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# 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

winning.

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.