Copyright ©2002 by Paul Niquette. All rights reserved. 

uperbowl
Sunday
is the perfect day to drive your car on the freeway or
ride your
bike in the city, to push a stroller in the park or take
a jog on the beach,
to wait on line for the chairlift or practice aerobatics
in the sky, to
peruse an exhibit in the museum or shop for bargains at
the swap meet.
Unless...
...you happen to share a partisan interest in the athletic contest, which will be viewed by a worldwide audience that would fill a thousand stadiums  or unless you otherwise happen to have a stake in the outcome. For the next Superbowl, you are offered
an opportunity
to join a football pool.
The winner will be
determined by the least significant digits of
the final score and
will receive $100. You are invited to purchase
as many squares in
the following matrix as you please for $1 each.
By the way, the team in is
favored to win.

The specific outcome of the athletic contest is not in play. Accordingly, sophisticated knowledge of the teams will afford no advantage in picking squares. Knowledge about the game and its scoring can make a difference, though.
0, 3, 6, 7, 9, 10, 12, 13, 14, ......from which you will conclude that a team scoring 20 points or below would never produce a cypher 1 for a least significant digit, and a team scoring less that 18 points would never pay off for purchasers of squares in the corresponding 8column or 8row. With final scores less than 31 points, the cypher 1 would be possible only once (21), the cyphers 4, 5, and 8 twice, cyphers 3, 6, 7, and 9 thrice, and the cypher 0 is four times more likely than 1. Perhaps with that in mind, the designers of some football pools are known to keep the rows and columns blank until all 100 squares have been sold. The numerical values are then applied to the full matrix, using some randomizing method (numbered slips drawn from a hat, say). At the time of your purchase, you would have one chance in a hundred of winning for each square you purchase. Later, as you sit down to watch the game, you may or may not be pleased with what your selections turned out to be, but as a sophisticated solver, you will understand that they resulted purely from the "luck of the draw." The payoff matrix in The Next Superbowl puzzle above does have its rows and columns already labeled numerically. Hmm, let's get to work. {Return} 