Problems
Olympiad and puzzle problems with hints that open one at a time. Try them before you peek.
Prove that the fraction \dfrac{21n + 4}{14n + 3} is irreducible for every natural number n.
Choose any n + 1 numbers from \{1, 2, \dots, 2n\}. Prove that one of the chosen numbers divides another.
Two diagonally opposite corner squares are cut from an 8 \times 8 chessboard, leaving 62 squares. Can the rest be covered exactly by 31 dominoes, each covering two adjacent squares?
- An irreducible fraction IMO 1959 P1
- One divides another Classic (Erdős)
- The mutilated chessboard Classic
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