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Omni-MATH / Let k be a positive integer. Suppose that the integers 1,2,3,…,3k+1 are written down in random order. What is the probability that at no time during this process, the sum of the in…

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problem

Let kk be a positive integer. Suppose that the integers 1,2,3,…,3k+11, 2, 3, \dots, 3k+1 are written down in random order. What is the probability that at no time during this process, the sum of the integers that have been written up to that time is a positive integer divisible by 3? Your answer should be in closed form, but may include factorials.
Plain-text mathematical notation (without MathML)
Let k be a positive integer. Suppose that the integers 1,2,3,…,3k+1 are written down in random order. What is the probability that at no time during this process, the sum of the integers that have been written up to that time is a positive integer divisible by 3? Your answer should be in closed form, but may include factorials.
Original LaTeX notation
Let $k$ be a positive integer. Suppose that the integers $1, 2, 3, \dots, 3k+1$ are written down in random order. What is the probability that at no time during this process, the sum of the integers that have been written up to that time is a positive integer divisible by 3? Your answer should be in closed form, but may include factorials.

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Source and history

task_id
af93980a-ad74-5a66-a2c0-7359c74a0b37
task_key
test--af93980a-ad74-5a66-a2c0-7359c74a0b37
task_revision_id
1
config / split
/ test

Official source

initial import