Minimum Information Sum

Algebra Level 2

Alice has written on a piece of paper a sequence of numbers, \(13, 16, 19, 22,\) and \(25,\) in that order. She keeps the paper hidden from Bob.

Alice tells Bob that there are exactly 5 numbers, written in order of magnitude, and the differences between adjacent terms are all the same.

Alice asks Bob to guess the sum of the numbers. She will allow Bob to ask for any of the numbers as a hint. What is the fewest number of hints Bob would need to correctly guess the sum?

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