Wei-Hwa Huang onigame@gmail.com [spielfrieks]

2017-07-25 09:02:40 UTC

[Bcc:ed to several board game mailing lists I'm on]

This year's International Mathematical Olympiad had one of their

hardest problems ever, but it was somewhat game-themed, so I figured

some folks here would be interested in thinking about it. I've

rephrased the question to be less "mathy":

You're playing a game of "catch the rabbit" on an infinite-sized

board. Each of you are on some location on the board, and you take

turns, with the rabbit going first. The goal of the rabbit is to get

far away from you; your goal is to stay close to the rabbit. Here are

the rules:

* You and the rabbit start on the same spot.

* On the rabbit's turn, it moves exactly 1 inch away, in any direction

(that is, it's somewhere on the edge of a 1-inch radius circle from

where it was).

* You don't see where the rabbit goes; it's invisible. However, you

have a rabbit tracker -- after the rabbit takes a turn, the rabbit

tracker gives you a location and says that "the rabbit is within 1

inch of this location". While the rabbit tracker can't lie, it is in

cahoots with the rabbit and can deliberately choose a location to

mislead you.

* On your turn, you must move exactly 1 inch away, in any direction.

The rabbit (and the rabbit-tracker) know exactly where you are.

* The game lasts 1,000,000,000 rounds (each of you get 1 billion turns).

Either come up with a strategy such that at the end of the game,

you're guaranteed to be within 100 inches of the rabbit -- or come up

with a strategy for the rabbit such that the end of the game, you're

guaranteed to be more than 100 inches away from the hunter.

This year's International Mathematical Olympiad had one of their

hardest problems ever, but it was somewhat game-themed, so I figured

some folks here would be interested in thinking about it. I've

rephrased the question to be less "mathy":

You're playing a game of "catch the rabbit" on an infinite-sized

board. Each of you are on some location on the board, and you take

turns, with the rabbit going first. The goal of the rabbit is to get

far away from you; your goal is to stay close to the rabbit. Here are

the rules:

* You and the rabbit start on the same spot.

* On the rabbit's turn, it moves exactly 1 inch away, in any direction

(that is, it's somewhere on the edge of a 1-inch radius circle from

where it was).

* You don't see where the rabbit goes; it's invisible. However, you

have a rabbit tracker -- after the rabbit takes a turn, the rabbit

tracker gives you a location and says that "the rabbit is within 1

inch of this location". While the rabbit tracker can't lie, it is in

cahoots with the rabbit and can deliberately choose a location to

mislead you.

* On your turn, you must move exactly 1 inch away, in any direction.

The rabbit (and the rabbit-tracker) know exactly where you are.

* The game lasts 1,000,000,000 rounds (each of you get 1 billion turns).

Either come up with a strategy such that at the end of the game,

you're guaranteed to be within 100 inches of the rabbit -- or come up

with a strategy for the rabbit such that the end of the game, you're

guaranteed to be more than 100 inches away from the hunter.

--

Wei-Hwa Huang, ***@gmail.com

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Verbing nouns may weird language, but nouning verbs is a language destroy.

Wei-Hwa Huang, ***@gmail.com

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Verbing nouns may weird language, but nouning verbs is a language destroy.