Estimation Case: Packing Soccer Balls Onto a Soccer Pitch

Estimate how many soccer balls can fit on a soccer field. Walk the interviewer through how you frame the problem, the assumptions you make, your arithmetic, and how you check that the final number is reasonable. ```hint Settle the geometry first Decide whether you are covering the ground with one layer or filling a volume, then size the field and a single ball. Remember that round balls never fill a space completely, wherever you put them. ``` ### Clarifying Questions - What kind of field is it: a full-size professional pitch, or a youth, indoor or small-sided field? - Do the balls form one layer on the grass, or may they be stacked, and if so up to what height? - Should the space inside the goals count? - Which ball size: the standard adult ball or a smaller youth ball? ### What a Strong Answer Covers - Clarifying field type, ball size and whether this is an area or a volume problem before calculating. - Reasonable, labeled assumptions for the field and ball dimensions, using round numbers. - Correct treatment of packing: balls cannot cover an area or fill a volume without gaps. - Clean arithmetic leading to a stated range, plus a sanity check by a second method. - A clear account of how the answer changes under the other interpretations and assumptions. ### Follow-up Questions - How does the number change if balls may be stacked up to the height of the crossbar? - Which assumption moves your answer the most, and by how much? - If you had to check the estimate cheaply on a real field, how would you do it?