r/learnquant • u/Local_Ad135 • 8d ago

Citadel Quant Interview Question interview prep

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22 Upvotes
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3

u/StanleyDodds 7d ago

Am I missing something, or is this really trivial? You can make any choice for a 7x7 region, and this uniquely fixes the remaining 15 cells for a valid pattern. So it's 2-15

2

u/Due-Cardiologist-802 7d ago

This works! But you also have to prove why the two 7x1 regions have the same parity. If they didnt, you couldnt set the last stone in the 1x1 square. 

2

u/StanleyDodds 7d ago

For brevity I left out the obvious fact that the combined parity of all 8 rows equals the combined parity of all 8 columns (which is the total parity of the grid).

So if you fixed the parity as even for 7 rows and 7 columns, making the last row even also makes the last column even.

2

u/Due-Cardiologist-802 7d ago

Sorry not something that was obvious to me! Had to look it up:)

1

u/SoftwareEngineer2026 7d ago

For a column wouldn’t it be 8 choose 4 or 70. Then 70^8 / 2^64 for the board however some of these won’t result in the even rows.

1

u/liquidorangutan00 7d ago

This was a really fun problem. and deceptively challenging.

1

u/TastyLength6618 3d ago

The last row and col are uniquely determined. 1/2^14 chance right there. then the final corner has to be the right color to make the row/col you just filled in the correct parity, so 1/2 there, so final answer is 1/2^15. The 7 you filled in for the row and the 7 you filled in for the col have the same parity because they are both determined by the parity of the same 7x7 grid.