Consider the following definitions of perfect pairs/trios. If there exist such numbers that fit the definition show how many exist, if no number exists, provide a proof: (Each number is assumed to be distinct)

1. When you add two numbers you get a certain answer. Using the same two numbers, subtract the larger from the smaller and get the same answer in the first sentence.

2. Using three numbers, add the first two numbers together then divide the sum by the third number. The result will be one of the three numbers.

3. Two numbers whose sum is equal to their quotient.

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Consider the following definitions of perfect pairs/trios. If there exist such numbers that fit the definition show how many exist, if no number exists, provide a proof: (Each number is assumed to be distinct)

1. When you add two numbers you get a certain answer. Using the same two numbers, subtract the larger from the smaller and get the same answer in the first sentence.

2. Using three numbers, add the first two numbers together then divide the sum by the third number. The result will be one of the three numbers.

3. Two numbers whose sum is equal to their quotient.

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