Nine men?Cantor, Cauchy, Descartes, Euler, Fermat, Gauss, Leibniz, Newton, and Pascal?play the nine positions on a baseball team (pitcher, catcher, first base, second base, third base, short stop, right field, center field, and left field). Determine the position of each player using the following information:
a. Descartes and Cauchy each lost $20 playing poker with the pitcher.
b. Fermat is taller than Newton and shorter than Gauss, but each of these weighs more than the first baseman.
c. The third baseman lives across the corridor from Pascal in the same apartment building.
d. Cantor and the outfielders play bridge in their spare time.
e. Gauss, Cantor, Cauchy, the right fielder, and the center fielder are bachelors; the rest are married.
f. Of Euler and Newton, one plays an outfield position.
g. The right fielder is shorter than the center fielder.
h. The third baseman is the brother of the pitcher?s wife.
i. Leibniz is taller than the first-, second-, and third-basemen, the shortstop, the pitcher and catcher, except for Pascal, Descartes, and Euler.
j. The third baseman, the shortstop, and Fermat made $300 betting on horse races.
k. The second baseman is engaged to Cantor?s sister.
l. The second baseman beat Pascal, Cauchy, Fermat, and the catcher at cards.
m. Euler lives in the same building as his own sister but dislikes the catcher.
n. Euler, Cauchy, and the shortstop lost $200 each playing slots.
o. The catcher and his wife have three daughters, and the third basemen and his wife have two sons, but Leibniz is being sued for divorce.