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Create: 2025-03-16 Update: 2025-07-10 21:51:50

на Московской математической олимпиаде была сегодня такая задача

«У хозяйки есть кусок мяса, которым она хочет накормить трёх котиков. Раз в несколько секунд хозяйка отрезает кусочек мяса и скармливает его одному из котиков на свой выбор, причём каждый кусочек должен составлять одну и ту же долю куска, от которого его отрезают. Через некоторое время хозяйка убирает остаток мяса в холодильник. Может ли она скормить котикам поровну мяса?» (А.Кушнир)

другими словами, можно ли разбить члены какой-нибудь геометрической прогрессии с 0<q<1 на 3 группы с одинаковыми суммами?

любая хозяйка, которая умеет резать мясо в золотом сечении, решит задачу для 2 котиков; для 3 котиков попробуйте решить на бумажке; для 4 котиков покажу попозже (пусть пока будет возможность подумать), как воспользоваться компьютером; какой ответ для 5 котиков — хотел бы знать

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Forwarded from Компьютерная математика Weekly (Grigory Merzon)

на Московской математической олимпиаде была сегодня такая задача

«У хозяйки есть кусок мяса, которым она хочет накормить трёх котиков. Раз в несколько секунд хозяйка отрезает кусочек мяса и скармливает его одному из котиков на свой выбор, причём каждый кусочек должен составлять одну и ту же долю куска, от которого его отрезают. Через некоторое время хозяйка убирает остаток мяса в холодильник. Может ли она скормить котикам поровну мяса?» (А.Кушнир)

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Telegram auto-delete message, expiring invites, and more

elegram is updating its messaging app with options for auto-deleting messages, expiring invite links, and new unlimited groups, the company shared in a blog post. Much like Signal, Telegram received a burst of new users in the confusion over WhatsApp’s privacy policy and now the company is adopting features that were already part of its competitors’ apps, features which offer more security and privacy. Auto-deleting messages were already possible in Telegram’s encrypted Secret Chats, but this new update for iOS and Android adds the option to make messages disappear in any kind of chat. Auto-delete can be enabled inside of chats, and set to delete either 24 hours or seven days after messages are sent. Auto-delete won’t remove every message though; if a message was sent before the feature was turned on, it’ll stick around. Telegram’s competitors have had similar features: WhatsApp introduced a feature in 2020 and Signal has had disappearing messages since at least 2016.

на Московской математической олимпиаде была сегодня такая задача

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