a word problem algebra

Question

Fred and George are to share a chocolate bar made up of an 8 by 6 square rectangular array. The top-left top-right squares each contain a visible nut.

They take it in turns, starting with Fred, to snap the chocolate into 2 pieces along a line between 2 rows or 2 columns, & then eat 1 of the 2 pieces.

Neither Fred nor George wants a nut. Which person can guarantee that they won’t get the nut? Is this true for any size of bar?

Answer 1

I'm pretty sure it only makes sense to keep the game going until one eats a nut. Here's the strategy for Fred to not eat the nut:

1. Fred breaks the chocolate bar along the top row (that is, so the row containing the two nuts is the only one remaining). He eats the non-nutty portion.
2. George must now eat a nut.
3. Game over. :)

I'll let the reader extend this to other size bars.

Answer 2

If the question is if it is possible to go on and have the opponent eat both nuts, this can't be done. Each division of the 2-nuts bar leaves either a 2-nut bar and a nutless bar, or two 1-nut bars. The exact way of dividing doesn't matter, as long as it divides the bar into two connected pieces.