Which of the following is NOT a valid arrangement of 24 flowers?

Four rows of six flowers.
Two rows of twelve flowers.
Four rows of nine flowers.
Eight rows of three flowers.

Question

Which of the following is NOT a valid arrangement of 24 flowers?

	Four rows of six flowers.
	Two rows of twelve flowers.
	Four rows of nine flowers.
	Eight rows of three flowers.

GPT-5 mini · Answer

Answer: Four rows of nine flowers.

Reason: If 4 rows each have 9 flowers then the total number of row-flower incidences is 4·9 = 36. With only 24 flowers, the sum of the numbers of rows through each flower is 36, so at least 12 flowers must lie in exactly 2 rows (and the rest in 1 row) — giving at least 12 pair-intersections of rows. But 4 rows have only C(4,2)=6 distinct pairs, so there can be at most 6 distinct pairwise intersections. This is a contradiction, so 4 rows of 9 is impossible.

Which of the following is NOT a valid arrangement of 24 flowers?

Four rows of six flowers.
Two rows of twelve flowers.
Four rows of nine flowers.
Eight rows of three flowers.

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Which of the following is NOT a valid arrangement of 24 flowers? Four rows of six flowers. Two rows of twelve flowers. Four rows of nine flowers. Eight rows of three flowers.

All Answers 1