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I have this question to answer and I need help with finding or creating a equation.

You own a license plate manufacturing company. Write a formula or equation that takes a population and determines the simplest pattern that will produce enough unique plates. Since all the plates that match the pattern will be generated, find the pattern that produces the least excess plates. Use a combination of letters (A-Z) and numbers (0-9).

It needs an a equation for the remainder too.

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Hint: how many plates of the pattern letter-number-number are there? I would assume the pattern you are looking for is some number of letters and some number of numbers. As long as you only accept one order, which order doesn't matter. Then you need to search over various combinations of letters and numbers to find the one which comes closest to the population.

Added: I don't think it will be an equation, but an algorithm. You can see how many letters it takes if you don't use any numbers, then how many it takes if you use one number, and so on. The closest one to the population will be the one you want. So if the population is 5000, you need 3 letters, giving 17576 plates, or 2 letters and 1 number, giving 6760, or 1 letter and 3 numbers giving 26000 or 4 numbers giving 10000. Clearly the winner is 2 letters 1 number, and the excess is 1760. You should be able to generalize this to an input population.

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it would be 2,600 but how would I make an equation to solve to solve any number of population? –  sherodtaylor Apr 18 '12 at 3:25
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