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The channel divinity option champion's challenge states that on a failed save, a creature can’t willingly move more than 30 feet away from you. How does this work with large creatures?

PHB states about ranges:

To determine the range on a grid between two things-whether creatures or objects-start counting squares from a square adjacent to one of them and stop counting in the space of the other one. Count by the shortest route.

A large creatures occupies a 2x2 area; where in this 2x2 area does the square determined by the range have to be? Can it be the nearest square, and therefore large creatures could actually move 1 square further with champion's challenge, or does it have to be the furthest?

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Size doesn't matter.

You quote the answer in the question itself.

To determine the range on a grid between two things-whether creatures or objects- start counting squares from a square adjacent to one of them and stop counting in the space of the other one. Count by the shortest route.

This means regardless of how large a monster is, 30 feet is 5 squares between you and the creature. You can have a monster that's so large it takes up 10x10 squares, but it will only be 30 feet from you when there's 5 empty squares between you and and it.

Here's a diagram to show how the distance should be measured. 5 feet from you is the square next to you, then on the 6th square the monster is 30 feet away. 5 empty squares between the two of you.

enter image description here

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The rule you quote from the PHB is clear: you start in a square (or hex) adjacent to one creature and count until you reach the space of the other. Note that you can start in any square adjacent to a creature. Similarly, you can reach any square of a creature's space and it would count. Then you choose the shortest of these. Thus the distance between them is the distance of their closest points to each other. Thus parts of a large creature can end up further than 30' from the paladin, as long as at least one square of its controlled area is in that range.

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