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This Note documents in mathematically rigorous fashion seven models of recent military problems. These problems, for the most part independent of each other, range from optimum pattern size of a tactical munitions device to the most effective allocation of interceptors in a multilayered strategic defense. Other topics considered include a game theoretic solution for mixing between two offensive systems; the optimal deployment of missiles in a multiple aim point scheme with a symmetrical agreement limiting the number of warheads and, in the case of a fixed enemy threat, an algorithm for determining the cost-effectiveness of aircraft penetration aids; and the optimal number of short-range attack missiles on a bomber. In each case, careful logic promotes the powerful use of elementary mathematics to produce an elegant solution to a rather complex problem.
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