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Omni-MATH / During a break, n children at school sit in a circle around their teacher to play a game. The teacher walks clockwise close to the children and hands out candies to some of them ac…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

During a break, nn children at school sit in a circle around their teacher to play a game. The teacher walks clockwise close to the children and hands out candies to some of them according to the following rule. He selects one child and gives him a candy, then he skips the next child and gives a candy to the next one, then he skips 2 and gives a candy to the next one, then he skips 3, and so on. Determine the values of nn for which eventually, perhaps after many rounds, all children will have at least one candy each.
Plain-text mathematical notation (without MathML)
During a break, n children at school sit in a circle around their teacher to play a game. The teacher walks clockwise close to the children and hands out candies to some of them according to the following rule. He selects one child and gives him a candy, then he skips the next child and gives a candy to the next one, then he skips 2 and gives a candy to the next one, then he skips 3, and so on. Determine the values of n for which eventually, perhaps after many rounds, all children will have at least one candy each.
Original LaTeX notation
During a break, $n$ children at school sit in a circle around their teacher to play a game. The teacher walks clockwise close to the children and hands out candies to some of them according to the following rule. He selects one child and gives him a candy, then he skips the next child and gives a candy to the next one, then he skips 2 and gives a candy to the next one, then he skips 3, and so on. Determine the values of $n$ for which eventually, perhaps after many rounds, all children will have at least one candy each.

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Source and history

task_id
c3927fd7-96e9-5125-96d0-93f2a5443aea
task_key
test--c3927fd7-96e9-5125-96d0-93f2a5443aea
task_revision_id
1
config / split
/ test

Official source

initial import