home email

Nicolas Fuss

b. 30 January 1755, Basel
d. 4 January 1826, St. Petersburg

Fuss was a Swiss mathematician. He was assistant to Euler from 1773 to 1783 at St. Petersburg. Fuss contributed two papers to the Acta Academiae Scientiarum Imperialis Petropolitanae in 1779 and 1780 concerning a problem posed by Jakob Bernoulli. This problem being:

Two players A and B, agree to throw a die, and that each will then have the
same number of throws as points thrown, the winner being the one who throws
the greatest aggregated number of points. Should they both obtain equal
numbers of points, the stake will be divided equally. However B tires of this
game and instead of an uncertain number of points, wishes to take a
particular number, and indeed wishes to acquire 12 at an appropriate cost. A
agrees. It is required to determine for each the strength of their hope of

Fuss learned of this problem through a paper by Mallet. He did not consult the Ars Conjectandi. For if he or Mallet had, they would have both discovered that Bernoulli had solved it. 

There are two interpretations of this problem: The first throw contributes to the total number of casts. So, for example, if the player should throw a 1 on his first cast, he will make no more. A second interpretation lets the first cast determine the number of subsequent casts. Thus if the player should throw a 1 on the first cast, that player is permitted one more cast.

The first paper considers the former interpretation, the second paper the latter.