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Photo: DER SPIEGEL
Fairness is important, even among pirates, who otherwise don't care about rules and laws.
The crew of the two-master “Black Cog” divides the booty fairly among themselves after each raid.
Where fair means that every simple pirate gets an equal share of the booty.
The right hand of the pirate boss, on the other hand, receives twice as much as a normal pirate - the pirate boss himself even five times as much.
During the last capture, the pirates stole 120 gold coins.
When they try to divide them up among themselves according to their rules, they find that this is not possible unless they want to saw up coins.
But then a pirate has an idea: He puts one of the 120 coins to one side - and suddenly the division succeeds, so that every pirate, their boss and their right hand are satisfied.
With the leftover gold coin they buy a couple of bottles of rum together for the next festival.
How many pirates (including the boss and his right hand) make up the crew of the two-master "Black Cog"?
There are either
twelve pirates
on board
(10 normal
pirates
, a boss and his right hand) or
114 pirates
(112 normal pirates plus the two superior ones).
The trick is to look at the prime factorization of 119.
Because - as we will see in a moment - 119 must be the product of two natural numbers.
One of the numbers shows how many coins each simple pirate gets.
The other number represents the total number of pirates, with the bosses counting multiple times.
The boss gets as many coins as five pirates - he counts as many as five normal pirates.
His right hand gets twice as many, so it counts as two pirates.
If p is the number of normal pirates, then I have to
divide
the 119 coins by
p + 2 + 5 = p + 7
.
The result should be a natural number because it is the number of coins a normal pirate gets.
119 is the product of the two prime numbers 7 and 17. In addition, 119 can also be represented as the product 119 times 1.
A divisor must be equal to p + 7 and p must be greater than zero.
Then only two solutions are possible:
p + 7 = 17
: Ten pirates get seven coins each, the boss 35 and his right hand 14.
p + 7 = 119
: 112 pirates get one coin each, the boss five coins and his right hand two.
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