I really enjoyed this week mainly because our class was able to spend one lecture day on problem solving. The reason why I enjoy these days is because we kind of get away from all the 165 concepts, and complexity and just focus on one problem that merely covers one concept from the week. These problems also help us practice Polya's problem solving techniques, which is always helpful. This week the problem was called "penny piles". The problem involved two drawers, one of which has 64 pennies while the other has 0. The goal was to get 48 pennies in one drawer by cutting the pennies in either drawer by half and adding it to the other.
Solution
Original : [ 64 ] [ 0 ]
1st Cut : [ 32 ] [ 32 ]
2nd Cut: [ 16 ] [ 48 ]
Immediately when I looked at the problem I was able to solve the problem, however I didn't use any of the problem solving techniques. The problem also asked to try more numbers, and figure out which numbers between the range [0,64] didn't work. My partner and I weren't able to find a number that didn't work, but the methods we used to come up with this conclusion wasn't efficient. We just tried random numbers and it definetly got more confusing because it wasn't organized. This week we learned about different sorting strategies, and ways we can solve problems efficiently. We ended up using a tree diagram to sort our answers, but we also realized that there were many more ways to solve the problem.
For the upcoming weeks I hope to familirize myself with the different sorting strategies such as insertion sort, and selection sort. I also learned that in 165 we only care about the worst speed when it comes to comparing algorithms, which is different and new to me. I also want to familirize myself with the rules of inference so I can come up with conclusions for different claims. This week we were also introduced to assignment 2 which I'm looking forward to, just because test 2 is also approaching and I need more practice.
Solution
Original : [ 64 ] [ 0 ]
1st Cut : [ 32 ] [ 32 ]
2nd Cut: [ 16 ] [ 48 ]
Immediately when I looked at the problem I was able to solve the problem, however I didn't use any of the problem solving techniques. The problem also asked to try more numbers, and figure out which numbers between the range [0,64] didn't work. My partner and I weren't able to find a number that didn't work, but the methods we used to come up with this conclusion wasn't efficient. We just tried random numbers and it definetly got more confusing because it wasn't organized. This week we learned about different sorting strategies, and ways we can solve problems efficiently. We ended up using a tree diagram to sort our answers, but we also realized that there were many more ways to solve the problem.
For the upcoming weeks I hope to familirize myself with the different sorting strategies such as insertion sort, and selection sort. I also learned that in 165 we only care about the worst speed when it comes to comparing algorithms, which is different and new to me. I also want to familirize myself with the rules of inference so I can come up with conclusions for different claims. This week we were also introduced to assignment 2 which I'm looking forward to, just because test 2 is also approaching and I need more practice.