12. The original (1999) Smash Brothers contained only 12 characters. If you play with 3 friends (4 players total, the max at the time), can everybody play as their own character? Which are the pigeons and which are the pigeonholes? In a tournament of 30 players and the same 1999 video game, can everybody play as their own character? Why or why not? Which are the pigeons and which are the pigeonholes? In the same 30-player tournament, is it guaranteed that there are any characters played by more than two players? Why or why not? 13. How many possible graphs can be created on 5 distinct vertices? n a Complete Graph with 8 vertices, how many possible Hamiltonian circuits are there?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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12. The original (1999) Smash Brothers contained only 12 characters. If you play with 3 friends (4
players total, the max at the time), can everybody play as their own character? Which are the
pigeons and which are the pigeonholes?
In a tournament of 30 players and the same 1999 video game, can everybody play as their own
character? Why or why not? Which are the pigeons and which are the pigeonholes?
In the same 30-player tournament, is it guaranteed that there are any characters played by more
than two players? Why or why not?
13. How many possible graphs can be created on 5 distinct vertices?
n a Complete Graph with 8 vertices, how many possible Hamiltonian circuits are there?
Transcribed Image Text:12. The original (1999) Smash Brothers contained only 12 characters. If you play with 3 friends (4 players total, the max at the time), can everybody play as their own character? Which are the pigeons and which are the pigeonholes? In a tournament of 30 players and the same 1999 video game, can everybody play as their own character? Why or why not? Which are the pigeons and which are the pigeonholes? In the same 30-player tournament, is it guaranteed that there are any characters played by more than two players? Why or why not? 13. How many possible graphs can be created on 5 distinct vertices? n a Complete Graph with 8 vertices, how many possible Hamiltonian circuits are there?
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