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AIME II Problem 6 2007
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AIME II Problem 6 2007
by zefuri » Tue Apr 03, 2007 10:28 pm
An integer is called parity-monotonic if its decimal representation [unparseable or potentially dangerous latex formula] satisfies [unparseable or potentially dangerous latex formula] is odd, and [unparseable or potentially dangerous latex formula] is even. How many four-digit parity-monotonic integers are there?
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by Quelloquialism » Wed Apr 04, 2007 4:23 am
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by AuSmith » Wed Apr 04, 2007 10:28 am
Given any digit 0 through 9, there are always 4 digits that we can append on the left (all the odds below the given digit and all evens above). Therefore, if we construct a parity monotonic integer starting from the right, we have 10 choices for the first digit and 4 choices for each digit thereafter. If we want a parity monotonic integer of length four, we have [unparseable or potentially dangerous latex formula] distinct constructions.
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