benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Rectangle WXYZ has WX=4,WZ=3, and ZV=3. The rectangle is curled without overlapping into a cylinder so that sides WZ and XY touch each other. In other words, W touches X and Z touc…

Problem

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

problem

Rectangle WXYZW X Y Z has WX=4,WZ=3W X=4, W Z=3, and ZV=3Z V=3. The rectangle is curled without overlapping into a cylinder so that sides WZW Z and XYX Y touch each other. In other words, WW touches XX and ZZ touches YY. The shortest distance from WW to VV through the inside of the cylinder can be written in the form a+bπ2cπ2\sqrt{\frac{a+b \pi^{2}}{c \pi^{2}}} where a,ba, b and cc are positive integers. What is the smallest possible value of a+b+ca+b+c?
Plain-text mathematical notation (without MathML)
Rectangle WXYZ has WX=4,WZ=3, and ZV=3. The rectangle is curled without overlapping into a cylinder so that sides WZ and XY touch each other. In other words, W touches X and Z touches Y. The shortest distance from W to V through the inside of the cylinder can be written in the form √((a+bπ²)/(cπ²)) where a,b and c are positive integers. What is the smallest possible value of a+b+c?
Original LaTeX notation
Rectangle $W X Y Z$ has $W X=4, W Z=3$, and $Z V=3$. The rectangle is curled without overlapping into a cylinder so that sides $W Z$ and $X Y$ touch each other. In other words, $W$ touches $X$ and $Z$ touches $Y$. The shortest distance from $W$ to $V$ through the inside of the cylinder can be written in the form $\sqrt{\frac{a+b \pi^{2}}{c \pi^{2}}}$ where $a, b$ and $c$ are positive integers. What is the smallest possible value of $a+b+c$?

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
fe2c7229-85cb-54e2-9e94-dd9410e389eb
task_key
test--fe2c7229-85cb-54e2-9e94-dd9410e389eb
task_revision_id
1
config / split
/ test

Official source

initial import