Problem Statement: There are five bales of hay. Somehow, the bales were weighed by groups instead of individually. There are ten groups, 1 & 2, 1 & 3, 1 &4, 1 & 5, 2 & 1, etc. There are eleven weights measured in kilograms that were not written down with their bale numbers, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, and 91. The problem asks you to not only find the pairs, but find out if there are more than 1 possible set of bales. Process: What I did first to try to solve this problem is write down what I knew from the problem. That did not work at all. It only made me think that this problem was even harder. I got stuck when I tried to randomly match all the bales. I got unstuck when I decided to divide all the weights by 2 until I got a number that made sense for a stack of bales. Solution: I did not find the solution for all the stacks of bale. I only got about half of them. To get those answers, I divided all the weights by 2 because it seemed like a good number to start with. I kept dividing by 2 until almost all my weights were about 20-10. Then, I divided by 2-7 on all the numbers until I got a decimal that was close to .5, like 2.5. Something like that would tell me that it's bales 2 & 3 because it is in the middle of those two numbers. I found out that that was much harder then I thought. I got numbers like 3.4167 and 1.83 which made me a little confused on what to do next. There was also some numbers that didn't get close to (1-4).5. Evaluation: This problem was, in my opinion, harder than the first POW. There's nothing wrong with a challenge though. I like challenging myself to be a better whatever, even if it's boring or too much work, it's always good for me. I think there probably is a much easier way to do and solve the whole problem. At first, I didn't understand it, but I kept re-reading and eventually I felt I had enough time to at least attempt the problem. To sum it all up, this problem was difficult and challenging and I hope that I can finish the next POW completely.
POW # 7
Problem Statement: This problem states that there are 5 ducks roaming around together, three adult ducks, and two ducklings. Their total weight combined is 14 kilograms. When two more ducks, one adult and one duckling, come along, the total weight adds up to 19 kilograms. Saying that all adult ducks have the same weight, as well as ducklings having their own common weight, how many kilograms are two ducks and one duckling?
Process: To start off, I drew a picture of three ducks (1x3), two ducklings (1x2), and their weight because that's the first thing the problem states. Next I added one more duck and duckling to represent the change of weight of 19 kilograms from 14 kilograms. After that I decided to make equations to figure out the weights of the ducks and ducklings.
Solution: First, I tried to figure out the weight of all of them by estimating numbers. I knew that, obviously, the ducks were going to weigh more. I guessed they weighed 4 kilograms. Then I added up 4 until I got close to 15. Once I got to 12 (three 4's), I knew that the ducklings must weigh 1 kilogram because I needed exactly three ducks and two ducklings in the equation. To check my answer, I added 14+4+1 to make sure that I got 19. Now knowing that the ducks weighed 4 kilograms and ducklings 1 kilograms, I just added two ducks and one duckling to get 9 kilograms. Two mothers + one duckling = 9 kilograms.
Evaluation: I felt like this problem was way too easy. I didn't really have to try hard to get my answer, it was just guessing then checking. I also felt like this wasn't educationally worthwhile because of how easy it was, but it's still my favorite POW so far.