Ms. JL
Many of you sent in excellent solutions to this problem!!! You tackled it using logic, order of operation, and algebra these are all great ways to go about solving the problem!
Here is the way the author of the problem saw the answer.
Please go back and look at the ways your peers solved the problem. Feel free to post comments, questions, or commend your peers for the way they approached the problem.
If x is the number you think of, you start with x,
Then when you add 1, you get x + 1
When you double it, it turns into 2x + 2
When you take away 3, it turns into 2x -1
Adding the number you first thought of makes 3x -1
When you add 7 it turns into 3x + 6
When you divide by 3 it turns into 1x + 2
Then take away the number you first thought of (x) it leaves 2.
See you Monday,
Ms. Leckman
27 comments:
The POW for this week said that we had to explain how the diagram below has a mathmatical solution.
To solve this problem, you would have to make an equation. The equation is y=x+1*2-3+x+7/3-x=2. We got this because in order to get the answer 2, you would have to make an equation. So, we made an equation that matched the data that we were given. X represents any number that you choose. When you put any number into "x" you will always get 2.
vb&ct
If you do the problem to the right with any number you will end up with 2. How does it work? Here’s how we think it works.
Skip take away 3 and have add 7 be add 4.
Skip add one and have add 4 be add 6.
Skip double it and add the number you first thought of (first one) and multiply by 3 instead.
Think of a number, triple it, add 6, divide by 3 take away number you first thought of, then you end up with 2.
When you add 6 to a number then divide it by 3 you get 3 more of the original number than there was in the first place then the rest of the problem was just getting the original number to 0.
We lowered down the problem to the simplest equation so that we could figure out how it worked in simplest form then we figured out that if you add 6 then divide by 2 you get 2 more than you just had then it subtracted until it got down to 0.
12*3=36+6=42/3=14-12=2
2 is the answer in a more simpler equation.
So we are confused and are having trouble figuring out the problem. We are puzzled when it says to add the number you first thought of, and then it asks us to deduct the number you first thought of. So we decided that those might cross each other out but when we did the problem with out those two directions we found that the problem cannot be solved. So we figured the number it asks you to think of are useful to the problem but we can’t figure out how.
For our P.O.W. we were given a problem and we had to figure out why it always was correct. This is always correct because you add one to the original number and then you double it. (EX:72+1=73). 73+73=146. Then you subtract 3 which is 143, it is double the original number subtracted by 1. When you add the original number it is 1 less than triple the original number. 143+72=215. After you have add 7 it will be 6 digits over the triple number. Since 6 can be divided by 3 then it just simplifies 2 numbers over your original number. 215+7=222. 222/3 is 74. 74-72=2.
For our P.O.W. we were given a problem and we had to figure out why it always was correct. This is always correct because you add one to the original number and then you double it. (EX:72+1=73). 73+73=146. Then you subtract 3 which is 143, it is double the original number subtracted by 1. When you add the original number it is 1 less than triple the original number. 143+72=215. After you have add 7 it will be 6 digits over the triple number. Since 6 can be divided by 3 then it just simplifies 2 numbers over your original number. 215+7=222. 222/3 is 74. 74-72=2.
M.G.
Why does this work with EVERY number? Our explanation for this question is this... since this is said to work with every number we created an equation of the problem: [(X+1)x2-3+X+7]/3-X=2 so when you plug in any number the equation should always leave you with an answer of 2 because when you think of a number like,75, you add 1 to get an answer of 76, double it (152), take away 3 (149), add the number you first thought of (224), add 7 (231), divide 3 (77), and take away the number you first thought of (75), which is 2.
A.R. & D.G.
First, we started thinking about the number. How could it work with every number? So we made an equation with all of the info. We then took all of the x's out and with the rest of the equation, we got 2. Then we made an equation out of the x's that we took out, and got x. How does the first equation get rid of that x? Well, when you divide by 3, that gets rid of 1/3 of it. Then you can add up the rest of it that you add which adds up to 1/5. with the rest of the equation, you can add it to that 1/3 and 1/5 and that equals 2, so the answer would always be 2.
R.S. and C.K.
The problem we are trying to solve is how this problem works. We have rewritten the problem in to an equation, 2=x+1*2-3+x+7/3-x.
1: In step one of the equation you have to pick a number and plug it in for x. we are going to use 20. So we would do 20 + 1. This would get us 21 and we would go on to step 2
2: We would now take 21 and double it, this gives us 42.
3: when you take the 42 and subtract 3 you would get a 39.
4: now when you add your “x” or original number u would get 59.
5: now 59 + 7 will equal 66 (3rd grade stuff).
6: 66 divided by 3 should equal 22.
7: 22 minus your original number (x) you will get 2.
There is the equation 2=x+1*2-3+x+7/3-x in step by step form. Unfortunately K.B. and I.W. aren’t good enough at logic to explain why this works but we can walk you through the steps anytime no matter what number you have.
IW KB
The way he knows is simple, he starts at zero and follows all the directions he gives you. When he says to "take away your original number" you break even. Ex. if u start at 5 he starts at 0. he tells you to add 5, you get 10 and he gets 5. he tells you to take away 3, you get 8 he gets 3. Then he will say "take away your original number" you get 3 and he gets 3. Thats how he does it.
It is a trick. No matter what number you choose you are left with two. It seems like a lot of steps but you can cancel some extra steps. For example, " Add the first number you started with" and a little later it said "Add the first number you thought of", and "Take away the number you first thought of."All it is pretty much asking you to do is add 2 to your number and subtract your first number. That would work for every number.
The way he knows is simple he starts at zero and follows all the steps he tells you to do "when he says take tour originalnumber" you break even. Example if you start at five he starts at zero. Then he says "add ten take seven away and hes at three then he says take away the original number" but he doesnt take away a number because he had zero so then that's how he knows what number you will get.
J.B.
E.K.
I am not sure how this works. I thought it over and I just can’t come up with a logical explanation. I was trying to figure out the ultimate thing that you are doing to your number but I can’t figure it out.
7+1=8
8x2=16
16-3=13
13+7=20
20+7=27
27/3=9
9-7=2
SV
I don’t really know why this works. I have picked several different numbers and the outcomes have all been 2. I’ve thought about an explanation but nothing came to mind. When trying to find an explanation I tried to think of some kind of an equation on what they were doing, but again nothing came to mind!
8+1=9
9+9=18
18-3=15
15+8=23
23+7=30
30/3=10
10-8=2
1+1=2
2+2=4
4-3=1
1+1=2
2+7=9
9/3=3
3-1=2
JL
I think this works because the problem does and then undoes the problem but then basically adds 2. It doesn’t really seem like this though because everything is all mixed up, in different operations, and in a different order, but it still does the same thing.
A.H.
O.k. so here is your first POW. I know all of you have received an e-mail like this one, but why do they work? Your task is to mathematically explain this quanrdy. Be as specific and concise as you can. (Remember - save a copy of your work in Word just in case. :-) and use your first and last initial ONLY!!!!)
26
26+1=27
27x2=54
54-3=51
51+26=77
77+7=84
84/3=28
28-26=2
I don’t really know why this work! It just seems to…! I couldn’t come up with an answer that would apply for every time other then it just works!
JL1
The Problem was to figure out why no matter what number you use to do the problem; you always come out with 2. What we are supposed to do, are find how it always comes up with 2, and explain why it happens.
First I did the problem several times and came up the answer 2, and then I thought it had something to do with the numbers and reversing it, but that wasn’t it.
Then I tried to break the problem down, and came up with this:
Number=1
Number + 1 = 2 x 2 = 4 – 3 =1 + Number = 2 + 7 = 9 / 3 = 3 – Number = 2
I then looked at it broken down, and I thought that there was something to do with the number at the beginning, middle, and end, and that they were doing some kind of adding in the middle, and after that, there was multiplying and dividing, and after, adding and subtracting.
The next thing I did was change the number in the process of getting 2. I used the number 0, and I got 2, but with any other numbers we tried, it didn’t work.
In conclusion, I did not get the answer to the question.
26
26+1= 27
27x2= 54
54-3= 51
51+26= 77
77+7= 84
84/3=28
28-26=2. I couldn’t come up with an answer that would apply for every time other than it just works. EK
Equation: 0+1x2-3+0+7/3-0=2
The Problem was two figure out why no matter what number you use to do the problem, you always come out with 2. What we are supposed to do is to explain why this happens.
First I did the problem several times, then I thought it might be that you’re just doing something to the number then revesing it, but that wasn’t it. Then I tried to break it down and that wasn’t the answer for this mind boggling equation!!!!!
I think that it might have to do with the number that u start out with…. Take a look:
?=1
?+1=2x2=4-3=1+?=2+7=9/3=3-?=2
First you have to add or put your number in then you have to add, then you have to subtract it.
The next thing I did was totally change the numbes in the process and that turned out to not work.
After all of this none of it worked so I don’t know.
sm pow 8/20
The Problem was to figure out why no matter what number you use to do the problem; you always come out with 2. What we are supposed to do, are find how it always comes up with 2, and explain why it happens.
First I did the problem several times and came up the answer 2, and then I thought it had something to do with the numbers and reversing it, but that wasn’t it.
Then I tried to break the problem down, and came up with this:
Number=1
Number + 1 = 2 x 2 = 4 – 3 =1 + Number = 2 + 7 = 9 / 3 = 3 – Number = 2
I then looked at it broken down, and I thought that there was something to do with the number at the beginning, middle, and end, and that they were doing some kind of adding in the middle, and after that, there was multiplying and dividing, and after, adding and subtracting.
The next thing I did was change the number in the process of getting 2. I used the number 0, and I got 2, but with any other numbers we tried, it didn’t work.
In conclusion, I did not get the answer to the question.
JW
POW
8/20
O.k. so here is your first POW. I know all of you have received an e-mail like this one, but why do they work? Your task is to mathematically explain this quandary. Be as specific and concise as you can. (Remember - save a copy of your work in Word just in case. :-) and use your first and last initial ONLY!!!!)
Number: 74 add one 75 Double it 150 Take away three 147 add 74 is 221 add seven 228 Divide by three is 76 Take away the number we first thought of minus 74. The number we finish off with is two.
Really all it goes through is adding two to your number so it can say subtract your starting number all those things in the middle are not actually needed. This is just a complicated way to get it down to two. Your could Be going through all those things to get the number to one. You could say pick a number You Could just say add one, Double it Take away three add the number you first thought of add 4 Divide by three take away the number you first thought off. It works and always ends up with the same number. It is just a way to make sure the number gets its way all the way down to one.
In Conclusion all that the Number formula is doing is doing a complicated way of getting your number down to Two on a formula of doubling and Subtracting dividing and Doubling.
SS
MG
FINAL:
7+1=8+8=16-3=13+7=20+7=27divded by 3=9-7=2. The number I chose is seven. When I added 1 it equaled 8. Then I doubled it and it equaled 16. Next, I subtracted 3 and it equaled 13. After, I added 7 and got 20, then added 7 again and got 27. Finally I divided 27 by 3 and got 9, then subtracted 7 and got 2. I think this works because the problem does and then undoes the problem but then basically adds 2. It doesn’t really seem like this though because everything is all mixed up, in different operations, and in a different order, but it still does the same thing.
BY:A.H.
I LOVED the idea of using variables and trying to express this algebraically!
Ms. Leckman
Nice job!!! Do you think you could write a "string of equations that might provide a clearer picture for you?
Ms. Leckman
AR and DG nice job of attempting to express this in terms of "x". Great work!
Ms. Leckman
Nice job vb&ct!!! You may want to look at your equation, are you sure you want two equals signs?
Ms. Leckman
O.k. so here is your first POW. I know all of you have received an e-mail like this one, but why do they work? Your task is to mathematically explain this quandary. Be as specific and concise as you can. (Remember - save a copy of your work in Word just in case. :-) and use your first and last initial ONLY!!!!)
14+1=15x2=30-3=27+14=41+7=48 divide by 3=16-14=2
This solution works because the number you start with ends up being reused and either subtracted or added back into the equation.
B.B.
O.k. so here is your first POW. I know all of you have received an e-mail like this one, but why do they work? Your task is to mathematically explain this quandary. Be as specific and concise as you can. (Remember - save a copy of your work in Word just in case. :-) and use your first and last initial ONLY!!!!)
14+1=15x2=30-3=27+14=41+7=48 divide by 3=16-14=2
This solution works because the number you start with ends up being reused and either subtracted or added back into the equation.
B.B. August 24, 2007
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