|
|
4 2 1 3 |
| Original Problem: |
2. Process
The method I used for solving the problem was to make a list of all the different orders of flavors. This is like the way I solved the rectangle problem. T he first thing I did to make the list was assign a number to each flavor. I did this because it is easier to write a single number than it is to write a whole word. That made the list much easier to make.
|
Flavor |
Number |
| Chocolate |
1 |
| Vanilla |
2 |
| Strawberry |
3 |
| Orange |
4 |
I thought of each combination of flavors as a line of numbers that were going vertical. Like this:
|
|
4 2 1 3 |
So I started making my list.
| 1
2 3 4 |
| 1
2 4 3 |
| 2
1 4 3 |
| 2
1 3 4 |
I had two problems with this list. First, making a list of vertical numbers was going to take a lot of paper. Second it was confusing to keep track of what orders I had already written down.
Then I thought, if you turned each vertical number on its side it would be one whole number with four places. This idea did two important things. It made my list much shorter and it gave me a way to put the list in order. Since each flavor combination was a number, I made my list from the least number to the greatest. Each "flavor number" had to start with a 1, 2, 3 or 4. That means it was a number in the one thousands, two thousands, three thousands or four thousands.
Since I wanted to go from least to greatest I knew I had to start with the numbers that started with 1. The next digit in the thousands group had to be a 2, 3 or 4 and by the same thinking, the least number would have a 2 in the hundreds place. So the first number had to be 1234. I wanted to list all the thousands group first so the next number started with a 1, and I tried keeping the 2 in the hundreds place. The only change was to switch the ones and tens place to get 1243.
There were no more numbers that started with 12 so I made the hundreds place 3 instead. That left 2 and 4 for the tens and hundreds place and the smallest number I could make was 1324. Then the other number starting with 13 had to be 1342. Now I was getting the pattern. It was easy to list 1423 and 1432 next. My list now had 6 numbers on it.
|
1234 |
| 1243 |
| 1324 |
| 1342 |
| 1423 |
| 1432 |
Next I did the same thing only with the numbers in the two thousands. The first number started with 2 and had a 1, 3, or 4 in the hundreds place. The 1 made it smallest so I added the pair 2134 and 2143 to the list. There was always a pair of numbers with the same thousands and hundreds digits. I went on to the numbers starting with 23 and 24 in the same way and added four more combinations to the list.
|
1234 |
2134 |
| 1243 |
2143 |
| 1324 |
2314 |
| 1342 |
2341 |
| 1423 |
2413 |
| 1432 |
2431 |
I only listed the numbers to the 3,000 group before I figured the final pattern out. There were 6 numbers in each thousands group. I didn't even have to fill out the rest of the table. (But I did.)
|
1234 |
2134 |
3124 |
4123 |
| 1243 |
2143 |
3142 |
4132 |
| 1324 |
2314 |
3214 |
4213 |
| 1342 |
2341 |
3241 |
4231 |
| 1423 |
2413 |
3412 |
4312 |
| 1432 |
2431 |
3421 |
4321 |
My Answer
So I only needed to multiply 6 by the 4 different thousands place numbers (flavors) to get my answer. There are 24 different flavor combinations at the store.
3. Evaluation
I thought the problem was easy. I liked the problem because it had something to do with a pattern. The hardest part was finding out the pattern to make sure my list was complete. I learned what a factorial is. I'm proud I figured out the problem in one day.
