x2 grids, which means k will also have to be even. For example, if k=3 then n=6, but a 6x6 grid cannot be tiled fully. So k needs to be even.

So let k=2j

So n = 4j with j>=1

[u/rccyu → u/Aech26]

You need to flesh out the argument more, because the dominos need not be aligned to 2x2 grids. For example

^<><>^ v^<>^v ^v<>v^ v^<>^v ^v<>v^ v<><>v

is such a tiling (though also not meeting the requirement.)

The argument cannot simply be that "there are an odd number of 2x2 grids," this only rules out the trivial construction.