- #1
jdinatale
- 155
- 0
Ok, so this problem looks like an induction problem to me, so I used that, but I only got as far as the induction hypothesis. The hint says to use the pigeon hole principle. I'm not sure how to use that for this problem.
A Math Olympiad problem is a challenging mathematical problem designed to test the problem-solving skills and critical thinking abilities of students. These problems often require creative thinking and advanced mathematical concepts to solve.
Induction is a mathematical proof technique used to prove that a statement holds for all natural numbers. It involves proving that the statement holds for a base case (usually n=1) and then showing that if the statement holds for a particular value of n, it also holds for n+1.
The pigeon hole principle is a mathematical principle that states that if there are n pigeons and m pigeonholes, and n>m, then at least one pigeonhole must contain more than one pigeon. This principle is often used in combinatorics and counting problems.
Induction is often used in Math Olympiad problems to prove that a statement or formula holds for all natural numbers. This technique is particularly useful for proving formulas involving sums and products.
The pigeon hole principle is often used in Math Olympiad problems to show that a certain outcome or arrangement is impossible. It can also be used to prove the existence of a solution to a problem by showing that there must be at least one possible outcome.