According to 'Guilford', divergent thinking requires:

J.P. Guilford's Structure-of-Intellect model splits problem-solving into two contrasting modes: convergent thinking, which narrows a problem down to one correct or best answer through logical, rule-bound reasoning, and divergent thinking, which generates many different possible ideas, answers, or approaches to an open-ended problem. Divergent thinking is measured chiefly through ideational (or associational) fluency — the ability to produce a large quantity of relevant ideas in a short span of time — along with flexibility, originality, and elaboration.

The question asks specifically what divergent thinking requires according to Guilford. Since divergent production is about generating many ideas rather than converging on a single correct one, the defining requirement is fluency of ideas — quickly producing multiple possible responses to the same prompt.

• Categorization sorts items into fixed, predetermined groups — a single-answer classification task. That is a hallmark of convergent thinking, not the open-ended idea generation Guilford describes for divergent thinking.

• Arithmetical reasoning applies a fixed procedure to reach one determinate numerical result. That single-answer, rule-bound process characterizes convergent thinking rather than the multiple-idea generation of divergent thinking.

• Producing a single solution is the defining goal of convergent thinking, which narrows possibilities down to one correct answer. Divergent thinking instead branches outward into multiple different possibilities.

Because divergent thinking is defined by generating a high volume of varied ideas, fluency of ideas is the trait Guilford identifies as required for it.