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Omni-MATH / Let n>0 be an integer. We are given a balance and n weights of weight 2⁰,2¹,⋯,2^(n−1). We are to place each of the n weights on the balance, one after another, in such a way that t…

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problem

Let n>0n > 0 be an integer. We are given a balance and nn weights of weight 20,21,⋯,2n−12^0, 2^1, \cdots, 2^{n-1}. We are to place each of the nn weights on the balance, one after another, in such a way that the right pan is never heavier than the left pan. At each step we choose one of the weights that has not yet been placed on the balance, and place it on either the left pan or the right pan, until all of the weights have been placed. Determine the number of ways in which this can be done. [i]
Plain-text mathematical notation (without MathML)
Let n>0 be an integer. We are given a balance and n weights of weight 2⁰,2¹,⋯,2^(n−1). We are to place each of the n weights on the balance, one after another, in such a way that the right pan is never heavier than the left pan. At each step we choose one of the weights that has not yet been placed on the balance, and place it on either the left pan or the right pan, until all of the weights have been placed.
Determine the number of ways in which this can be done.

[i]
Original LaTeX notation
Let $n > 0$ be an integer. We are given a balance and $n$ weights of weight $2^0, 2^1, \cdots, 2^{n-1}$. We are to place each of the $n$ weights on the balance, one after another, in such a way that the right pan is never heavier than the left pan. At each step we choose one of the weights that has not yet been placed on the balance, and place it on either the left pan or the right pan, until all of the weights have been placed.
Determine the number of ways in which this can be done.

[i]

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Source and history

task_id
b5cf1271-4168-5314-b5e4-7ee05b97205a
task_key
test--b5cf1271-4168-5314-b5e4-7ee05b97205a
task_revision_id
1
config / split
/ test

Official source

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