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Title: How would you answer this job interview question?
Source: an interview
URL Source: [None]
Published: Sep 25, 2008
Author: some propellerhead
Post Date: 2008-09-25 01:05:33 by Tauzero
Keywords: None
Views: 247
Comments: 20

You and an opponent are going to play a turn-based game with quarters on a circular table.

On each turn, you place one quarter on the table. Quarters may not overlap.

You may assume the table is large enough to hold many quarters.

Do you go first or second? Why?

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Begin Trace Mode for Comment # 18.

#16. To: Tauzero (#0)

Whoever goes first will always win.

bluegrass  posted on  2008-09-25   23:32:39 ET  Reply   Untrace   Trace   Private Reply  

Whoever goes first will always win.

Not quite.

I'll spill.

The correct answer is to go first -- and to place your first quarter smack in the middle.

The key (which I got) is parity -- will there, at the end of the game, be an odd or even number of quarters on the table?

If the shape and/or size of the table can vary, then parity can depend on the sequence of moves. But, with a circular table -- or any other table with the symmetry element known as an inversion point -- you can force odd parity by placing your first quarter on the inversion point. Then, by symmetry, wherever your opponent moves, you are guaranteed to also have an available move in the mirror spot across the inversion point -- and this is where you should place quarters on subsequent turns to guarantee the win.

Tauzero  posted on  2008-09-25   23:41:34 ET  Reply   Untrace   Trace   Private Reply  

The correct answer is to go first -- and to place your first quarter smack in the middle.

That's what I meant. : )

Tengen is a Go opening that employs the same idea, though under different rules, with great success.

bluegrass  posted on  2008-09-25   23:56:36 ET  Reply   Untrace   Trace   Private Reply  

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