benchmarks.wiki / Public workspace
.·:=+#%%%#*+=-:··....····::::::····::--=++**#**+=-:·.. ..·:-=++****++======++*#####**+=-:···.··::-=+***+=-:·.
.·:-=+*++=--:·.. ...············::---===--::·.. ..··:--=====---::::::-***##**+=-::·....··:-=++**+=-:·.
..···::··... ..............·······... ...·········......::++***++==-:··....··:-==++*+=:·..
..::==++++==-:··......·:--=+++=-:·..
..··--====--::·.......·:--=++++-:·..
.·::-----::··......··:-==+**+=-··.
..··:::::::··......·::-=+***+=-:·.
..··:::::········::-=+**##*=-:·.
...··::::::::::::--=+**###*=-:·..
..··:::::::::···············..... ......···.... ..·::-----------==++*####*=-:·.
..·:=+*********++=---::---------::··......··::::::::·.. .·::-==++++=====+++******+=:·..
...·:-+*%@@@@@@@@@@@%*++=====++++++==-::···.···::--==--::·. ..:-=+**###***++++++++++++=-:·.
.·:-==++=-:··......··::---==-----==++*#%%@@@%#*+=:·. ...······.....··:-=++**##*++=-:::·::--=+##%@@@%#+-:·.
..·::---::·.. ...··::::::::::::--===+++==-:·.. ...····.......··::--*###**+=--:::::-=+*#%%@@%%*=-·..
...···... ...............·········... ......... ......--#####*+=--:::::-=+**#%%%##+-:..
..-=####**+=--:::::--=+*####*+=:·.
..--*###*++=-:::::::-=++****+=-·.
..--*****+=--::···::--=++**++=:·.
..:-+++++==-::·····::-==++++==:·.
..::======--::·····::-==++++==:·..
.··--===---:::··:::--==++++==-:·..
..···::::·····......·····..... ...········.... .·:---==----:::::--==+++++==-:·..
.·:-=+*****++==-------------::···......··:--=====--:··.. ...:--=======------===+++++==::·..
.·:=+#%@@@@@@@@%#**++++++++++++=-::······:-==+****++=-:·. ..·:-=++***+++=============--:·..
..·····.. .··:--=======+++*#%@@@@@@@@@@@#*=-:·............ .·:-==+++==-::·····:-=+*#%@@@@@%#+=:·..
...·.... ..··:::---------==+*********+=-:·.. ..·::--+++==-::::::-=+*#%@@@@@@%*=-·.
.. ....·············:::::::::··.. ....--***++=--::--==+#%@@@@@@#*+-·.
.·==##**++=-----=+*#%%@@@%#*=-·.
··==%##**+===--==++*##%##*+=:·.
··=+%%##*++==---==++****+=-:·.
··=+%%##*+==------===++==-:·..
··==###*++=--:::::----=---:··.
··==#***+==-::::::::-----:::··..
..··········.............. ...·······...........--**+++=--:::··::::-----:::··......
.·:--=+++++==--:::::::::::··.. ..·:--=====--::·······:::-+++++==--:::::::::-----:::··.....
.·:=+#%%@@@%##*+===---===---::·.. .·:-+*##%%##*+=-::····::-=+++**++==--:::::::::---::::··.....
.. ..··::::::::--=+*%@@@@@@@@@@@@@#*+=------:::··.. ..·:-=++++=--:··...··:-=*#%%@@@%##+=-:·..
..···::::::::--==+************=--:···......... ..·::----==-::····:-=+*#%@@@@@%#*=-·.
..........····:::::::::::::··... ....·--+==--::::-=+*#%@@@@@%#+=:·
··=-*++==---==+*#%%@@@@%*+-·.
··==#**++====++*##%%%#*+=:·
··++%##*+++===+++***++=-:.
::++%%#**+==========--:·. ...
::++%%#*+==--::::::::··.. ..··..
::++%#*+=--:···········.........·····..
...···:::::::············.... ....····......·······==#*+=-::··......··········::::::··.
...... ..·::-=+*****+++==-------:::··. .·::-======---::::----====*++=-:··.......···:::::----:::···.
............·:-+*#@@@@@@@%##*++====---::·. ·:=+*#%%%%#**+==---==+++****+==-:··.......··::--------:::··..
...·····.......·:-=*#@@@@@@@@@%#*++======---::··. ..·:=+*#####*+=-:··..··:-=+*#####**+=-:·..
.............··:-=+*********+=--:::········... ..·::-====--:-::·····:-=+*#%@@%#*+=:·.
... ....··:::::::::::···....... ...······-:--::·::--=*#%%@@%%*+-:.
··--=------=++*#%%%%#*=-·.
··=-++======+**###**=-:. ....
··==**++=====++++==-:·. .····.
::++#*++==------::··.. .·:--:·.
::++#*+=-::····..... .·:--==-:·.
::+=*+=::·.. ......··:--==+==-:·.
..···::::::::::::::::::::··.. .....·············:::··=-+-:·.. ..··::--==+++++==-:·
....·:-==+**********+++++++==--:·. .·:-========-----=======--:-:·. .··:-==+++****+=--:·.
.......··:-=*#%@@@@@@@@@@@%###***+==-:. .:=+#%@@@@@%#**+++++++***++=--:·. .·:-=++*******+=-::·..
..··:--===--::··....··:-=+*#%%%##*+==-::::::::::··.. .·:-+#%@@@@@@%*+=:··...··:-==+++++=--:·.... .....
...········.... ...·:--=+++++==-::····....·...... ..·:-=++***+==-:···...··:-=+**##*+=-:·. ....
...... ...···:::::···.... ...····::····.·······::-=+*###*+=-·. ..··.
..:·::·::--=+**#**+=:·. .·:::·.
·.::------==++++==-·. .·:---:·.
··-:=-----------:·.. ·:-=+=-:·.
··--=--:::·····... .·:=+**+=-:·.
··-:-::·... ..·:-=+#%#*+=-:·.
··:·:·. ..··::-=+*#%@%#*+=-:·
...············:::::::::··.. ....·····················.·.. ..·:-=+**##%%@@%#*+=:·.
..·:--=++*****++++++****++=-:·. .·:-=++++++====---=====--::·.. .·:-+*#%%@@@@%%%#*=-:·.
..·:=+*%@@@@@@@@@@@@%%%%##*+=-:. .·-+#@@@@@@@%%#*+++=+++++==-:·.. .·-=*#%@@@@@@%##*+--:·..
..·:=*##%%%##*+==-----=+**#%%%%#**+=-:···........ .·:=*%@@@@@@@@@#+-:·.. ..··:--===--:··......··::::··.
..·:-=======--::·····::--======--::·.... ..·:-=+*******+=:·.. .·:-==+++==-:·.. ..·:::::·..
..········..... .....········.... ....··:::::::··.. ..·:-=++*++=-:·. .·:--=--:·.
. ..··:-=++++==-·. ·:-=++=-:·.
. ..··::--====--:·. .·-+*#*+=-:·.
..··::::::::::··.. .·:=*%%#*+=-:·.
..·····........... ...·:-+#@@%#*+=-:·.
...... ....··:--=+#%@@@%#*+=-:.
. . ..·:-==+*#%%@@@@@%#*+=:·.
..............·····::::···.. ..······················... .·:-+*#%@@@@@@@@@@%#+-:·.
.··::---====---====+++++==-:·. .·:-=++***++==----------:::··. .:-+*%@@@@@@@@@@%##+=-:·.
..·-=+*##%%%%%%%########**+=-·. .:=*%@@@@@@@@%*+==---------:··. ·:=*%@@@@@@@@@%#*+==-:·..
.·:=*#%@@@%%#**+++**##%@@@@@@%#*+=-:··...... .·-+#@@@@@@@@@@%+-·. .··:------::·····:--=+*++=-:·.
..·-=++**+++==-------==+++++==-::·.. ..·:-=+********+=:·. .·:-==++==-:··...··:-=+**++=-·.
..··::::::····......·········... ....···::::::::··.. .·-=+++++=-:··.....·:-+*##*+=-:.
.·:-==++++=-:·.. .·:-=*%%#*+=-:.
.·::--====-::·... ..·:-+*%@%#*+=-:.
..··::::::::··.....··:=+#@@@%#*+=-·.
.....············::-=+*%@@@@%#*+=:·.
..···::--==+*#%@@@@@@%#*+-·.
..·:-=+**##%%@@@@@@@@%#+-:.
....................······... ...···::·····................ .:-=*#%@@@@@@@@@@@@%%*=-:.
..··:::::::::::::::---===--:·.. ..:-=++****+==-:::·····::::···.. .·:=*#@@@@@@@@@@@%##*++-:·.
..·:-==+++++++++++++++++++=-:·. .·-+#@@@@@@@@%*+=-::···::::::··.. .·-=*%@@@@@@@@@@%#*+=--:·..
.·-=+*##***+++++**#%%@@@@@%#*+=-::··..... .·:=*%@@@@@@@@@@#=:. .·:--=====-------=+*#%%@%#+=:·.
.·:-=+++===------===++++++==-:··.. ...·:-=+*********+-:. .·-=++**++=--::::--=+*#%%%*+=:·.
..··::::··················... ....···:::::::::··.. ·:-=+****+==-::··::-=+*#%@%#+=:·.
.:-++****+==-:·····:-=+#%@@%#+=:·.
.·-=++++++=--:·····:-=+*%@@@%#+=:·.
··--=====---::···::-=+*%@@@@%#+=:·.
..::::------::::--=+*#%@@@@@%#+-·.
...···::---=====++**#%@@@@@@%*=:·.
..·:-==++***####%%@@@@@@%*=-·.
.......... ........... ..···::::···.... .......... .·:-=+*#%%@@@@%%%%%%%%##*=-·.
...··::::····.....··:::---:::·.. .··:-=+****+=--:··.....···::::··.. .·:-+*%@@@@@@@@@%%###**++=-·.
..··::-==-----:::---=======-:··. .·-=*#@@@@@@@#*+-:··...···::--::··.. .·:=*#@@@@@@@@@@%##*+==--::·.
.·:-=+++===---==++*######**+=--:···........ ..·:-=*%@@@@@@@@@%+-· .·:-=++++++=====++*#%%@@@@%#+-:..
.··:--=---::::::---=======-::·.. ....··:--=+********+-:·. .-=+*####*++======+*##%%%%#*=:·.
...······.......·········... ....·····:::::::···.. ·:+*#%%%%#*+==----==+*###%##+-:·.
.:-*#%%%%#*+=--::::-==+*####*+-:.
..--##%%##*+=-::::::-==+*####*=-·.
..--*****++=--::::::-=+**####*=-·.
..::=++++==---:::::-==+*#####*=-·.
..··--======-------==+*######*=:·.
..:--============++**#####*+=:·.
........ .......... ...···:::···... ....··..... ..:--=++******+++****####*++-·.
...·····.... ....··::::-:::···......··:--=++++==-:··.. ...··::---::··.. ..:-=**#%%%%###**********+==:·.
..···:::::·····::--=======-::···.···:-=+*#%%%%#*+=-:·.....··:--=====-:·.. ..·:-+*#%@@@@@%%##**++++++==-:·.
.··:--===-::::::--==++++++==--:::···········..···::-+*#@@@@@@@@%*=:. .·:=+******++===++*##%@@@@@%#*=:·.
..··::::········::---==---::·... ....···::--==++*****+=-:·. ..·:-#%%%%##*++===++*##%%%%%#*=-·.
................·······... ....······:::·····... ..·=+@@@@%%#*+=====++**#####*+-:.
··++@@@@%#*+==----==++****++=:·.
··++@@@%#*+=--::::--=+++*++=-:.
··++%%%#*+=-:::·:::-==++++==-:.
··==##*++=-::····::--==+++=-:·.
..--+++==--::····::--==+++=-:·.
..::=====--:::··:::-==++++=-:·.
............. .....········.. ...·······.... .·:=====---::::::--==++++=--:.
....... ...··::-----:::········::---==--::·.. ..·::-=====--:··........··-=======-------==+++++=--:..
....········:::-===+++++==-:::::::--==+****+==-:·......·:-=+**##**+=-:·......··:-=+++++++===---===+++++=-::..
.·::::::··...···:--==+++===---:::::::::::···::::-=+*#%@@@@@%#+=:· .:-=+*****++==--===+*#%%@@@@%#*+=-··..
...···.........··:-------::··...........···::::---===+++===-:·.. .··:-==+%##**+=====++*#%%@@@%#*+=-:·.
....······... ....··············.... ..···++@%%#*+======+**#%%%%#*+=-:·.
::**@@%#*+==---==+**####*+=-:·.
::**@%#*+==-----==+*****+=-:·.
::*+@%#*+=-:::::-==+++++=-:·.
::++##*+=-::···::--==++==-:·.
··==*++=-::·····::--====-:·.
··--+==-::··..···:---==--:·.
......·...............······... ..···::·····...........::==-::··....··::------:·.
.........···::-------:::·······:::---:::··. .·:-==++*+++=--:········::::---::··....··::------:·.
...···:::::--==+++++++==--::::::::--=====--:··......·:-+*#%@@@@%#*+=-:······::------::····.···::------:·..
..··... ..·::-=++***+++==---::::::::::·::::--=++*##%##**=-:·. .·:-=+****+==-::···::-=++*####**+==---:::··..
.. ..·::-======--:··.........····::::::-----===---:··. ..·:--====-+=--:::::-==+*######*++=--::····..
...···:····... ....··········......... ...·····=-++=-::::--=+*##%%%##*+==--:···...
··==*+=--:::--=+*##%%%##*+=-::··.....
:·==*+=---:--==+*##%%%#*+=--:·.....
:·+=*+=--:::--=+**#####*+=-:·..
:·==*+=--:::--=++*###**+=-:·..
··==+==-:::::--=++****+=-:·..
··=-+=-::···::-==+++++==-·..
.......................·····... ..············...········--=-::·····::-==+++==-:·.
......····::::-----:::········::::::::··.. .·:-==++**++==---::::--------:--:·······:--=====-:·.
..···:::-----==++++++==--:::··:::-------::·.. ..·:=+#%@@@@@@%#*++=----====++==--::··...···:--===--:·.
..·-=+*##%%##*++=--:::::···········::-==+*####**+=-:··....··:-=+**#**+=-::·......··::----:::·····:::--:::·.
.·:-=++**++==-:··... .....·······:::::---===---::·... ...··:-------:····......·::--===---::::::-----::·.
..··::::::··.. ...............···...... ....·····..···......··:-===++===-----------::·.
..····....··:-==++**+++==---------::·.
..····...··::-=+******++==-------::··.
..:·:······:-=+**####**+==------:::·..
·.:·:·····:--=+*#%%%##*+==----::::··..
·.:·::···::-=+*##%%%##*+=--::::····..
·.:::::·:::-=+*#%%%%##*+=-::·····....
............. .....········... .....··...........········.::-:::::--=+*##%%##*+=-:··........
.......·····:::::::········:::------::·.. ..·::--====---::::::---====---::-:::::--=+*#####*+=-:··..
..·····::::---=====---:::::::--======--:·. .·:-+*##%%%##*++=====++******++=-:::·:::-=+**###**+=:·..
.:-+*#%@@@%%#*+=-::···········...···::-=+**####*+==-::···::-=+*#%%%%#*+=-:···...········.. .··:::::·..
.·:-=+*****+=-:·.. ......·······::---=====--::···...··::--======-::·.........······... ..·:---::·..
..·::::::::·.. .............·········..... ....·······... . ...·······.......··:-----::·.
..···:::···....··:-====--:·.
.··::::::::····::-==++==-:·.
..·::-------::::--==++++=-:·.
.·::-===+===-----==+++++=-:·.
.··:-=++***++=======++++==-:·.
..·:-=+*####**++=====+++==-:·..
...···:::::···... ........ ........... . ....·:-=+*#%%%%#**++========-::·.
.......············::-==+++++=-::·.. ..···:::····.....···:::::::···.....··:-=+*#%@@@%%#*+==-------::·..
.......···:::------::---==+**####**+-:·.. .·::-=====--:::·:::--===++==--:······::=+*#%@@@@%%#*+=-::::::···...
.·-+#%@@@@%#*+=-:···...·········..···::-=++**#**++=-:·····:-=+*#%@@@@%%#*+==----======--:··. .··:---::·..
..·:=+*****+=-:·.. ..........···:::--=====--::··...···:--=++++++==-::···:::------:··.. .·::----:·..
..··::::::·.. ............··········..... .....····::····......···::::::··.. ..·:-==--:·..
.....········.. .··:-===-::·.
...······... ..·:-=++==-:·.
..······.......··:-=+**+=-:·..
..·············::-=+*#**+=:·..
..··:::::::::::--=+**##*+=:·..
.·::--===------==+**###*+=:·.
..··:::::::::···................. ....... .·:--=++++++====+++**##*+=-:·.
.....·::-=+********+=-::··...····::::···.... ....·······... .·:-=+**###***+++++++***+=-:·..
...······:::--=+*%@@@@@@@@@#*=-:·······::-----::··......··:::--::··.. .·:-=+*#%%%%%##*+++===+++=-::·.
██████╗ ███╗ ███╗███╗ ██╗██╗ ███╗ ███╗ █████╗ ████████╗██╗ ██╗
██╔═══██╗████╗ ████║████╗ ██║██║ ████╗ ████║██╔══██╗╚══██╔══╝██║ ██║
██║ ██║██╔████╔██║██╔██╗ ██║██║█████╗██╔████╔██║███████║ ██║ ███████║
██║ ██║██║╚██╔╝██║██║╚██╗██║██║╚════╝██║╚██╔╝██║██╔══██║ ██║ ██╔══██║
╚██████╔╝██║ ╚═╝ ██║██║ ╚████║██║ ██║ ╚═╝ ██║██║ ██║ ██║ ██║ ██║
╚═════╝ ╚═╝ ╚═╝╚═╝ ╚═══╝╚═╝ ╚═╝ ╚═╝╚═╝ ╚═╝ ╚═╝ ╚═╝ ╚═╝$ open /benchmarks/omni-math/tasks/test--9616b78e-5ac8-…▌ posts · files
Omni-MATH / A hexagonal prism has a height of 165 cm. Its two hexagonal faces are regular…
Problem
Answer published by the source. Consult the official source to check your work against its answer.
problem
A hexagonal prism has a height of 165 cm. Its two hexagonal faces are regular hexagons with sides of length 30 cm. Its other six faces are rectangles. A fly and an ant start at point on the bottom face and travel to point on the top face. The fly flies directly along the shortest route through the prism. The ant crawls around the outside of the prism along a path of constant slope so that it winds around the prism exactly times, for some positive integer . The distance crawled by the ant is more than 20 times the distance flown by the fly. What is the smallest possible value of ?
Plain-text mathematical notation (without MathML)
A hexagonal prism has a height of 165 cm. Its two hexagonal faces are regular hexagons with sides of length 30 cm. Its other six faces are rectangles. A fly and an ant start at point X on the bottom face and travel to point Y on the top face. The fly flies directly along the shortest route through the prism. The ant crawls around the outside of the prism along a path of constant slope so that it winds around the prism exactly n+(1)/(2) times, for some positive integer n. The distance crawled by the ant is more than 20 times the distance flown by the fly. What is the smallest possible value of n?
Original LaTeX notation
A hexagonal prism has a height of 165 cm. Its two hexagonal faces are regular hexagons with sides of length 30 cm. Its other six faces are rectangles. A fly and an ant start at point \(X\) on the bottom face and travel to point \(Y\) on the top face. The fly flies directly along the shortest route through the prism. The ant crawls around the outside of the prism along a path of constant slope so that it winds around the prism exactly \(n + \frac{1}{2}\) times, for some positive integer \(n\). The distance crawled by the ant is more than 20 times the distance flown by the fly. What is the smallest possible value of \(n\)?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
9616b78e-5ac8-5a9a-b25d-f5f9feb462f8- task_key
test--9616b78e-5ac8-5a9a-b25d-f5f9feb462f8- task_revision_id
- 1
- config / split
- / test
initial import