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loopy walt
loopy walt
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Let's focus on the

bisector of the two animals' positions just before the next move.

A few observations:

The zebra can never cross it without immediately being caught.

Conversely:

As long as the zebra moves a straight 100m without touching the bisector the lion cannot catch it in the next move.

This already resolves C as

once the zebra is outside the confinement there will always be an obstruction free direction away from the bisector.

To avoid tedious edge cases I'll assume that the enclosure is a rectangle with one side completely open.

B

The lion wins precisely when the opening falls entirely on the lions side of the bisector. Indeed, by mirroring the zebraszebra's moves the lion can fix the bisector exactly where it is and there is no way for the zebra to make any progress.

A

If the bisector is outside the confinement or crosses the opening at least one of the two corners flanking the opening will be on the zebra's side. The zebra can move straight there being careful to use up whatever is left of the last 100m step moving as far away from the lion as possible.

Let's focus on the

bisector of the two animals' positions just before the next move.

A few observations:

The zebra can never cross it without immediately being caught.

Conversely:

As long as the zebra moves a straight 100m without touching the bisector the lion cannot catch it in the next move.

This already resolves C as

once the zebra is outside the confinement there will always be an obstruction free direction away from the bisector.

To avoid tedious edge cases I'll assume that the enclosure is a rectangle with one side completely open.

B

The lion wins precisely when the opening falls entirely on the lions side of the bisector. Indeed, by mirroring the zebras moves the lion can fix the bisector exactly where it is and there is no way for the zebra to make any progress.

A

If the bisector is outside the confinement or crosses the opening at least one of the two corners flanking the opening will be on the zebra's side. The zebra can move straight there being careful to use up whatever is left of the last 100m step moving as far away from the lion as possible.

Let's focus on the

bisector of the two animals' positions just before the next move.

A few observations:

The zebra can never cross it without immediately being caught.

Conversely:

As long as the zebra moves a straight 100m without touching the bisector the lion cannot catch it in the next move.

This already resolves C as

once the zebra is outside the confinement there will always be an obstruction free direction away from the bisector.

To avoid tedious edge cases I'll assume that the enclosure is a rectangle with one side completely open.

B

The lion wins precisely when the opening falls entirely on the lions side of the bisector. Indeed, by mirroring the zebra's moves the lion can fix the bisector exactly where it is and there is no way for the zebra to make any progress.

A

If the bisector is outside the confinement or crosses the opening at least one of the two corners flanking the opening will be on the zebra's side. The zebra can move straight there being careful to use up whatever is left of the last 100m step moving as far away from the lion as possible.

Source Link
loopy walt
loopy walt
  • 21.5k
  • 1
  • 34
  • 96

Let's focus on the

bisector of the two animals' positions just before the next move.

A few observations:

The zebra can never cross it without immediately being caught.

Conversely:

As long as the zebra moves a straight 100m without touching the bisector the lion cannot catch it in the next move.

This already resolves C as

once the zebra is outside the confinement there will always be an obstruction free direction away from the bisector.

To avoid tedious edge cases I'll assume that the enclosure is a rectangle with one side completely open.

B

The lion wins precisely when the opening falls entirely on the lions side of the bisector. Indeed, by mirroring the zebras moves the lion can fix the bisector exactly where it is and there is no way for the zebra to make any progress.

A

If the bisector is outside the confinement or crosses the opening at least one of the two corners flanking the opening will be on the zebra's side. The zebra can move straight there being careful to use up whatever is left of the last 100m step moving as far away from the lion as possible.