Problem 467. Mr. Pyramidad & Ms. Whissy Bolower

Created by AMITAVA BISWAS

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<p>Businessman Mr. B. M. Pyramidad was drinking with his new girlfriend Ms. Whissy Bolower. He disclosed to her that he has an illegal business plan:</p><ol><li>He, as Boss-I, will recruit x individuals as Operator-II,</li><li>Each of these operators will recruit x individuals at Helper-III,</li><li>Every helper must recruit x individuals as Peddler-IV.</li><li>All of them will be promoted to next higher level as soon as each of those peddlers deposit $1,000 cash to their acting Boss-I.</li><li>Then, whoever was the acting Boss-I, he or she must retire, but the business will continue to expand as usual.</li></ol><p>Ms. Whissy Bolower has decided to blow the whistle. She is calculating that Mr. Pyramidad may come back at the Peddler-IV level after retiring. What could be the minimum x so he collects minimum y dollars net after retiring z times? Please try a general solution, the test suite may expand. For more information, see <a href="http://en.wikipedia.org/wiki/Pyramid_scheme">Pyramid Scheme</a>.</p>

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