Each number from 1 to 6 replaces one of the letters P, Q, R, S, T, and U.
The sum of P and Q is 5 and the difference between R and S is 5.
If T is greater than U, what number replaces the letter T?
Source: 2023 Gauss Math Contest
Answer:
Since the sum of P and Q is 5, P and Q must be 1 and 4 or 2 and 3.
Since the difference between R and S is 5, R and S must be 1 and 6.
This means that P and Q must be 2 and 3.
This leaves 4 and 5, and since T is greater than U, the number that replaces the letter T is 5.
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