Tag Archives: midnight-math

A Puzzle by Midnight Math: February

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midnightmathOn a circle are placed an equal number of “x”s and “o”s.

Starting with a value of zero, you chose a starting place on the circle and begin moving clockwise around the circle.

Every time you pass an “x”, you add 1 to your value, and every time you pass an “o” you subtract 1. Once you have returned to your starting location you stop.

Show that no matter how the “x”s and “o”s are placed (as long as there are an equal total number of each) there will always be a starting location such that your value is never less than zero.

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A Puzzle by Midnight Math: November

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A puzzle, courtesy of the Midnight Mathematicians: “A passel of math students are kidnapped and held captive in some unknown, and probably unfriendly, vector space. On the forehead of each student, without their knowledge, is drawn either a 1 or a 0. The hyper-intelligent, pan-dimensional captor will only give the information necessary to leave said vector space to students who correctly identify the mark on their forehead. At the end of each day, each student has the opportunity to guess, but an incorrect guess means they will be trapped forever. The students are not allowed to communicate in any way, but every day they see each other for their one meal together (also, there are no surfaces which produce clean reflections in this space). The only information they are given is that there is at least one student with a 1 and at least one student with a 0. What is the largest number of days it could need to take for n students (n>=2) to all set themselves free?”

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