benchmarks.wiki / Public workspace
.·:=+#%%%#*+=-:··....····::::::····::--=++**#**+=-:·.. ..·:-=++****++======++*#####**+=-:···.··::-=+***+=-:·.
.·:-=+*++=--:·.. ...············::---===--::·.. ..··:--=====---::::::-***##**+=-::·....··:-=++**+=-:·.
..···::··... ..............·······... ...·········......::++***++==-:··....··:-==++*+=:·..
..::==++++==-:··......·:--=+++=-:·..
..··--====--::·.......·:--=++++-:·..
.·::-----::··......··:-==+**+=-··.
..··:::::::··......·::-=+***+=-:·.
..··:::::········::-=+**##*=-:·.
...··::::::::::::--=+**###*=-:·..
..··:::::::::···············..... ......···.... ..·::-----------==++*####*=-:·.
..·:=+*********++=---::---------::··......··::::::::·.. .·::-==++++=====+++******+=:·..
...·:-+*%@@@@@@@@@@@%*++=====++++++==-::···.···::--==--::·. ..:-=+**###***++++++++++++=-:·.
.·:-==++=-:··......··::---==-----==++*#%%@@@%#*+=:·. ...······.....··:-=++**##*++=-:::·::--=+##%@@@%#+-:·.
..·::---::·.. ...··::::::::::::--===+++==-:·.. ...····.......··::--*###**+=--:::::-=+*#%%@@%%*=-·..
...···... ...............·········... ......... ......--#####*+=--:::::-=+**#%%%##+-:..
..-=####**+=--:::::--=+*####*+=:·.
..--*###*++=-:::::::-=++****+=-·.
..--*****+=--::···::--=++**++=:·.
..:-+++++==-::·····::-==++++==:·.
..::======--::·····::-==++++==:·..
.··--===---:::··:::--==++++==-:·..
..···::::·····......·····..... ...········.... .·:---==----:::::--==+++++==-:·..
.·:-=+*****++==-------------::···......··:--=====--:··.. ...:--=======------===+++++==::·..
.·:=+#%@@@@@@@@%#**++++++++++++=-::······:-==+****++=-:·. ..·:-=++***+++=============--:·..
..·····.. .··:--=======+++*#%@@@@@@@@@@@#*=-:·............ .·:-==+++==-::·····:-=+*#%@@@@@%#+=:·..
...·.... ..··:::---------==+*********+=-:·.. ..·::--+++==-::::::-=+*#%@@@@@@%*=-·.
.. ....·············:::::::::··.. ....--***++=--::--==+#%@@@@@@#*+-·.
.·==##**++=-----=+*#%%@@@%#*=-·.
··==%##**+===--==++*##%##*+=:·.
··=+%%##*++==---==++****+=-:·.
··=+%%##*+==------===++==-:·..
··==###*++=--:::::----=---:··.
··==#***+==-::::::::-----:::··..
..··········.............. ...·······...........--**+++=--:::··::::-----:::··......
.·:--=+++++==--:::::::::::··.. ..·:--=====--::·······:::-+++++==--:::::::::-----:::··.....
.·:=+#%%@@@%##*+===---===---::·.. .·:-+*##%%##*+=-::····::-=+++**++==--:::::::::---::::··.....
.. ..··::::::::--=+*%@@@@@@@@@@@@@#*+=------:::··.. ..·:-=++++=--:··...··:-=*#%%@@@%##+=-:·..
..···::::::::--==+************=--:···......... ..·::----==-::····:-=+*#%@@@@@%#*=-·.
..........····:::::::::::::··... ....·--+==--::::-=+*#%@@@@@%#+=:·
··=-*++==---==+*#%%@@@@%*+-·.
··==#**++====++*##%%%#*+=:·
··++%##*+++===+++***++=-:.
::++%%#**+==========--:·. ...
::++%%#*+==--::::::::··.. ..··..
::++%#*+=--:···········.........·····..
...···:::::::············.... ....····......·······==#*+=-::··......··········::::::··.
...... ..·::-=+*****+++==-------:::··. .·::-======---::::----====*++=-:··.......···:::::----:::···.
............·:-+*#@@@@@@@%##*++====---::·. ·:=+*#%%%%#**+==---==+++****+==-:··.......··::--------:::··..
...·····.......·:-=*#@@@@@@@@@%#*++======---::··. ..·:=+*#####*+=-:··..··:-=+*#####**+=-:·..
.............··:-=+*********+=--:::········... ..·::-====--:-::·····:-=+*#%@@%#*+=:·.
... ....··:::::::::::···....... ...······-:--::·::--=*#%%@@%%*+-:.
··--=------=++*#%%%%#*=-·.
··=-++======+**###**=-:. ....
··==**++=====++++==-:·. .····.
::++#*++==------::··.. .·:--:·.
::++#*+=-::····..... .·:--==-:·.
::+=*+=::·.. ......··:--==+==-:·.
..···::::::::::::::::::::··.. .....·············:::··=-+-:·.. ..··::--==+++++==-:·
....·:-==+**********+++++++==--:·. .·:-========-----=======--:-:·. .··:-==+++****+=--:·.
.......··:-=*#%@@@@@@@@@@@%###***+==-:. .:=+#%@@@@@%#**+++++++***++=--:·. .·:-=++*******+=-::·..
..··:--===--::··....··:-=+*#%%%##*+==-::::::::::··.. .·:-+#%@@@@@@%*+=:··...··:-==+++++=--:·.... .....
...········.... ...·:--=+++++==-::····....·...... ..·:-=++***+==-:···...··:-=+**##*+=-:·. ....
...... ...···:::::···.... ...····::····.·······::-=+*###*+=-·. ..··.
..:·::·::--=+**#**+=:·. .·:::·.
·.::------==++++==-·. .·:---:·.
··-:=-----------:·.. ·:-=+=-:·.
··--=--:::·····... .·:=+**+=-:·.
··-:-::·... ..·:-=+#%#*+=-:·.
··:·:·. ..··::-=+*#%@%#*+=-:·
...············:::::::::··.. ....·····················.·.. ..·:-=+**##%%@@%#*+=:·.
..·:--=++*****++++++****++=-:·. .·:-=++++++====---=====--::·.. .·:-+*#%%@@@@%%%#*=-:·.
..·:=+*%@@@@@@@@@@@@%%%%##*+=-:. .·-+#@@@@@@@%%#*+++=+++++==-:·.. .·-=*#%@@@@@@%##*+--:·..
..·:=*##%%%##*+==-----=+**#%%%%#**+=-:···........ .·:=*%@@@@@@@@@#+-:·.. ..··:--===--:··......··::::··.
..·:-=======--::·····::--======--::·.... ..·:-=+*******+=:·.. .·:-==+++==-:·.. ..·:::::·..
..········..... .....········.... ....··:::::::··.. ..·:-=++*++=-:·. .·:--=--:·.
. ..··:-=++++==-·. ·:-=++=-:·.
. ..··::--====--:·. .·-+*#*+=-:·.
..··::::::::::··.. .·:=*%%#*+=-:·.
..·····........... ...·:-+#@@%#*+=-:·.
...... ....··:--=+#%@@@%#*+=-:.
. . ..·:-==+*#%%@@@@@%#*+=:·.
..............·····::::···.. ..······················... .·:-+*#%@@@@@@@@@@%#+-:·.
.··::---====---====+++++==-:·. .·:-=++***++==----------:::··. .:-+*%@@@@@@@@@@%##+=-:·.
..·-=+*##%%%%%%%########**+=-·. .:=*%@@@@@@@@%*+==---------:··. ·:=*%@@@@@@@@@%#*+==-:·..
.·:=*#%@@@%%#**+++**##%@@@@@@%#*+=-:··...... .·-+#@@@@@@@@@@%+-·. .··:------::·····:--=+*++=-:·.
..·-=++**+++==-------==+++++==-::·.. ..·:-=+********+=:·. .·:-==++==-:··...··:-=+**++=-·.
..··::::::····......·········... ....···::::::::··.. .·-=+++++=-:··.....·:-+*##*+=-:.
.·:-==++++=-:·.. .·:-=*%%#*+=-:.
.·::--====-::·... ..·:-+*%@%#*+=-:.
..··::::::::··.....··:=+#@@@%#*+=-·.
.....············::-=+*%@@@@%#*+=:·.
..···::--==+*#%@@@@@@%#*+-·.
..·:-=+**##%%@@@@@@@@%#+-:.
....................······... ...···::·····................ .:-=*#%@@@@@@@@@@@@%%*=-:.
..··:::::::::::::::---===--:·.. ..:-=++****+==-:::·····::::···.. .·:=*#@@@@@@@@@@@%##*++-:·.
..·:-==+++++++++++++++++++=-:·. .·-+#@@@@@@@@%*+=-::···::::::··.. .·-=*%@@@@@@@@@@%#*+=--:·..
.·-=+*##***+++++**#%%@@@@@%#*+=-::··..... .·:=*%@@@@@@@@@@#=:. .·:--=====-------=+*#%%@%#+=:·.
.·:-=+++===------===++++++==-:··.. ...·:-=+*********+-:. .·-=++**++=--::::--=+*#%%%*+=:·.
..··::::··················... ....···:::::::::··.. ·:-=+****+==-::··::-=+*#%@%#+=:·.
.:-++****+==-:·····:-=+#%@@%#+=:·.
.·-=++++++=--:·····:-=+*%@@@%#+=:·.
··--=====---::···::-=+*%@@@@%#+=:·.
..::::------::::--=+*#%@@@@@%#+-·.
...···::---=====++**#%@@@@@@%*=:·.
..·:-==++***####%%@@@@@@%*=-·.
.......... ........... ..···::::···.... .......... .·:-=+*#%%@@@@%%%%%%%%##*=-·.
...··::::····.....··:::---:::·.. .··:-=+****+=--:··.....···::::··.. .·:-+*%@@@@@@@@@%%###**++=-·.
..··::-==-----:::---=======-:··. .·-=*#@@@@@@@#*+-:··...···::--::··.. .·:=*#@@@@@@@@@@%##*+==--::·.
.·:-=+++===---==++*######**+=--:···........ ..·:-=*%@@@@@@@@@%+-· .·:-=++++++=====++*#%%@@@@%#+-:..
.··:--=---::::::---=======-::·.. ....··:--=+********+-:·. .-=+*####*++======+*##%%%%#*=:·.
...······.......·········... ....·····:::::::···.. ·:+*#%%%%#*+==----==+*###%##+-:·.
.:-*#%%%%#*+=--::::-==+*####*+-:.
..--##%%##*+=-::::::-==+*####*=-·.
..--*****++=--::::::-=+**####*=-·.
..::=++++==---:::::-==+*#####*=-·.
..··--======-------==+*######*=:·.
..:--============++**#####*+=:·.
........ .......... ...···:::···... ....··..... ..:--=++******+++****####*++-·.
...·····.... ....··::::-:::···......··:--=++++==-:··.. ...··::---::··.. ..:-=**#%%%%###**********+==:·.
..···:::::·····::--=======-::···.···:-=+*#%%%%#*+=-:·.....··:--=====-:·.. ..·:-+*#%@@@@@%%##**++++++==-:·.
.··:--===-::::::--==++++++==--:::···········..···::-+*#@@@@@@@@%*=:. .·:=+******++===++*##%@@@@@%#*=:·.
..··::::········::---==---::·... ....···::--==++*****+=-:·. ..·:-#%%%%##*++===++*##%%%%%#*=-·.
................·······... ....······:::·····... ..·=+@@@@%%#*+=====++**#####*+-:.
··++@@@@%#*+==----==++****++=:·.
··++@@@%#*+=--::::--=+++*++=-:.
··++%%%#*+=-:::·:::-==++++==-:.
··==##*++=-::····::--==+++=-:·.
..--+++==--::····::--==+++=-:·.
..::=====--:::··:::-==++++=-:·.
............. .....········.. ...·······.... .·:=====---::::::--==++++=--:.
....... ...··::-----:::········::---==--::·.. ..·::-=====--:··........··-=======-------==+++++=--:..
....········:::-===+++++==-:::::::--==+****+==-:·......·:-=+**##**+=-:·......··:-=+++++++===---===+++++=-::..
.·::::::··...···:--==+++===---:::::::::::···::::-=+*#%@@@@@%#+=:· .:-=+*****++==--===+*#%%@@@@%#*+=-··..
...···.........··:-------::··...........···::::---===+++===-:·.. .··:-==+%##**+=====++*#%%@@@%#*+=-:·.
....······... ....··············.... ..···++@%%#*+======+**#%%%%#*+=-:·.
::**@@%#*+==---==+**####*+=-:·.
::**@%#*+==-----==+*****+=-:·.
::*+@%#*+=-:::::-==+++++=-:·.
::++##*+=-::···::--==++==-:·.
··==*++=-::·····::--====-:·.
··--+==-::··..···:---==--:·.
......·...............······... ..···::·····...........::==-::··....··::------:·.
.........···::-------:::·······:::---:::··. .·:-==++*+++=--:········::::---::··....··::------:·.
...···:::::--==+++++++==--::::::::--=====--:··......·:-+*#%@@@@%#*+=-:······::------::····.···::------:·..
..··... ..·::-=++***+++==---::::::::::·::::--=++*##%##**=-:·. .·:-=+****+==-::···::-=++*####**+==---:::··..
.. ..·::-======--:··.........····::::::-----===---:··. ..·:--====-+=--:::::-==+*######*++=--::····..
...···:····... ....··········......... ...·····=-++=-::::--=+*##%%%##*+==--:···...
··==*+=--:::--=+*##%%%##*+=-::··.....
:·==*+=---:--==+*##%%%#*+=--:·.....
:·+=*+=--:::--=+**#####*+=-:·..
:·==*+=--:::--=++*###**+=-:·..
··==+==-:::::--=++****+=-:·..
··=-+=-::···::-==+++++==-·..
.......................·····... ..············...········--=-::·····::-==+++==-:·.
......····::::-----:::········::::::::··.. .·:-==++**++==---::::--------:--:·······:--=====-:·.
..···:::-----==++++++==--:::··:::-------::·.. ..·:=+#%@@@@@@%#*++=----====++==--::··...···:--===--:·.
..·-=+*##%%##*++=--:::::···········::-==+*####**+=-:··....··:-=+**#**+=-::·......··::----:::·····:::--:::·.
.·:-=++**++==-:··... .....·······:::::---===---::·... ...··:-------:····......·::--===---::::::-----::·.
..··::::::··.. ...............···...... ....·····..···......··:-===++===-----------::·.
..····....··:-==++**+++==---------::·.
..····...··::-=+******++==-------::··.
..:·:······:-=+**####**+==------:::·..
·.:·:·····:--=+*#%%%##*+==----::::··..
·.:·::···::-=+*##%%%##*+=--::::····..
·.:::::·:::-=+*#%%%%##*+=-::·····....
............. .....········... .....··...........········.::-:::::--=+*##%%##*+=-:··........
.......·····:::::::········:::------::·.. ..·::--====---::::::---====---::-:::::--=+*#####*+=-:··..
..·····::::---=====---:::::::--======--:·. .·:-+*##%%%##*++=====++******++=-:::·:::-=+**###**+=:·..
.:-+*#%@@@%%#*+=-::···········...···::-=+**####*+==-::···::-=+*#%%%%#*+=-:···...········.. .··:::::·..
.·:-=+*****+=-:·.. ......·······::---=====--::···...··::--======-::·.........······... ..·:---::·..
..·::::::::·.. .............·········..... ....·······... . ...·······.......··:-----::·.
..···:::···....··:-====--:·.
.··::::::::····::-==++==-:·.
..·::-------::::--==++++=-:·.
.·::-===+===-----==+++++=-:·.
.··:-=++***++=======++++==-:·.
..·:-=+*####**++=====+++==-:·..
...···:::::···... ........ ........... . ....·:-=+*#%%%%#**++========-::·.
.......············::-==+++++=-::·.. ..···:::····.....···:::::::···.....··:-=+*#%@@@%%#*+==-------::·..
.......···:::------::---==+**####**+-:·.. .·::-=====--:::·:::--===++==--:······::=+*#%@@@@%%#*+=-::::::···...
.·-+#%@@@@%#*+=-:···...·········..···::-=++**#**++=-:·····:-=+*#%@@@@%%#*+==----======--:··. .··:---::·..
..·:=+*****+=-:·.. ..........···:::--=====--::··...···:--=++++++==-::···:::------:··.. .·::----:·..
..··::::::·.. ............··········..... .....····::····......···::::::··.. ..·:-==--:·..
.....········.. .··:-===-::·.
...······... ..·:-=++==-:·.
..······.......··:-=+**+=-:·..
..·············::-=+*#**+=:·..
..··:::::::::::--=+**##*+=:·..
.·::--===------==+**###*+=:·.
..··:::::::::···................. ....... .·:--=++++++====+++**##*+=-:·.
.....·::-=+********+=-::··...····::::···.... ....·······... .·:-=+**###***+++++++***+=-:·..
...······:::--=+*%@@@@@@@@@#*=-:·······::-----::··......··:::--::··.. .·:-=+*#%%%%%##*+++===+++=-::·.
██████╗ ███╗ ███╗███╗ ██╗██╗ ███╗ ███╗ █████╗ ████████╗██╗ ██╗
██╔═══██╗████╗ ████║████╗ ██║██║ ████╗ ████║██╔══██╗╚══██╔══╝██║ ██║
██║ ██║██╔████╔██║██╔██╗ ██║██║█████╗██╔████╔██║███████║ ██║ ███████║
██║ ██║██║╚██╔╝██║██║╚██╗██║██║╚════╝██║╚██╔╝██║██╔══██║ ██║ ██╔══██║
╚██████╔╝██║ ╚═╝ ██║██║ ╚████║██║ ██║ ╚═╝ ██║██║ ██║ ██║ ██║ ██║
╚═════╝ ╚═╝ ╚═╝╚═╝ ╚═══╝╚═╝ ╚═╝ ╚═╝╚═╝ ╚═╝ ╚═╝ ╚═╝ ╚═╝$ open /benchmarks/omni-math/tasks/test--73c3d088-709a-…▌ posts · files
Omni-MATH / A Vandal and a Moderator are editing a Wikipedia article. The article originally…
Problem
Answer published by the source. Consult the official source to check your work against its answer.
problem
A Vandal and a Moderator are editing a Wikipedia article. The article originally is error-free. Each day, the Vandal introduces one new error into the Wikipedia article. At the end of the day, the moderator checks the article and has a chance of catching each individual error still in the article. After 3 days, what is the probability that the article is error-free?
Plain-text mathematical notation (without MathML)
A Vandal and a Moderator are editing a Wikipedia article. The article originally is error-free. Each day, the Vandal introduces one new error into the Wikipedia article. At the end of the day, the moderator checks the article and has a 2/3 chance of catching each individual error still in the article. After 3 days, what is the probability that the article is error-free?
Original LaTeX notation
A Vandal and a Moderator are editing a Wikipedia article. The article originally is error-free. Each day, the Vandal introduces one new error into the Wikipedia article. At the end of the day, the moderator checks the article and has a $2 / 3$ chance of catching each individual error still in the article. After 3 days, what is the probability that the article is error-free?
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
73c3d088-709a-54eb-912d-fd213e5cff9e- task_key
test--73c3d088-709a-54eb-912d-fd213e5cff9e- task_revision_id
- 1
- config / split
- / test
initial import