A group of k Vikings independently set out to make a new home. Each Viking has a
ID: 3902140 • Letter: A
Question
A group of k Vikings independently set out to make a new home. Each Viking has a copy of the same map, showing n islands. Each Viking decides to set sail for some random island. If two or more Vikings land on the same island, they have a battle. (No matter how many Vikings land on that island, it counts as one battle.)
(a) How many islands do we expect will be visited by Vikings?
(b) How many battles do we expect will occur?
(c) Do your solutions conrm the intuitive answer for the special case where there is only one island on the map? Or what if there's only one Viking? What answers do you get for 400 Vikings and 100 islands? (use a calculator for this last part)
Explanation / Answer
case 1 only one island
in this case two possiblities are there
A. one vikings, in this case no fight will be there
B. more then one vikings, there will be exact one fight
case 2. only one vikings
in all cases there will be no fight
case 3 more than one island
A. one vikings -> no fight
B. more than vikikings
max fight=vikings/2
min fight =0, if island>vikings else 1 fight
case 4 more than one islan more than one wikings
min fight =0 if vikings<island else 1 fight
max fihgt=vikings/2
(a) at most visited island=no. of vikings
al least visited=1
(b) atmost vikings/2
atlest 0
(c) yeah my solution covers these sceneraios
for 400 wikings and 100 island
min fight=1(99 on different island and others are on one)
max fight=100(4 on each,other case are also possible for same 100 fights)
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