Art of Problem Solving

2024 AMC 10B Problems/Problem 25: Difference between revisions

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Replaced content with "The test will be administered in November 2024. It should be replaced with an actual problem later. I added this text because of weird characters on it."
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H̵̨̡̨̡̨̧̡̢̢̡̡̡̧̨̧̢̨̧̨̡̡̧̨̛̛̛̛̛͙̳̘͕̹̦̳͓̥͕͉̼̗̤̥͕͕̜̬̲̗̭͇̻̫̖̼̻̤̣̰̱̪̯̼̲̖͕̘̖͖̬͎̻̖̣̯̲̤̩̯͍̜͚̪͉̳̤͕͖͔̯̩̩̝̯̯͈̰͈̰̬̞̱̭̱̬͖̬͎͇̪͈̜͓̪̩̟͕̞̖̤̰̥͎̲̟̰̰̟̲̹̰̞̟͈͚̺̺͓̰͇͉̞̭̬̤͎̜̤̥̞͉̜̟̮͕̼̳͍̰̩̪̼̜͙̲͓̳̱͙͚̪̤̖̠̞̠̞̖̺̣̘͉͔͙̭̘̲̟͓̯̜̞̖̗̮̟̣̦͖̞̫̗̺͍͚̗̙̺͕͇̜͉̮̦̆̽̐̈̍͛̀͐̀́̽̋̓̀͂̌̄̊̈́͗̎͑͛̽̍̾̀̽̅͒̋̈́͒͊̃͑͆̈̇̾̊̀̌̀̽́̂͋̊̎͒̽̇̀̏̈́̃̿͑̾̂͊̇͒̈́͊̑̈́̑̀͋̽̓̿̇̽̉̆̌͐̄̇̔̒̃̈̃͆͑̑̑̈́̀́̎̓͌̌̃͊̈́̆͌̾̆̈́̾̈́͌̎̽̀̀̇͑͗̏̒͑͐̽͑̈̈̀̃̋̈͗̈́́͂̃̎̒̓̐̓̕̚̕̕͘̕͘̚͘͘͘̚͜͝͝͝͝͝͠͠͝͠͝͝͝͝͠͠ͅͅͅͅe̵̡̨̨̡̨̡̧̨̨̨̨̨̛̛̛̛̯͎͇̯͉̮͉̣̞͎̰̤̹̳̹̱͔̗͉̖̗͚̲̘͖̙̹̤̫͇̼̼̯̹̯̖̰͔̩̦͕̻̗̠̰͎̟̝͇̣̫͓̰̻̭͔̥͇͉͈̟̜͍̭̼̖̩̗̣̲̹͈̪̙̤̱͍̻̘̘̱͈͔̳͔͆̊́̃̊̋̿̋̒́͛̀̈̀̇̊͑̈́̅̐̒̿̈̋͆͒̒̑̾́͋͐̑̎̏́͒̃̉̔͛̆̑͂͐͌͆̅͂̑̌̂̂̉̉̿̊͛̐̑̎́͆́͊̽̈́͛́̀͊͛̒̆͌͐͛̃͋̆̄̌̓͛͋̌͒̊̈́́͛͐̀̈́̅͛̂̀̀̾̍̓́̌̃́̈́͂́͐̍̽͐́̋̀̈́̓̎̀̓́̓͋̏̇̓̐̏̄͆̒̂͊̒̔̽́͐̏̈́́͛͛̆̎̃̈̈́̄̽͒̀̔̍̏̈͆͛̆̚̚̚̕͘̚̕̚̕͘̕̕̚̕͜͝͝͝͝͠͠͝͝͝͠͝͠͠͝͝ͅͅͅͅ’̶̢̛̳̼͉̬̦̬̣̱̲̫̝̼̱̙̯̫̗͔̤̬̻̳̗̹̤̻̣̻̠͍̓̈́͋̎̋̆͑͊͑̈̀́̑̉̚͝s̶̨̨̧̢̨̨̧̨̡̡̢̛̤͙̦͎͍̤̜͎̲͍̪͙̥̳̳̬̖̜̯̰͓̥̟̺̗̱̥͙͇̬̥̗͓͚̹͉̺͓̜̣̯̬̗̟̞̞̣̫̼̜̗̣̫̗̮̱͕͖̺̺̣̻͎̞͎̜͎͖̝͓̺̹̲͙͔̖̹̘͇̬̤͎͖̠͔͙͎̟̟͕̝̳̦̝̙̹̦͕̱͔̰̘͚͎̣̫͇̙͍͍̖̲̜͇̖̲͓͚̘̹̤̓͐̀͛̀̆͆̓͛̎͋́̌̓̀̈́̎̅̒̐̐̑̓͂̔̇͐̍́̾̀̑͑̋̐̋̋̍̒͑́̓̈́͑̈́̒̀́̒̅͒͊̄̾̂̍̇͋̄͐̒͋͊̎̈̚͘̕̕͜͜͜͜͜͜͜͝͠͝ͅͅͅͅͅ ̶̨̨̡̡̧̡̨̢̡̨̧̡̨̛̛̛̛͚̪̤͙̱̖̠͍͙̗͓̘̮̦̣̩̬͇̩͕͇͕͎̦̖͚̝̬͍̳̭̜̮͉̹̦̲̹̠̰̗̰̭̳̻̣̞̲̩̟͕͇̭͔̺̻̣͔̲̜̱͙̘̠̙̰̠̥̻̱̱͎̩̜̞̦̦̩̗̳̤̪̮̘̠͔͕̰͖̱͚̹̞͕̻̠̙̘̞̯͓̥͙̟̱̰̦̲͍͍̟̬̹̤̼̪͇̗̪͚͕̝̲̝̻̼͍͕̯̤͎͙̩̼̮͔̬̟̳̣̞̤̻̭͕̱̝̩̜̺̝̤̼̘̬̙̺͓̻̦͕̝̮̟̥̯̠̤͍̦̾̿͛̊̅̍̆̈̌́̔͐̊͆̎̋̓͒̉̑͋̈̈́̍̾̔͂̀̇̅̂̎͗͆͛̏̑͗̂̑͌̂͂̽͊͂͊͂͌̈͆̓̈͛̿̔̽̆̀̉͒̇͌̃̉̓͂͋͂͌̈́̈́̔̄̆́̀̐̉̔̊̃͆͂́̌̊͗̔́̆̈̎̈̌̓̂͊̐̂̽͗̾̄̅̀̌̓̏̄̑͛̋̈́͑̿̓̂̉̈́̈́̈́̃̈̈́̉͐͌͊̐̽̾͑̿̆̔̀̇̀̇̎͛͐͑̒͐̎̑̌͂̄̽̓̋̐̈̑̓̾̀̉͐͒̈́̀̔̽̈́͛͆̽̎́̉̿̂͒͗̿̐͌̈́̈́̒̃̀̎͊͛̃͐̓̏̀͛̃͗̅̈̑̇͂̏͐̌̀̃̀͑̃̅͛̐̀͌̉͗̂́̄̽́̄̑̾̅̇͑̐͆́̏̓̑́̆̃̀̈́́̈́͐̋̓̕̕̕̕͘͘̚͘̚̕͘̕͘̕͘̕̕̚̚̕͜͜͜͝͝͠͝͝͝͝͝͝͠͝͝͠͝͝͝͠͝͝͝͝͠͠ͅͅͅͅͅͅͅͅͅc̸̛̛̛̛̛͕̟̭͚̩͈͇̰̲͖͖̺̫̪̦̿̐̋̆̆́̒͊̑̆̄̂̓̀͋̒̍̀̀̌́͋̄̉̽̑͆͂̈́̃́͛̀͗̎̔͑̀̄͒̐̐̎̀͊͌̉̃̊̉̀͛̽̈́̎̏̑̓͆̊̾̓̅̾̉̒̾́̍̒̈́̋̈̂̓̂͑̋̀̇͂̄̈̓̀͒͊̀͛͂́̄͒̐͊͋̈̍̍̈́̈́̔̓̊̋̋̎̍͋̂̅̿̾̒̏͐̏̊̌́̎͂̈́͑̾͂̔̈́̅̃̇̈̃̃̌͆̇͒̑͌͊̎͒̀̍̔͛̉̇̐̔͗̓̌̏͋́̔̃͗̏̃͐̌͂̃́̏̅͒̈́͐̓̉̔̊̈́̐̾̑̈̈́͐̉̀͂̈͌̎̔̅̅̀̏̑͛͆̽͊̍̋̓̀͌̌̀͋̒̌̊̊̒̇̐̐̅͑͒̽̕͘̚̚̚͘͘̕̕͘̕̕̕̚̕̕͘͜͝͝͠͝͠͠͝͝͝͝͝͝͠͝͠͠͝͠͝͝͠͠͝ͅò̶̢̨̧̡̡̧̡̢̨̡̨̢̨̧̡̡̧̢̩͕͓̩̖̰͚͈̣͈̮̹̖̟͇̼̹̱̟̺̦̹͇͎̲̦̬̳͙̦̫͕̰̼̲̗͙͙̜̮̪͓̫̮̟͕̦͉̖̣͚͓̭̞̦̠̫̬̤͇̠̤̹͇̘͔̝̤̩͈̻͓͍̯̯͇̘͙̫̰̖̘̜̰̭̰̺̙̠̖͔̬͍̖̹͚̳̮̜̳͚̯̬͍̭̩͕̱̙͕͉̳̖̩̬͉̮͚̞͈͈̫͓͚̜͕̻͕̗̱̻̱̪͚̠̙͖͓̫͓̥̟̮̬̯̮̠̟͖͇̲͚̗̟͕͔͙̠̩͙̭̯͍̬̪̙̣͎͎̗̭̣̲̹͇̖͉̙̘̳͕͍͈̦̩̥͓̜͙͇͙̘̮̲̼̬̮͙̻̗̰̭̠̱͔̘̬̙̼̙̥̩̗̮̤̖̗̫̪͇̖͚̓̚̚͜͜͜͜͜͠ͅͅͅͅͅͅͅm̸̢̧̢̛̱̙̳̬͈̘̜̭̠͔͕͕͇̼͎͙̘̗̖̳̼̦̞̯̦̙͇͚̯̫̟͎̠͖̘͐͒̓̈́͂͂̔̄̂͐͑͐͐̎̒͛̿͊̀͊̅͒̈́̏̀̀͑́́̓̀͗̅͑̔̓̈̊̓̓̋̈́́͆̇̓͐̊̓͒̍͗̉̋͆́̿̀͌͆́̀͛̈̀̈̒̈́͊̏͐̈́̈̑͋͌͆͌̐̎͋͆̂̌́͐͐̓̀͂̀̇̓̆͒̈̽̑̑͊͗̍̏̿̓̆̎̈́̓̏́̍̏̃̽͂͊̈́͗͂̽̍̽̆̃̈́͋̓̽̆̅͑̐̆̒͒̈̊͑̒̆̏̓̅̓̽͗̈́͋͐́͆̉͌̿̃̀̅͆̇̃́̐͘͘͘̕̚̕̚̕̕̚̕͘͠͝͝͠͝͠͝͠͝͠͝͠͝͠͝͝͝͝ͅi̴̡̡̢̨̨̧̧̢̢̧̢̢̡͚̹̱̲̻̘̮̳̲̘̠̻̗̲̣͓̪̹͎̜̮͖̮̻͖̳̤̟̜̥͓͉͙̘̻̦̫̹̤̝̦̬̩̥̲̳͚̥͙͔̬̮̘̤̳̮̬͖͕͕͈̻̪͕̗̜̬̫̩̟̠͉͚̞̗̩̺͖̙͎̳̯̺̥̫̰̫̗̳̞̻̹͙̲̮̥̩̖͈̬͖̮̘̫̲͖̘͈̪͖͇̹̪͔͎͖̼͓̯̥̱͍͕̺̤̦̳̜͈̬̦̠͖͔̘̙̤̲̪͖̹͓̗̩̳̰̪̹̩̫̥͂̈̒͑̈̒͋̉̑͛̿̔̈́̅̈̆̋̌̾̔̏̔̈́͗̾̽̀̒̎̾̌́͋̋͆͐̓͌̿̅̑́͌̉̂̍̅͗̈́̎̐̌͋̎̊̐̄͛̅̍͋̏̅̑̅̈́̀̑̔͑̔̒̋̋̊̆͒̚̕̚̚͘͜͜͜͠͠͝͝͠ͅn̶̨̢̠̦̪̭̞̟̩͔̳̆̿̽̿̈́̿̔̐̓͋̂̋̇̓̓͂̋̒͌̓̎̓͂̇̓̚̕͝͝͝͝ĝ̸̡̡̢̢̨̡̡̢̢̢̧̢̢̨̛͙̮̫̝͉̝̩̹̩̙̯̠͖̙͇̥̱̖̙̲͓̣̱͈͉̤̣͍͍̱͔̦͈̖̖̩̙̫̯̭͔͚̹̼̰̳̭̟̬̻̬̬̯̪͖͖̯̞͓̰̖̫̳̤͍̗̗̯̫̠̟̝̪͈̣̦̰̭̱͇̣͎͕͇̠͍̰̝̼̞̘̹̩̞͈̺̗̮͙̜͙̠̠͕̘̖̭͙͎̼͍̮̯̮̺̫͇̥̬͎̯̦̮̪̳͇̥̦̱̲͇̰͉͔̤̟̯̱̜̞̖̘͔̝͇̞͖̻̭͙̞̜͙̦̣̮̜͎̬͇̩͕͎̠̞͓̱̠̲̤̞̳͔̱̮̤̤̻̭͎̻̻͍̖̮͈͇̝͖̭̳̰͚̝͍̬͈̪̺̲͇͚͕͚͇͖̫͚͉͔̫͖͉̝͎̺͇̺̲̼͓͕͇̺̩̼̫̻̙̖̲̟̘̰͇͕̳͈͉̯̤̗̤̺͕̏͛̒͌̎̽͑̂̆̒͂̽͊͛͑̿̐̎͑̓̋̾̍̂̄̏͑̈́͗̉͂͆̑̾̇́̇́̈́͗͊̐̅̐̊̈̑͗̒͆̃͆͌̈́̽̍̆͂͗̈́̀̇̀͊͒͋̑́̒̈́̃͆̑̈͂̓̾̓̈́̽̌͋̊̈̍̏̊̊̃́͌͑͂́̍̈́̈́́͐̽̈́̀̔͊̃͒͗̆͋́̑̆͆̄͊̀̒̏́̀̓́̓̽͒̽̑́́̇̈́̾̅̀̇͛̍̃͐͗́͛̄̔͑͆̄̋̿̅̾̊̑́͑̽̂̈͌̽̔̾̔͊̓̃̓̿̂́̓̌̊́̂̈́̾̀̅̐́̌́̊̿͆̓͌̎͊̏̋̓͛̈̈́̃̅͗̇̀̔́̀̈̈̈́̾̆͐̑̀͐̍̑̒̂̂́̀̐̉͒͆́̇͋͛̓̌͋̇̀̈́́͆̉̉̉͌̑͑̈́͛̏̾̋̀̚̚̕͘̚̚̚̕̕̕̚̕̕͘̚͘̕̕̕̕̚͘̕͘͘̚̚̚̕̕̚̕͘͜͜͜͜͜͜͜͝͠͠͝͝͝͠͝͝͝͠͠͝͠͠͝ͅͅͅͅͅͅ.̷̡̢̡̧̢̛̛̟̗͉̘̹̯̝͚̦̫̖͉͙̤̲̬̠̺͈̰̠͍̲͉̦͓̺̦̰͍͕̝̬͓͉̖̬̜͖̱̲̫̜̠͎͖̙̪̖̹̗͖̜̗̳̳̤̦̠̥̻̥͈̤͙̬͈̯̣̪̱͎̩͍̳̤̹̯͐̄͒̔̾̇̔́̈̐̓́̄̅̅̑̄̍͐̀͆́̊̑̎̆̆͒̾͌̀̀̀͌̿̀̚̚̕͜͝͠͝͠͝ͅͅͅ
The test will be administered in November 2024. It should be replaced with an actual problem later. I added this text because of weird characters on it.

Revision as of 13:40, 10 July 2024

The test will be administered in November 2024. It should be replaced with an actual problem later. I added this text because of weird characters on it.