Difference between revisions of "2024 AMC 10B Problems/Problem 25"

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H̵̨̡̨̡̨̧̡̢̢̡̡̡̧̨̧̢̨̧̨̡̡̧̨̛̛̛̛̛͙̳̘͕̹̦̳͓̥͕͉̼̗̤̥͕͕̜̬̲̗̭͇̻̫̖̼̻̤̣̰̱̪̯̼̲̖͕̘̖͖̬͎̻̖̣̯̲̤̩̯͍̜͚̪͉̳̤͕͖͔̯̩̩̝̯̯͈̰͈̰̬̞̱̭̱̬͖̬͎͇̪͈̜͓̪̩̟͕̞̖̤̰̥͎̲̟̰̰̟̲̹̰̞̟͈͚̺̺͓̰͇͉̞̭̬̤͎̜̤̥̞͉̜̟̮͕̼̳͍̰̩̪̼̜͙̲͓̳̱͙͚̪̤̖̠̞̠̞̖̺̣̘͉͔͙̭̘̲̟͓̯̜̞̖̗̮̟̣̦͖̞̫̗̺͍͚̗̙̺͕͇̜͉̮̦̆̽̐̈̍͛̀͐̀́̽̋̓̀͂̌̄̊̈́͗̎͑͛̽̍̾̀̽̅͒̋̈́͒͊̃͑͆̈̇̾̊̀̌̀̽́̂͋̊̎͒̽̇̀̏̈́̃̿͑̾̂͊̇͒̈́͊̑̈́̑̀͋̽̓̿̇̽̉̆̌͐̄̇̔̒̃̈̃͆͑̑̑̈́̀́̎̓͌̌̃͊̈́̆͌̾̆̈́̾̈́͌̎̽̀̀̇͑͗̏̒͑͐̽͑̈̈̀̃̋̈͗̈́́͂̃̎̒̓̐̓̕̚̕̕͘̕͘̚͘͘͘̚͜͝͝͝͝͝͠͠͝͠͝͝͝͝͠͠ͅͅͅͅe̵̡̨̨̡̨̡̧̨̨̨̨̨̛̛̛̛̯͎͇̯͉̮͉̣̞͎̰̤̹̳̹̱͔̗͉̖̗͚̲̘͖̙̹̤̫͇̼̼̯̹̯̖̰͔̩̦͕̻̗̠̰͎̟̝͇̣̫͓̰̻̭͔̥͇͉͈̟̜͍̭̼̖̩̗̣̲̹͈̪̙̤̱͍̻̘̘̱͈͔̳͔͆̊́̃̊̋̿̋̒́͛̀̈̀̇̊͑̈́̅̐̒̿̈̋͆͒̒̑̾́͋͐̑̎̏́͒̃̉̔͛̆̑͂͐͌͆̅͂̑̌̂̂̉̉̿̊͛̐̑̎́͆́͊̽̈́͛́̀͊͛̒̆͌͐͛̃͋̆̄̌̓͛͋̌͒̊̈́́͛͐̀̈́̅͛̂̀̀̾̍̓́̌̃́̈́͂́͐̍̽͐́̋̀̈́̓̎̀̓́̓͋̏̇̓̐̏̄͆̒̂͊̒̔̽́͐̏̈́́͛͛̆̎̃̈̈́̄̽͒̀̔̍̏̈͆͛̆̚̚̚̕͘̚̕̚̕͘̕̕̚̕͜͝͝͝͝͠͠͝͝͝͠͝͠͠͝͝ͅͅͅͅ’̶̢̛̳̼͉̬̦̬̣̱̲̫̝̼̱̙̯̫̗͔̤̬̻̳̗̹̤̻̣̻̠͍̓̈́͋̎̋̆͑͊͑̈̀́̑̉̚͝s̶̨̨̧̢̨̨̧̨̡̡̢̛̤͙̦͎͍̤̜͎̲͍̪͙̥̳̳̬̖̜̯̰͓̥̟̺̗̱̥͙͇̬̥̗͓͚̹͉̺͓̜̣̯̬̗̟̞̞̣̫̼̜̗̣̫̗̮̱͕͖̺̺̣̻͎̞͎̜͎͖̝͓̺̹̲͙͔̖̹̘͇̬̤͎͖̠͔͙͎̟̟͕̝̳̦̝̙̹̦͕̱͔̰̘͚͎̣̫͇̙͍͍̖̲̜͇̖̲͓͚̘̹̤̓͐̀͛̀̆͆̓͛̎͋́̌̓̀̈́̎̅̒̐̐̑̓͂̔̇͐̍́̾̀̑͑̋̐̋̋̍̒͑́̓̈́͑̈́̒̀́̒̅͒͊̄̾̂̍̇͋̄͐̒͋͊̎̈̚͘̕̕͜͜͜͜͜͜͜͝͠͝ͅͅͅͅͅ ̶̨̨̡̡̧̡̨̢̡̨̧̡̨̛̛̛̛͚̪̤͙̱̖̠͍͙̗͓̘̮̦̣̩̬͇̩͕͇͕͎̦̖͚̝̬͍̳̭̜̮͉̹̦̲̹̠̰̗̰̭̳̻̣̞̲̩̟͕͇̭͔̺̻̣͔̲̜̱͙̘̠̙̰̠̥̻̱̱͎̩̜̞̦̦̩̗̳̤̪̮̘̠͔͕̰͖̱͚̹̞͕̻̠̙̘̞̯͓̥͙̟̱̰̦̲͍͍̟̬̹̤̼̪͇̗̪͚͕̝̲̝̻̼͍͕̯̤͎͙̩̼̮͔̬̟̳̣̞̤̻̭͕̱̝̩̜̺̝̤̼̘̬̙̺͓̻̦͕̝̮̟̥̯̠̤͍̦̾̿͛̊̅̍̆̈̌́̔͐̊͆̎̋̓͒̉̑͋̈̈́̍̾̔͂̀̇̅̂̎͗͆͛̏̑͗̂̑͌̂͂̽͊͂͊͂͌̈͆̓̈͛̿̔̽̆̀̉͒̇͌̃̉̓͂͋͂͌̈́̈́̔̄̆́̀̐̉̔̊̃͆͂́̌̊͗̔́̆̈̎̈̌̓̂͊̐̂̽͗̾̄̅̀̌̓̏̄̑͛̋̈́͑̿̓̂̉̈́̈́̈́̃̈̈́̉͐͌͊̐̽̾͑̿̆̔̀̇̀̇̎͛͐͑̒͐̎̑̌͂̄̽̓̋̐̈̑̓̾̀̉͐͒̈́̀̔̽̈́͛͆̽̎́̉̿̂͒͗̿̐͌̈́̈́̒̃̀̎͊͛̃͐̓̏̀͛̃͗̅̈̑̇͂̏͐̌̀̃̀͑̃̅͛̐̀͌̉͗̂́̄̽́̄̑̾̅̇͑̐͆́̏̓̑́̆̃̀̈́́̈́͐̋̓̕̕̕̕͘͘̚͘̚̕͘̕͘̕͘̕̕̚̚̕͜͜͜͝͝͠͝͝͝͝͝͝͠͝͝͠͝͝͝͠͝͝͝͝͠͠ͅͅͅͅͅͅͅͅͅc̸̛̛̛̛̛͕̟̭͚̩͈͇̰̲͖͖̺̫̪̦̿̐̋̆̆́̒͊̑̆̄̂̓̀͋̒̍̀̀̌́͋̄̉̽̑͆͂̈́̃́͛̀͗̎̔͑̀̄͒̐̐̎̀͊͌̉̃̊̉̀͛̽̈́̎̏̑̓͆̊̾̓̅̾̉̒̾́̍̒̈́̋̈̂̓̂͑̋̀̇͂̄̈̓̀͒͊̀͛͂́̄͒̐͊͋̈̍̍̈́̈́̔̓̊̋̋̎̍͋̂̅̿̾̒̏͐̏̊̌́̎͂̈́͑̾͂̔̈́̅̃̇̈̃̃̌͆̇͒̑͌͊̎͒̀̍̔͛̉̇̐̔͗̓̌̏͋́̔̃͗̏̃͐̌͂̃́̏̅͒̈́͐̓̉̔̊̈́̐̾̑̈̈́͐̉̀͂̈͌̎̔̅̅̀̏̑͛͆̽͊̍̋̓̀͌̌̀͋̒̌̊̊̒̇̐̐̅͑͒̽̕͘̚̚̚͘͘̕̕͘̕̕̕̚̕̕͘͜͝͝͠͝͠͠͝͝͝͝͝͝͠͝͠͠͝͠͝͝͠͠͝ͅò̶̢̨̧̡̡̧̡̢̨̡̨̢̨̧̡̡̧̢̩͕͓̩̖̰͚͈̣͈̮̹̖̟͇̼̹̱̟̺̦̹͇͎̲̦̬̳͙̦̫͕̰̼̲̗͙͙̜̮̪͓̫̮̟͕̦͉̖̣͚͓̭̞̦̠̫̬̤͇̠̤̹͇̘͔̝̤̩͈̻͓͍̯̯͇̘͙̫̰̖̘̜̰̭̰̺̙̠̖͔̬͍̖̹͚̳̮̜̳͚̯̬͍̭̩͕̱̙͕͉̳̖̩̬͉̮͚̞͈͈̫͓͚̜͕̻͕̗̱̻̱̪͚̠̙͖͓̫͓̥̟̮̬̯̮̠̟͖͇̲͚̗̟͕͔͙̠̩͙̭̯͍̬̪̙̣͎͎̗̭̣̲̹͇̖͉̙̘̳͕͍͈̦̩̥͓̜͙͇͙̘̮̲̼̬̮͙̻̗̰̭̠̱͔̘̬̙̼̙̥̩̗̮̤̖̗̫̪͇̖͚̓̚̚͜͜͜͜͜͠ͅͅͅͅͅͅͅm̸̢̧̢̛̱̙̳̬͈̘̜̭̠͔͕͕͇̼͎͙̘̗̖̳̼̦̞̯̦̙͇͚̯̫̟͎̠͖̘͐͒̓̈́͂͂̔̄̂͐͑͐͐̎̒͛̿͊̀͊̅͒̈́̏̀̀͑́́̓̀͗̅͑̔̓̈̊̓̓̋̈́́͆̇̓͐̊̓͒̍͗̉̋͆́̿̀͌͆́̀͛̈̀̈̒̈́͊̏͐̈́̈̑͋͌͆͌̐̎͋͆̂̌́͐͐̓̀͂̀̇̓̆͒̈̽̑̑͊͗̍̏̿̓̆̎̈́̓̏́̍̏̃̽͂͊̈́͗͂̽̍̽̆̃̈́͋̓̽̆̅͑̐̆̒͒̈̊͑̒̆̏̓̅̓̽͗̈́͋͐́͆̉͌̿̃̀̅͆̇̃́̐͘͘͘̕̚̕̚̕̕̚̕͘͠͝͝͠͝͠͝͠͝͠͝͠͝͠͝͝͝͝ͅi̴̡̡̢̨̨̧̧̢̢̧̢̢̡͚̹̱̲̻̘̮̳̲̘̠̻̗̲̣͓̪̹͎̜̮͖̮̻͖̳̤̟̜̥͓͉͙̘̻̦̫̹̤̝̦̬̩̥̲̳͚̥͙͔̬̮̘̤̳̮̬͖͕͕͈̻̪͕̗̜̬̫̩̟̠͉͚̞̗̩̺͖̙͎̳̯̺̥̫̰̫̗̳̞̻̹͙̲̮̥̩̖͈̬͖̮̘̫̲͖̘͈̪͖͇̹̪͔͎͖̼͓̯̥̱͍͕̺̤̦̳̜͈̬̦̠͖͔̘̙̤̲̪͖̹͓̗̩̳̰̪̹̩̫̥͂̈̒͑̈̒͋̉̑͛̿̔̈́̅̈̆̋̌̾̔̏̔̈́͗̾̽̀̒̎̾̌́͋̋͆͐̓͌̿̅̑́͌̉̂̍̅͗̈́̎̐̌͋̎̊̐̄͛̅̍͋̏̅̑̅̈́̀̑̔͑̔̒̋̋̊̆͒̚̕̚̚͘͜͜͜͠͠͝͝͠ͅn̶̨̢̠̦̪̭̞̟̩͔̳̆̿̽̿̈́̿̔̐̓͋̂̋̇̓̓͂̋̒͌̓̎̓͂̇̓̚̕͝͝͝͝ĝ̸̡̡̢̢̨̡̡̢̢̢̧̢̢̨̛͙̮̫̝͉̝̩̹̩̙̯̠͖̙͇̥̱̖̙̲͓̣̱͈͉̤̣͍͍̱͔̦͈̖̖̩̙̫̯̭͔͚̹̼̰̳̭̟̬̻̬̬̯̪͖͖̯̞͓̰̖̫̳̤͍̗̗̯̫̠̟̝̪͈̣̦̰̭̱͇̣͎͕͇̠͍̰̝̼̞̘̹̩̞͈̺̗̮͙̜͙̠̠͕̘̖̭͙͎̼͍̮̯̮̺̫͇̥̬͎̯̦̮̪̳͇̥̦̱̲͇̰͉͔̤̟̯̱̜̞̖̘͔̝͇̞͖̻̭͙̞̜͙̦̣̮̜͎̬͇̩͕͎̠̞͓̱̠̲̤̞̳͔̱̮̤̤̻̭͎̻̻͍̖̮͈͇̝͖̭̳̰͚̝͍̬͈̪̺̲͇͚͕͚͇͖̫͚͉͔̫͖͉̝͎̺͇̺̲̼͓͕͇̺̩̼̫̻̙̖̲̟̘̰͇͕̳͈͉̯̤̗̤̺͕̏͛̒͌̎̽͑̂̆̒͂̽͊͛͑̿̐̎͑̓̋̾̍̂̄̏͑̈́͗̉͂͆̑̾̇́̇́̈́͗͊̐̅̐̊̈̑͗̒͆̃͆͌̈́̽̍̆͂͗̈́̀̇̀͊͒͋̑́̒̈́̃͆̑̈͂̓̾̓̈́̽̌͋̊̈̍̏̊̊̃́͌͑͂́̍̈́̈́́͐̽̈́̀̔͊̃͒͗̆͋́̑̆͆̄͊̀̒̏́̀̓́̓̽͒̽̑́́̇̈́̾̅̀̇͛̍̃͐͗́͛̄̔͑͆̄̋̿̅̾̊̑́͑̽̂̈͌̽̔̾̔͊̓̃̓̿̂́̓̌̊́̂̈́̾̀̅̐́̌́̊̿͆̓͌̎͊̏̋̓͛̈̈́̃̅͗̇̀̔́̀̈̈̈́̾̆͐̑̀͐̍̑̒̂̂́̀̐̉͒͆́̇͋͛̓̌͋̇̀̈́́͆̉̉̉͌̑͑̈́͛̏̾̋̀̚̚̕͘̚̚̚̕̕̕̚̕̕͘̚͘̕̕̕̕̚͘̕͘͘̚̚̚̕̕̚̕͘͜͜͜͜͜͜͜͝͠͠͝͝͝͠͝͝͝͠͠͝͠͠͝ͅͅͅͅͅͅ.̷̡̢̡̧̢̛̛̟̗͉̘̹̯̝͚̦̫̖͉͙̤̲̬̠̺͈̰̠͍̲͉̦͓̺̦̰͍͕̝̬͓͉̖̬̜͖̱̲̫̜̠͎͖̙̪̖̹̗͖̜̗̳̳̤̦̠̥̻̥͈̤͙̬͈̯̣̪̱͎̩͍̳̤̹̯͐̄͒̔̾̇̔́̈̐̓́̄̅̅̑̄̍͐̀͆́̊̑̎̆̆͒̾͌̀̀̀͌̿̀̚̚̕͜͝͠͝͠͝ͅͅͅ
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Prove that two humans cannot be congruent, given that they are both of age 25 and the year is 2024. (Also know they are earthlings.)

Revision as of 14:55, 23 July 2024

Prove that two humans cannot be congruent, given that they are both of age 25 and the year is 2024. (Also know they are earthlings.)