[rc5] Chess, RC5-64 & wheat

Tim Charron tcharron at interlog.com
Sat Nov 1 16:55:59 EST 1997


All the recent talk about chessboards and RC5-64 reminded me of an 
old story.

A man asks a King for a favor.  He asks the King to give him one grain
of wheat for the first square of a chessboard, 2 grains of wheat for
the second square, 4 grains for the third, and so on.  Each of the 64
squares represents twice the number of grains as the prior one.  The
King sees what he believes will be a cheap opportunity to be 
generous, and he agrees. Only later does he realize that he has 
promised to provide more grain than he will ever own, and he has the 
man executed.

Ironically, the number of grains of wheat in this problem is the same
as the number of 'wrong' keys in the RC5-64 problem (2^64-1).  A
discussion of this problem can be found at:
http://forum.swarthmore.edu/dr.math/problems/drumm.10.7.96.html

Using the dimensions of a grain of wheat there (2mm x 2mm x 5mm), and 
assuming Australia is 984,000 square km in area, my calculations show 
that:

If keys were grains of wheat, the keyspace would be large enough to
cover Australia 15 inches deep.

-- Tim
Tim Charron
tcharron at interlog.com
tcharron at ctfinance.com
http://www.interlog.com/~tcharron/

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