 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ib/paper-4/18h/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

A pure optimum is a saddle point: an entry minimal in its row and maximal in its column. In

A_{1}

c

(2, 1)

is a saddle; in

A_{2}

c

(2, 2)

is a saddle. Matrix

A_{3}

has row maximin

b

and column minimax

c

, so no saddle exists. Thus

A_{1}, A_{2} admit pure optimal strategies; A_{3} does not .

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