benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / For a string of P 's and Q 's, the value is defined to be the product of the positions of the P 's. For example, the string PPQPQQ has value 1⋅2⋅4=8. Also, a string is called antip…

Problem

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

problem

For a string of PP 's and QQ 's, the value is defined to be the product of the positions of the PP 's. For example, the string PPQPQQP P Q P Q Q has value 1⋅2⋅4=81 \cdot 2 \cdot 4=8. Also, a string is called antipalindromic if writing it backwards, then turning all the PP 's into QQ 's and vice versa, produces the original string. For example, PPQPQQP P Q P Q Q is antipalindromic. There are 210022^{1002} antipalindromic strings of length 2004. Find the sum of the reciprocals of their values.
Plain-text mathematical notation (without MathML)
For a string of P 's and Q 's, the value is defined to be the product of the positions of the P 's. For example, the string PPQPQQ has value 1⋅2⋅4=8. Also, a string is called antipalindromic if writing it backwards, then turning all the P 's into Q 's and vice versa, produces the original string. For example, PPQPQQ is antipalindromic. There are 2¹⁰⁰² antipalindromic strings of length 2004. Find the sum of the reciprocals of their values.
Original LaTeX notation
For a string of $P$ 's and $Q$ 's, the value is defined to be the product of the positions of the $P$ 's. For example, the string $P P Q P Q Q$ has value $1 \cdot 2 \cdot 4=8$. Also, a string is called antipalindromic if writing it backwards, then turning all the $P$ 's into $Q$ 's and vice versa, produces the original string. For example, $P P Q P Q Q$ is antipalindromic. There are $2^{1002}$ antipalindromic strings of length 2004. Find the sum of the reciprocals of their values.

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
864d5801-ecfd-5c43-80ba-8f481f6fbe84
task_key
test--864d5801-ecfd-5c43-80ba-8f481f6fbe84
task_revision_id
1
config / split
/ test

Official source

initial import