Maths Olympiad Daily Problems

Source: Allen IOQM Mock Posting Date: 4 September 2025 Section 2 Problem 1:

A house has an even number of lamps distributed among its rooms in such a way that there are at least three lamps in every room. Each lamp shares a switch with exactly one other lamp, not necessarily from the same room. Each change in the switch shared by two lamps changes their states simultaneously. Prove that for every initial state of the lamps there exists a sequence of changes in some of the switches at the end of which each room contains lamps which are on as well as lamps which are off. try really good problem of graph theory

🚀 #ProblemMODP 18 Try and send ur solution :)

Try #ProblemMODP 15 ,9, 13 , and send ur solutions :)

🚀  #ProblemMODP 17 Send your solution :)

🚀 #ProblemMODP 16 Send your solution :)

🚀 #ProblemMODP 15 Send your solution Also try #ProblemMODP 9 and 13 and send ur solution :)

What's the radius? please 🙏🥺

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🚀 #ProblemMODP 13 Send ur solution Also solve #ProblemMODP 9 and 10 and send ur solution :)

IOQM 2025 Final Answer Key

🚀 #ProblemMODP 11 Send ur solution with explanation:)

🚀 #ProblemMODP 11 Send ur solution :)

🚀 #ProblemMODP 10 Send ur solution