IOQM2022 Part-4 скачать в хорошем качестве

IOQM2022 Part-4

#ioqm2022 #imo #olympiad_maths IOQM2022 Questions 23 & 24 𝐼𝑛 𝑎 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 𝐴𝐵𝐶, 𝑡ℎ𝑒 𝑚𝑒𝑑𝑖𝑎𝑛 𝐴𝐷 𝑑𝑖𝑣𝑖𝑑𝑒𝑠 ∠𝐵𝐴𝐶 𝑖𝑛 𝑡ℎ𝑒 𝑟𝑎𝑡𝑖𝑜 1 : 2. 𝐸𝑥𝑡𝑒𝑛𝑑 𝐴𝐷 𝑡𝑜 𝐸 𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝐸𝐵 𝑖𝑠 𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝐴𝐵. 𝐺𝑖𝑣𝑒𝑛 𝑡ℎ𝑎𝑡 𝐵𝐸 = 3, 𝐵𝐴 = 4, 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟 𝑛𝑒𝑎𝑟𝑒𝑠𝑡 𝑡𝑜 𝐵𝐶^2. "Let N be the number of ways of distributing 52 identical balls into 4 distinguishable boxes such that no box is empty and the difference between the number of balls in any two of the boxes is not a multiple of 6. If N = 100a + b, where a and b are positive integers less than 100, find a + b."