Engineering Projects/Poppit/Howard Community College/Fall2011/501 jdjengineers

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Problem Statement

The goal for us was trying to pop up as many balloons as possible and see if it is mathematically possible to pop up all the balloons. Here are several problem statements we had. How many balloons for each color at the beginning and after a game? Do the amount of different color balloons affect the result? Does it matter that which way I start popping up the balloons? Is there any methods in Math and Statistics that I can use to calculate it? Can I just pop up all the balloons using logical thinking?

Team Members

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Joon Kim

James Morgan

Di Zhang

Summary

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We spent two weeks to do the Chunk Poppit project. The goal of this project is to find out a solution to pop up as many balloons as possible or even pop up all the balloons. In order to achieve the goal, we did several tests trying to figure out a pattern. It included comparing the amount of each color balloons at the beginning and the end of a game; starting games from different directions, such as from the left, the right and the bottom and counting how many steps to go from the beginning to the end. We didn't get a good and helpful result from doing those tests. Then we tried to just play the game basing on our logical thinking. The main idea of doing this was trying to group up all the single color balloons as many as possible. By doing in this way, we got less balloons left than simply starting it from single direction. The best we got to was 2 balloons left. Then we asked one of the math professors and an online game expert for help. Professor Lang gave us more detail ideas to test it from math division. And he suggested us to do it using shifted graphs. However, we didn't have enough time to finish this project, but the suggestions gave us a better direction if somebody needs to continue doing it in the future. In the meanwhile, we asked the online game expert to help us playing the game. She spent about 3 days and 5 to 6 hours everyday to get all the balloons popped. She had the same concept as the way we were using logical thinking. The only difference was she spent more time on it and she undo the steps to be thoughtful. It proved that it is possible that all the balloons can be popped. It is just time consuming.

Poster

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Story

The project is Chunk Poppit. The goal is to pop as many balloons as possible or even get all the balloons popped. We started with doing different tests. Through the tests, we hoped to find a pattern and corresponding relationship to pop the balloons. Joon Kim tested the relationship between the amount of different color balloons at the begining and the end of a game. James Morgan tested how many steps were cost to go from the beginning to the end. Di Zhang was responsible for starting from different directions. From the data, I couldn't find the relationship between the amount of different color balloons at the beginning and at the end. And the amount for each color balloons at the beginning doesn't have much different. They are all around 20 to 30 balloons for each color. Also, the test showed that doing from the bottom had less balloons left than doing from the left or the right. However, it would still have at least 15 to 30 balloons left doing from the bottom. It seems like simply popping from one direction didn't work.

Then we tried to play it basing on our logical thinking. We would start from the lower level. For instance, if we saw there was one red balloon by itself on top and there were some grouped red balloons at the bottom, we won't pop the grouped red balloons. we would wait for the group rise up and group up the single red balloon. When we tried to pop up the balloons in the middle, we would look at the lower levels, trying to pop the balloons which were grouped horizontally first because once we pop the balloons in the middle, the following balloons would rise which might cost horizontal grouped balloons separate.

The best result we can get from playing it basing on logical thinking was 4 left and 2 left.

Then we asked Professor Lang and an online game expert for help. Professor Lang showed great interest in it and gave us some great advices. He said,"You might analyze the colors in the top row and compare with colors in rows below to see what balloons you will need to have when they rise to the top. This could be done by doing a row-by-row comparison of colors to look for any patterns and what colors appear in which columns in each row. Analyze column-by-column to see what colors appear in each column. Perhaps some sort of correlation analysis, either one-dimensional or two-dimensional would help. You might apply the concept of shifts in a way similar to what you do with the graphs of functions." This suggestion is also about counting the color balloons. However, it had more details. That might be the reason why we couldn't find a relationship by counting colors before, because the method we used was too general. This might narrow down the possibilities. And the graph shifting model part was very interesting too. We need to do more research to actually put it to practical. Since we don't have enough time to do the project, we haven't figure out a good way to test it yet. So we didn't do it but it is a good direction to go if we want to continue it in the future.

Lorita Yau told me she played the game for three days, about 5 or 6 hours everyday, she finally got all the balloons popped. The pictures on the right are the proves. We saw how she did it. Basically, we had the same concept. She tried to get all the single color balloons grouped up. And she followed the rules I mentioned in the week 0 activities. The only difference was she was really patient and spent a lot of time to play one game. She tried to be really thoughtful from step to step and she undo the steps once she messed up. We don't know if undoing steps is agaist the rules, but it proved that it is possible to pop up all the balloons. It just required a lot of thinking and energy. It was a breakthrough for our team.

Decision List

1. The amount of different color balloons are given randomly, but each color balloons have approximately same amount.

2. Popping simply from one direction won't work.

3. Have to group up all the single same color balloons.

Material List

The material we used was computer and Pogo.com.

Software List

We didn't use any software.

Time

We spent almost two weeks to get to where we are at now. If we want to find a final solution for this project, we will probably consume at least 2 months.

Tutorials

Consulting math professor is nessacery. And doing large amount of tests in significant.

Next Steps

The next step will be analyzing the color balloons in each row and column and use shifted graph method to find out a pattern. You might analyze the colors in the top row and compare with colors in rows below to see what balloons you will need to have when they rise to the top. This could be done by doing a row-by-row comparison of colors to look for any patterns and what colors appear in which columns in each row. Analyze column-by-column to see what colors appear in each column. Perhaps some sort of correlation analysis, either one-dimensional or two-dimensional would help. You might apply the concept of shifts in a way similar to what you do with the graphs of functions.