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HMMT 1999 T1

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A combination lock has a 3 number combination, with each number an integer between 0 and 39 inclusive. Call the numbers n1,n2n_{1}, n_{2}, and n3n_{3}. If you know that n1n_{1} and n3n_{3} leave the same remainder when divided by 4 , and n2n_{2} and n1+2n_{1}+2 leave the same remainder when divided by 4 , how many possible combinations are there?

Dataset text NuminaMath olympiads. Quoted with source.

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4000

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