Top-Rated Free Essay

Pow Write-Up 1

Better Essays
Emily Shiang
6/27/13

POW Write-up In this POW write-up, I am trying to prove that there can be only one solution to this problem, and demonstrate and corroborate that all solutions work and are credible. What the problem of the week is asking is that the number that you put in the boxes 0-4 is the number of numbers in the whole 5-digit number. For example, if you put zero in the “one” box, you would be indicating that there is zero ones in the number. Another example is if you put a two in the “three” box. This would indicate that there are two threes in the whole 5-digit number. I was asked to find solutions where are the numbers would work in heir perspective boxes. From there I started working on the problem that would fit this criterion. When I first saw the POW, I thought that finding the solution would be fairly easy, by just plugging different numbers into the boxes and play around with them. I soon discovered that that wasn’t the case. So using deductive reasoning, I began off by acknowledging that there couldn’t be any number over four in the boxes, because if it was above four, it wouldn’t be the right solution. If I put a five in any box, I knew that there would only be four boxes left, which wouldn’t work. So I ruled out any number over four. From there, I began by using the largest number box, which was four. I noticed that if I used any number other than zero in the four box, the problem wouldn’t work. To prove this, if I put a one in the “four” box, that means that there would be another box from 0-3 that would contain the number four, which means that there would be four of that number. This is impossible because there are only three boxes left. Any other solution wouldn’t work either, so I left the “four” box as a zero. Then I went down to the “three” box, being quite confident of my decision on the “four” box. I used the same approach, and found out that there couldn’t be any number over two, because if you put a three in the “three” box, there would have to be three more three’s in the rest of the three boxes, which wouldn’t make sense because there would be no space to fit the three zeros, ones, or twos. If I put a two, then that means that there would be two threes in the rest of the boxes, which wouldn’t work either. I tried plugging in a one in the “three” box, but that wouldn’t work either because then there would be one three in any of the boxes, which wouldn’t be fulfilled. So the only solution left would be a zero in the “three” box. Moving on to the last boxes, I figured out that the only numbers to work with would be zero, one, and two. I noticed that in the “zero” box, there were already two zeros in play, so the number in the “zero” box had to be two or above. I tried plugging in a three, but that wouldn’t work out because there is already a zero in the “three” box. So I left it as a two. From there on, I had two numbers left to work with (hopefully). I used my reasoning to find out that there was a two in the “zero” box, which meant that there had to be at least one “one” in the two box. I tried that, and I found out that if I put a one in the “two” box, I wouldn’t have any correct solution for the “one” box. If I put a one in the “one” box, there would be two ones, which would contradict the solution I was trying to find. If I put a two in the “two” box, then it would be perfect, because then there would be two twos; one in the “zero” box and another in the “two” box. So then I was left alone with the “one” box, where I conveniently found out I could put a one in the “one” box, and it would work. The answer to the POW is the number 21200. I know this is the only solution because our geometry teacher, Mr. Carter (or as he likes us to call him, Dave), told our class so. Starting over, I know that there could only be a zero in the “four” box, because any other number wouldn’t work in the four box, because there wouldn’t be enough boxes to fulfill the problem. I am certainly definite that there could only be a zero in the “four” box. As I said before, there could only be numbers 4 and under. Moving onto the “three” box, there could only be a zero because if you put a one in the box, there would eventually have to be a three somewhere in the other three boxes, which wouldn’t work because there wouldn’t have space to fit those because there would only be two boxes left. So moving on to the “zero” box, there would have to be a number two or above. If there was a three in the “zero” box, then that would mean there would have to be a zero in the “one” or “two” box, which wouldn’t add up because one or the other wouldn’t have a right solution. So the answer to that would be a “two” to make up for the “four” and “five” boxes. Being left with the “one” and “two” boxes, I noticed that since there was a two in the “zero” box, there would be at least a one in the “two” box. I tried that, but then the “one” box would have to contain a two, which wouldn’t work. Therefore, the “two” box has to contain a two. In the “one” box, there could only be a one to show that there is only one “one”. I know this is the only solution because I used deductive reasoning and slowly eliminated choices and came down to only one answer. Therefore I stand by my conclusion that the only solution is the number 21200. For this POW write-up, I think I deserve an A/A- because I spent a lot of effort and time into my POW write-up and tried to defend my thinking as well as possible. I tried to make the reader see what I was seeing and look into my logic and my thinking. I also think I completed the rubric to the best of my ability and did all the steps that were asked for. I used a step-by-step process to get to my solution. I also mentioned some problems and difficulties I faced while solving the POW. Therefore, I think I am worthy of receiving an A/A- for the POW write-up. Thank you!

You May Also Find These Documents Helpful

  • Good Essays

    Pow #1- a Digital Proof

    • 678 Words
    • 3 Pages

    One box down, four to go. Easy, right? That’s what I thought as I filled in the ‘three’ box, again with a zero for the same reasons that I’d put a zero in the ‘four’ box. Four wouldn’t work because that would require three to be in four boxes, and then that wouldn’t leave room for any other numbers. Again, this was the reason that three, two, and one didn’t work. For three, too, the only possibility was zero.…

    • 678 Words
    • 3 Pages
    Good Essays
  • Satisfactory Essays

    A Digital Proof

    • 503 Words
    • 3 Pages

    This problem of the week has a main gain goal set upon boxes. There are five boxes numbered one through zero. Underneath the boxes have the numbers written under them. In the boxes, there are numbers that should be entered in the boxes that all evenly works out. For instance, the number that you put in box zero must be the same as the number of zeros that were used. The same procedures apply when using other boxes. The same number cannot be used in the box, for example, a four cannot be placed in box four or the number two cannot be enlisted in box two. The same number is tolerable to be used more than once. The only exception is that no number higher than four can be expended. My goal for this POW is to corroborate and demonstrate that I have found all solutions and that all solutions work and is credible.…

    • 503 Words
    • 3 Pages
    Satisfactory Essays
  • Good Essays

    Color and Probability

    • 434 Words
    • 2 Pages

    5. Andrew has a box which contains 4 pink blocks, 5 yellow blocks and 6…

    • 434 Words
    • 2 Pages
    Good Essays
  • Satisfactory Essays

    A. A farmer is going to sell her eggs at the market when along the way she hits a pot hole causing all of her eggs to spill and break. She meets an insurance agent to talk about the incident, and during the conversation he asks, how many eggs did you have? The farmer did not know any exact number, but proceeded to explain to the insurance agent that when she was packing the eggs, she remembered that when she put the eggs in groups of 2-6 she had even groups with 1 left over, but when she put them in groups of 7 she had even groups of 7 with none left over.…

    • 654 Words
    • 3 Pages
    Satisfactory Essays
  • Good Essays

    Pow #2

    • 1106 Words
    • 5 Pages

    There’s a standard 8 x 8 checkerboard made up by 64 small squares. Each square is able to combine with others squares to make other squares of different sizes. Our job is to find out how many squares there’s in total. Once you get all the number of squares get all the number of squares and feel confident with your answer you next explain how to find the number of squares on any size checkerboard. You will know you have the answer when no matter how what size board you have you can give a clear description of to easily compute the total number of squares. So basically what you’re doing is finding the total number of squares in a 8 x 8 checkerboard and pretty much finding an equation on how to find the total number of squares on any size board.…

    • 1106 Words
    • 5 Pages
    Good Essays
  • Satisfactory Essays

    Pow #10 Possible Patches

    • 278 Words
    • 2 Pages

    Keisha is making a quilt that will be made up of rectangular patches of rectangular material. When she finds a box of satin material that is 17 by 22 inches long she wonders how many 3 by 5 inch patches she could include into the quilt. However, after we found out that 22 at minimum, rectangular patches can fit into the quilt and 24 at maximum, she decides to see how many 9 by 10, 10 by 12 and 8 by 9 inch boxes she can fit into the 17 by 22 inch quilt. Lastly, she had to find the number of 3 by 5 inch and 8 by 9 inch pieces she could fit into the quilt if the piece was 4 inches wide and 18 inches long.…

    • 278 Words
    • 2 Pages
    Satisfactory Essays
  • Good Essays

    Imp 2 Pow: Kick It

    • 591 Words
    • 3 Pages

    Problem Statement: A football league scores points for field goals as five points and touchdowns as three points. They want to know what the highest amount of points that is impossible to score.…

    • 591 Words
    • 3 Pages
    Good Essays
  • Satisfactory Essays

    NT1210 Lab 1

    • 319 Words
    • 4 Pages

    3. First 4 digits of a Base 5 numbering system would be (left to right) 625 125 25 5…

    • 319 Words
    • 4 Pages
    Satisfactory Essays
  • Good Essays

    3) Attached Work: Attach all work you and your group members used to try and solve the POW.…

    • 459 Words
    • 3 Pages
    Good Essays
  • Satisfactory Essays

    ii) Why did you select it? This is the number furthest from 1 or -1…

    • 258 Words
    • 3 Pages
    Satisfactory Essays
  • Satisfactory Essays

    Simpsons

    • 982 Words
    • 4 Pages

    4. Using the symbol > arrange the following numbers: • • 1 237 456 1 273 462…

    • 982 Words
    • 4 Pages
    Satisfactory Essays
  • Good Essays

    Problem of the Week

    • 587 Words
    • 3 Pages

    Problem Statement: A farmer is carrying her eggs in a cart when she accidentally spills every one of them and they all break. She decides to go to her insurance agent, who asks her how many eggs she had. She’s not sure but she does know some information from various ways she tried to pack her eggs. She knows that when she put her eggs in groups of one, two, three, four, five, and six, there was always one egg left over. When she put them in groups of seven, there were no eggs left over. The task is to use this information to find out how many eggs the farmer had,…

    • 587 Words
    • 3 Pages
    Good Essays
  • Good Essays

    Nothing

    • 1097 Words
    • 5 Pages

    8) Write (in the same base) the counting numbers just before and just after 1044 five. A) 1043five, 1045 five C) 1043five, 1111 five B) 1042five, 1101 five D) 1043five, 1100 five…

    • 1097 Words
    • 5 Pages
    Good Essays
  • Better Essays

    Imp 1 Pow 4

    • 892 Words
    • 4 Pages

    The next scenario is very similar. In this one, Ms. Hernandez passed a different gumball machine the next day with three different colors Once again her twins each want a gumball of the same color, and each gumball is still one cent. What is the most amount of money that Ms. Hernandez would have to spend in order to get each of her daughters the same color gumball?…

    • 892 Words
    • 4 Pages
    Better Essays
  • Satisfactory Essays

    NT1210 Lab 1

    • 473 Words
    • 3 Pages

    = 1 + 2 + 0 + 0 + 16 + 32 + 64 = 115…

    • 473 Words
    • 3 Pages
    Satisfactory Essays