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You are invited to submit a solution to the Problem of the Fortnight!

The intent of this activity is simply to have fun thinking about mathematical problems. Anyone may submit a solution. You need not be a mathematics major to submit a solution.

See guidelines for submission of a solution here.

Problem of the Fortnight (30 January 2017; deadline for solutions is noon, 6 February 2017)

Problem of the Fortnight (30 January, 2017)

A student came to her professor’s office, wanting to know her score on the final examination. The professor did not have the graded exams with her. But she looked up the student’s score in her gradebook, and asked the student if she wanted the number outright, or she wanted a puzzle to figure it out. The student opted for the puzzle.

The professor said, “Your score left a remainder of 1 when divided by 2, 3, 4, 5, and 6; and a remainder of zero when divided by 11.” As the student started walking away, the professor said, “Oh, just as a reminder, the exam was out of 150 points.” What was the student’s score?

As a bonus, can you find the next number that is larger than the student’s score and that satisfies all the divisibility conditions? (So it may not satisfy being less than 150.)

Remember, full explanations are needed!

Putnam Competition — Sep 20, 2016 3:18:57 PM