Problem of the Week #63: Monday September 16th, 2024
As before, these problems are the results of me following my curiosity, and I make no promises regarding the topics, difficulty, solvability of these problems.
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This problem is inspired by this twitter post.
a). From the list of numbers 1 to n, cross out every other number starting with the smallest and repeat the process with the remaining numbers until only one number is left. What number would that be for a given n?
b). If we alternate starting from the smallest and the biggest number at each round, what number would be left for a given n?
c). If we list the numbers in a circle and continue crossing out every other number from the remaining numbers, what number would be left for a given n?
d). If we cross out every third number in the line and alternate starting with the smallest or biggest number each round, what would be the last remaining number for a given n?
e). If we list the numbers in a circle and continue crossing out every third number from the remaining numbers, what number would be left for a given n?
f). If we list the numbers in a circle and continue crossing out every kth number from the remaining numbers, what number would be left for a given pair of n and k?
g). Share your own problem inspired by this one.
h). Give one of these questions to a friend/colleague/student/family member to start a mathematical discussion.