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Let's start by considering some incorrect answers.

17 — This would be correct if 9 people fit in a queue with 2 metre separation, and you wanted to know how many people would fit in the same space if you reduced that to 1 metre. Imagine fitting one person in each gap. There are a total of 8 gaps: one per pair of neighbours in the line. We could think of this as halving the size of each gap means we end up doubling the number of gaps.
18 — This would be correct if the first person in the queue could stand 1 metre from the entrance, rather than two. Image putting an extra person in front of every member of the queue. Of course, everybody would be polite about it. But it's wrong.
36 — Good try! You've correctly realized that people in a two dimensional area don't interact in the same way as a queue. But when we halve the gaps in the queue, we don't quite double the number of people, because of the people at the ends. The effect is much larger here.

The correct answer is 25.

Picture 9 people optimally spaced in a square: 8 of the 9 are configured in a square, with one person at each of the four corners, and one in the middle of each of the four edges. The 9th person is in the middle.

There are 3 people along each edge, and 3 in each line across the middle of the square. That means we have 2 spaces, each of 2m. If we shrink the minimum spaces to 1m each, we double the number of spaces along each edge. So each edge will have 4 spaces, meaning we can fit 5 people.

However, this is a two-dimensional space. We can fit more people on each row, and we can fit more rows. We need to think not in terms of 2m distances along the edges, but in terms of 2m × 2m squares. If we halve the distance to 1m, we shrink the squares to 1m × 1m — these are a quarter of the size of the previous squares, and so we have 4 times the squares in the same space. From the original 4 squares we now have 16.

We started with 2 gaps along each edge, and 2 × 2 = 4 squares. That corresponded to 3 people along each edge, and 3 × 3 = 9 people. Halving the distance means we have 4 gaps along each edge, and 4 × 4 = 16 squares. The number of people along each edge is now 5, so that means we can fit 5 × 5 = 25 people.

This means that if we halve the minimum distance, the maximum number of people more than doubles. The maximum number of spaces will approximately quadruple — the precise number varies once square grids are no longer the most space efficient method of packing.