3 Consider an island with 3 types of pokemon: blue pokemons, red pokemons and green pokemons. a) At the beginning, there are 13 blue pokemons, 15 red pokemons, 17 green pokemons. b) Whenever two pokemons meet, if the two pokemon are of different color, they will both transformed to the other color. For example, if a blue pokemon and a red pokemon meets, they both transform to a green pokemon resulting in 1 less blue pokemon, 1 less red pokemon and 2 more green pokemons. c) Those that already transformed can meet and transform again. Show that it is impossible for the island to be left with exactly one type of poke- mon(ex: all blue) with any series of meeting and transformation. Hint: Modulo 3
3 Consider an island with 3 types of pokemon: blue pokemons, red pokemons and green pokemons. a) At the beginning, there are 13 blue pokemons, 15 red pokemons, 17 green pokemons. b) Whenever two pokemons meet, if the two pokemon are of different color, they will both transformed to the other color. For example, if a blue pokemon and a red pokemon meets, they both transform to a green pokemon resulting in 1 less blue pokemon, 1 less red pokemon and 2 more green pokemons. c) Those that already transformed can meet and transform again. Show that it is impossible for the island to be left with exactly one type of poke- mon(ex: all blue) with any series of meeting and transformation. Hint: Modulo 3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem 6 Consider an island with 3 types of pokemon: blue pokemons, red pokemons and
green pokemons.
a) At the beginning, there are 13 blue pokemons, 15 red pokemons, 17 green
pokemons.
b) Whenever two pokemons meet, if the two pokemon are of different color, they
will both transformed to the other color. For example, if a blue pokemon and
a red pokemon meets, they both transform to a green pokemon resulting in 1
less blue pokemon, 1 less red pokemon and 2 more green pokemons.
c) Those that already transformed can meet and transform again.
Show that it is impossible for the island to be left with exactly one type of poke-
mon(ex: all blue) with any series of meeting and transformation.
Hint: Modulo 3
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