Number Theory - The question asks for the smallest natural number 'a' such that 'a456' is divisible by 11 [1] Education/Career - In India, aspiring railway workers often study for years for the entrance exam [1] - The railway entrance exams in India can be brutally hard [1]

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HS2, the over-budget railway, is a lesson in failure. Critics were bought off and losers were compensated. Yet those who opposed HS2 at the start oppose it still https://t.co/YQAxVcSYwh ...

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Core Insights - Jacobs has been appointed as a multi-disciplinary consultant to Iarnród Éireann (Irish Rail) for the expansion and modernization of a section of Ireland's rail network, aiming to enhance capacity and passenger experience over an 87-mile (140 kilometer) route from Galway to Portarlington [1][2] - The project will focus on increasing track capacity, decarbonization, higher speeds, and service frequency, with a framework agreement lasting four years and an option to extend for another four years [2][3] - The initiative is supported by the National Transport Authority and is part of Project Ireland 2040, aligning with the National Development Plan 2018-2027 to promote sustainable mobility and climate resilience [3][4] Company Overview - Jacobs operates across various sectors including Advanced Manufacturing, Cities & Places, Energy, Environmental, Life Sciences, Transportation, and Water, with approximately $12 billion in annual revenue and a workforce of nearly 45,000 [5] - The company has extensive experience in global rail infrastructure projects, including significant initiatives in New York City, the U.K., Malaysia, and the UAE [6]