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Omni-MATH / Lucas chooses one, two or three different numbers from the list 2,5,7,12,19,31,50,81 and writes down the sum of these numbers. (If Lucas chooses only one number, this number is the…

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Lucas chooses one, two or three different numbers from the list 2,5,7,12,19,31,50,812, 5, 7, 12, 19, 31, 50, 81 and writes down the sum of these numbers. (If Lucas chooses only one number, this number is the sum.) How many different sums less than or equal to 100 are possible?
Plain-text mathematical notation (without MathML)
Lucas chooses one, two or three different numbers from the list 2,5,7,12,19,31,50,81 and writes down the sum of these numbers. (If Lucas chooses only one number, this number is the sum.) How many different sums less than or equal to 100 are possible?
Original LaTeX notation
Lucas chooses one, two or three different numbers from the list $2, 5, 7, 12, 19, 31, 50, 81$ and writes down the sum of these numbers. (If Lucas chooses only one number, this number is the sum.) How many different sums less than or equal to 100 are possible?

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