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Complements

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Definition

         

Due to superstition, the Chinese do not like the number 4 as it is phonetically similar to the character for death. They will avoid using the number 4, and some buildings do not have a level which has the number 4 in it.

Out of the first 100 positive integers, how many of them do not have any instances of the digit 4?

Alissa and Bertram each name one integer from \(1\) through \(18\) inclusive. How many ways can they choose a pair of integers with sum less than or equal to \(34?\)

Silas has one $1 bill, one $5 bill, one $10 bill and one $20 bill in his wallet. How many ways are there for him to pull out 2 bills and have enough to pay $8 for his lunch?

Details and assumptions

Silas has no other bills in his wallet.

The order in which he pulls out the bills is not important.

In the Star Wars Universe, you can be aligned with the Rebel Alliance, or the Galactic Empire. Some people align themselves with both or neither parties, in order to gain additional favors.

What is the complement of those who are aligned with the Rebel Alliance, but not the Galactic Empire?

Alexi and Beatrice each pick one integer from \(1\) through \(15\) inclusive. How many ways can they choose a pair of integers with product less than or equal to \(202?\)

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