POW #8 All-Variables Sudoku
1. Solve the Sudoku puzzle that is all variables and find the values for each letter. There are three basic rules:
1) Each column, each row and each box (3x3 subgrid) must have the numbers 1 through 9.
2) No column, row or box can have two squares with the same number.
3) In addition to the above two basic rules, the puzzle can be solved by finding the values of the 9 given variables in the squares of the 9x9 grid.
At the bottom and right side of the grid are groups of similar variables. Each set of the variables is the sum of a coumn or row of the variables. 10 equations can be formed from the columns and rows of variables.
2. I started off by trying solve the puzzles first with just using the variables. I did that for a while but for some reason as I was almost done, I messed up at a part and it got very confusing and I couldn't figure it out so I gave up on that and I decided to focus on finding the values of the variables. First I started by writing out all the equations. Then I simplified some of the equations so they equaled to one letter if it was possible. After I did that I really got stuck because I did not know what to do after that. I then made a chart to see if I could just guess the numbers right for each letter. I did that for a while and I was going no where with that because I couldn't get them all to work. I'd get a few numbers and then not know what to do with the others. So then I asked Jocelyn how she got started on figuring out the values and what she did. She told me she just started to look at each number and seeing what number would work for each equation. After she told me that it was like a light bulb went off in my head and I finally could do something that was worth my time on this problem. So after I made a graph that I could keep track of which letters and numbers worked and didn't work. It was a graph where if I knew a number didn't work, I would go the the column of that letter and go down to the number I wanted and but a X. So I started with the equation m + n = a. I knew a couldn't be 1 or 2. It also couldn't be three because that would mean m or n would either be 1 or 2 and since m or n were one of the letters that simplified to 2 letters that equaled to it it couldn't be it since no 2 numbers are the same. Then I figured out that a couldn't be 4, 5, 6, 7, or 8. So it obviously was 9. and m = 4 and n = 5. Once I got those values it was easy to figure out the rest because you just had to plug in the numbers. After I got all the values, I copied the grid onto a separate sheet of paper because I wanted to do the puzzle in numbers instead of letters since it was easier for me. So I copied it, finished the puzzle, then I plugged in the values of those numbers with the matching variable into the grid on the original paper and that was when I stopped.
3. My solution is the picture to the left. Also the values of the variables are a=9 b=8 c=6 d=2 e=7 f=1 g=3 m=4 n=5. I know this is the only solution because it works with the grid.
4. I considered this problem educationally worthwhile because there were a few steps to it. I also enjoyed working on the problem because I usually enjoy doing sudoku problems. I foud this problem to be challenging becuase I got stuck a few times but I eventually got the answer which was great.
POW #13 The Absent-Minded Teller
1. An absent-minded teller switched the dollars and cents when she cashed a check for Mr. Brown, giving him dollars instead of cents and cents instead of dollars. After buying a five-cent newspaper, Brown discovered that he had exactly twice as much left as his original check. What was the amount of the check?
2.The way I started this problem was that I tried to come up with a formula. This first one I came up with was C - .05 = 2M. C is the changed amount and M is the original amount of money. This is showing that after 5 cents were taken away from the changed amount, it equaled exactly double the original amount. I moved on from this equation because Jocelyn told us that we should try to break down the variables even more to dollars and coins. We did this all in class and Jocelyn wrote all of our equations on the board and we compared them all. We found that we had a lot of different variables and that we used *2 frequently and -.05. Then Jocelyn asked us to try to simplify our formulas and to try to use just the variables C and D for cents and dollars. So then my next formula was D + C > 2(D + C - .05). I showed Jocelyn this formula and she said that say D = 30 and C = 50, then D + C would equal 80 and that didn't really make sense. So I needed to find a way to make it so it equaled 30.50. Then I figured out that it worked if you times it but .01. So then the equation I got was 2(D + C.01) = C + D(.01) -.05. Then Jocelyn explained to us that decimals are never good in equations so in the end the equation was 2(D + C/100) = C + D/100 - .05. After, I just tried to plug in numbers to try to find it where the equation would equal the same. I tried a lot of time of just plugging in random numbers but then I got confused and frustrated so I asked someone for help and they told me that Jocelyn suggested trying to isolate one of the variables and one side and she showed us how she did it for D and she got D = 98C - 5 / 199. So after that she told us to plug the equation into google spreadsheets and to use that to plug in the numbers instead of writing it all down because that would take a very long time. So I just plugged that formula into the B column and instead of C I put A1 and I just kept changing A1 until B1 was a whole number and that was how I found my answer.
1. An absent-minded teller switched the dollars and cents when she cashed a check for Mr. Brown, giving him dollars instead of cents and cents instead of dollars. After buying a five-cent newspaper, Brown discovered that he had exactly twice as much left as his original check. What was the amount of the check?
2.The way I started this problem was that I tried to come up with a formula. This first one I came up with was C - .05 = 2M. C is the changed amount and M is the original amount of money. This is showing that after 5 cents were taken away from the changed amount, it equaled exactly double the original amount. I moved on from this equation because Jocelyn told us that we should try to break down the variables even more to dollars and coins. We did this all in class and Jocelyn wrote all of our equations on the board and we compared them all. We found that we had a lot of different variables and that we used *2 frequently and -.05. Then Jocelyn asked us to try to simplify our formulas and to try to use just the variables C and D for cents and dollars. So then my next formula was D + C > 2(D + C - .05). I showed Jocelyn this formula and she said that say D = 30 and C = 50, then D + C would equal 80 and that didn't really make sense. So I needed to find a way to make it so it equaled 30.50. Then I figured out that it worked if you times it but .01. So then the equation I got was 2(D + C.01) = C + D(.01) -.05. Then Jocelyn explained to us that decimals are never good in equations so in the end the equation was 2(D + C/100) = C + D/100 - .05. After, I just tried to plug in numbers to try to find it where the equation would equal the same. I tried a lot of time of just plugging in random numbers but then I got confused and frustrated so I asked someone for help and they told me that Jocelyn suggested trying to isolate one of the variables and one side and she showed us how she did it for D and she got D = 98C - 5 / 199. So after that she told us to plug the equation into google spreadsheets and to use that to plug in the numbers instead of writing it all down because that would take a very long time. So I just plugged that formula into the B column and instead of C I put A1 and I just kept changing A1 until B1 was a whole number and that was how I found my answer.
3. My solution to this problem is that the man originally had $31.63 on his check.
4. My evaluation for this problem is that I enjoyed doing this problem and I though it was fun because it had a good amount of equations to work with and I would enjoy doing another problem like this again.
4. My evaluation for this problem is that I enjoyed doing this problem and I though it was fun because it had a good amount of equations to work with and I would enjoy doing another problem like this again.