2. Apply the pigeonhole principle
If each of the 25 cells contained at most 2 ants, then the total number of ants would be at most:
25 × 2 = 50
But there are 51 ants, so at least one cell must contain
3 or more ants.
3. Show one disk covers that entire cell
Place the center of the glass disk at the center of the crowded small square.
The farthest points in the cell are the corners.
needed radius = √[(1/10)² + (1/10)²] = √2 / 10 ≈ 0.14142
glass radius = 1 / 7 ≈ 0.14286
√2 / 10 < 1 / 7
So the radius-1/7 disk covers the whole small square, and therefore
covers all ants in that square — at least 3 ants.