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By January 2020, Papadimitriou had been thinking about the pigeonhole principle for 30 years. So he was surprised when a playful conversation with a frequent collaborator led them to a simple twist on the principle that they’d never considered: What if there are fewer pigeons than holes? In that case, any arrangement of pigeons must leave some empty holes. Again, it seems obvious. But does inverting the pigeonhole principle have any interesting mathematical consequences?It may sound as though this “empty-pigeonhole” principle is just the original one by another name. But it’s not, and its subtly different character has made it…

مراسلو الجزيرة نتأغلقت باكستان حدودها التجارية المهمة مع الهند عبر معبر عطاري-واغا للمرة الثانية خلال 6 سنوات، مما أدى إلى تعليق الصادرات الأفغانية إلى الهند ووجود عقبات أمام استيراد السلع منها. وبينما تتصاعد التوترات بين الجارتين النوويتين، (الهند وباكستان) تجد أفغانستان نفسها مجددًا تدفع ثمنًا اقتصاديًا باهظًا لصراع لا تشارك فيه بشكل مباشر. وقال خان الكوزي عضو مجلس إدارة غرفة التجارة والاستثمار الأفغانية -للجزيرة نت- إن إغلاق معبر عطاري-واغا بين باكستان والهند “أدى إلى توقف التجارة” مع نيودلهي بشكل كبير. وأضاف “تُعد هذه الحدود الأقل تكلفة للصادرات الأفغانية إلى الهند، حيث يتم نقل نحو 80% من الصادرات الأفغانية، وخاصة الفواكه…

League leaders Napoli moved one step closer to winning the Serie A title with a 1-0 win at relegation-threatened Lecce on Saturday, keeping the visitors three points clear of Scudetto rivals Inter Milan.Napoli move to 77 points, with Inter on 74 after they beat Hellas Verona later on Saturday. Lecce remain 17th in the standings, one place and one point above the relegation zone.A Giacomo Raspadori first-half free kick was enough to earn Napoli the all-important three points and a fourth successive win, while Lecce have now gone 12 games without victory.”It’s an important step, I can’t lie,” Napoli coach Antonio…

I’m a huge fan of Star Wars. The first movie (no, not Episode 1) came out when I was young, so I grew up thinking about the Millennium Falcon and lightsabers. Perhaps it sparked my interest in science—even if it’s not exactly science fiction. Oh, there’s a nice way to start a nerd fight: Is Star Wars “science fiction” or is it “space fantasy”?Either way, you have to admit there are things in there that look like science. I mean, anytime you deal with stuff in space, it’s an opportunity to talk about science. That’s exactly what I’m going to…

مع استمرار الحصار على غزة، بدأ الجوع يفتك بسكان القطاع وخاصة الفئات الهشة.ووفق إحصاءات أممية فإن الاحتياجات الغذائية لا تلبي لأكثر من 92% من الأطفال بين 6 – 23 شهرا ولا الحوامل والمرضعات بسبب نقص التنوع الغذائي الأدنى. كما يحتاج نحو 290 ألف طفل دون الخامسة و150 ألفا من الحوامل والمرضعات إلى التغذية والمكملات الدقيقة. ويُقدر أن أكثر من 60 ألف طفل سيحتاجون العام الجاري إلى علاج سوء التغذية الحاد فضلا عن أكثر من 16 ألفا من الحوامل والمرضعات. تفاصيل وأرقام أكثر في تقرير وليد العطار.

Monaco striker Folarin Balogun scored his first Ligue 1 goal this year following shoulder surgery, as struggling Saint-Etienne was beaten 3-1.The United States forward was picked out by Maghnes Akliouche and beat the offside trap to seal Monaco’s win from the edge of the box. The goal came in Balogun’s first Monaco start since Dec.1, 2024.Akliouche put Monaco ahead after just two minutes. Zuriko Davitashvili leveled for Saint-Etienne in the second half, three minutes before Moatasem Al Musrati put the visitors back in control.Monaco moved into second place, level on points with Marseille, which has one match in hand and…

Somewhere in an animated New York, a minion slips and tumbles down a sewer. As a wave of radioactive green slime envelops him, his body begins to transform—limbs mutating, rows of bloody fangs emerging—his globular, wormlike form, slithering menacingly across the screen.“Beware the minion in the night, a shadow soul no end in sight,” an AI-sounding narrator sings, as the monstrous creature, now lurking in a swimming pool, sneaks up behind a screaming child before crunching them, mercilessly, between its teeth.Upon clicking through to the video’s owner, though, it’s a different story. “Welcome to Go Cat—a fun and exciting YouTube…

دير رافات قرية فلسطينية مهجرة من قضاء القدس وتقع على بعد 25 كيلومترا من مدينة القدس. اجتاحها الجيش الإسرائيلي يومي 17 و18‏ يوليو/تموز 1948، في أثناء المرحلة الثانية من عملية داني، التي نفذها الاحتلال آنذاك. وتذكر المصادر الإسرائيلية أن القرية سقطت في قبضة وحدات من لواء هرئيل في نهاية العملية. الموقع تقع قرية رافات في أقصى الغرب من قضاء القدس، وتوجد على بعد 25 كيلومترا من مدينة القدس، وهي إحدى قرى وادي الصرار وقريبة من منطقة باب الوادي، على حدود قضاء الرملة. تقع القرية على سفح جبل من نهاية سلسلة جبال القدس الغربية، وتربطها بالقرى المجاورة طرق غير معبدة، خصوصا…

LOUISVILLE, Ky. — Sovereignty gave trainer Bill Mott a second Kentucky Derby victory. This time there was no doubt about it and no asterisk.Sovereignty outdueled 3-1 favorite Journalism down the stretch to win the 151st Derby in the slop on Saturday, snapping an 0-for-13 skid by owner Godolphin.Mott won his first Derby in 2019, also run on a sloppy track, when Country House was elevated to first after Maximum Security crossed the finish line first and was disqualified during a 22-minute delay.It took a few minutes for Saturday’s results to be made official while the stewards sorted out a photo…

Unlock the Editor’s Digest for freeRoula Khalaf, Editor of the FT, selects her favourite stories in this weekly newsletter.British counterterrorism officers have arrested eight men, including seven Iranian nationals, in relation to two separate alleged plots, London’s Metropolitan Police said on Sunday morning.One of the alleged plots was a planned attack on an unspecified location, police said.Yvette Cooper, home secretary, said the arrests were “serious events that demonstrate the ongoing requirement to adapt our response to national security threats”. She added: “The government continues to work with police and intelligence agencies to support all the action and security assessments that are…