My Favorite Math Problem
What are all 3 ordered triples of integers (a,b,c), with 0<a≤b≤c, for which 1/a+1/b+1/c=1?
Hint 1
Hint 2
Hint 3
Solution
Deciding my favorite math problem was a hard choice to make. The problem above stuck out the most because of the higher level thinking skills needed. I think that students should face higher level thinking problems in order to exercise their skills. This is an essential part of learning mathematics. In the problem, the students are provided with the equation 1/a+1/b+1/c=1 and told that there are 3 solutions. The students know that a,b, and c are greater than 0 and that they can all be equal. That leads you to the first hint. Each of the hints that are provided build off of each other to help the students through the process of solving the equation. By the end of the problem the students will realize that if you start with the largest fraction possible you can keep reducing it to find the next solution.
What are all 3 ordered triples of integers (a,b,c), with 0<a≤b≤c, for which 1/a+1/b+1/c=1?
Hint 1
Hint 2
Hint 3
Solution
Deciding my favorite math problem was a hard choice to make. The problem above stuck out the most because of the higher level thinking skills needed. I think that students should face higher level thinking problems in order to exercise their skills. This is an essential part of learning mathematics. In the problem, the students are provided with the equation 1/a+1/b+1/c=1 and told that there are 3 solutions. The students know that a,b, and c are greater than 0 and that they can all be equal. That leads you to the first hint. Each of the hints that are provided build off of each other to help the students through the process of solving the equation. By the end of the problem the students will realize that if you start with the largest fraction possible you can keep reducing it to find the next solution.