Here are three problems to enjoy over the break!

Problem 1

Three friends make the following statements:

  • Ben says, “Exactly one of Dan and Cam is telling the truth.”
  • Dan says, “Exactly one of Ben and Cam is telling the truth.”
  • Cam says, “Neither Ben nor Dan is telling the truth.”

Which of the three friends is lying?

Source: Senior Maths Challenge 2016

Problem 2

Compute the remainder when 10002000400080016003200640128025605121024204840968192 is divided by 100020004000800160032.

Source: HMMT Guts Round, Feb 2022

Problem 3

Find the positive integer n such that 32 is the product of the real number solutions of x^{\log_2{(x^3)}−n} = 13.

Source: Purple Comet Math Meet, 2019

Happy problem solving! 

Feel free to email your solutions to [email protected] or check the solutions page in a few weeks’ time!

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