Checking a number trick using algebra

[Probability]

I remember this trick being played on me at school in the school playground. I never understood it then and I'm thinking that actually it does not work for every number as the author says.

Think of a number...10
Multiply it by 3..........30
Add 2............................32
Double the result.....64
Add 2............................66
Divide by 6.................11
Take away first number thought of...10
Answer = 1

Using algebra to do the same trick;

Think of a number
[MATH]{n}[/MATH]
Double it
[MATH]{2n}[/MATH]
Add 7
[MATH]{2n}+{7}[/MATH]
Double the result
[MATH]{2}({2n+7})={4n}+{7}[/MATH]
Add 6
[MATH]{4n}+{14}+{6}={4n}+{20}[/MATH]
Divide by 4
[MATH]\frac{4n+20}{4}=\frac{4n}{4}+\frac{20}{4}={n}+{5}[/MATH]
Take away the number first thought of;

[MATH]{n}+{5}-{n}={5}[/MATH]
The way I'm understanding this at the moment is that you end up with their number by using your own number but not your own thoughts of the number you thought of!

Look at my think of a number above, which is (10). That is the number I thought of. Enter that into the algebra and see the result, which will be their number (5), which is not the number I thought of!

 

[JeffM]

Double it? Add 7?

Think of an arbitrary number

n

Multiply by 3 rather than 2

3n

Add 2 rather than 7

3n + 2

Double it

2(3n + 2) = 6n + 4

Add 2

6n + 6

Divide by 6

n + 1

Subtract the original number of n

n + 1 - n = 1.

Works for any n.

What is going on is

[MATH]\dfrac{6n + 6}{6} - n = \dfrac{6n + 6}{6} - \dfrac{6n}{6} = \dfrac{6}{6} = 1.[/MATH]
They make you construct 6n + 6. But you can't change the instructions and expect to get back to 1.

 

[JeffM]

Take an arbitrary number.

Triple it

Subtract 1 from that product

Multiply that difference by 5

Add 20 to that product.

Divide that sum by 15

Subtract the original number

What do you get? Why?

You can construct an infinite number of these tricks. I am not sure they teach much about math.

 

[Probability]

What the author is saying JeffM is that I can test the trick with whatever number I wish?

Clearly this statement by the author is untrue. While there will be some ways of making it work with limited numbers, it's not been explained out properly just as you have had to change some numbers to make it work.

 

[JeffM]

What the author is saying JeffM is that I can test the trick with whatever number I wish?

Clearly this statement by the author is untrue. While there will be some ways of making it work with limited numbers, it's not been explained out properly just as you have had to change some numbers to make it work.

You can. You did not follow the directions.

 

[Deleted member 4993]

I remember this trick being played on me at school in the school playground. I never understood it then and I'm thinking that actually it does not work for every number as the author says.

Think of a number...10
Multiply it by 3..........30
Add 2............................32
Double the result.....64
Add 2............................66
Divide by 6.................11
Take away first number thought of...10
Answer = 1

Using algebra to do the same trick;

Think of a number
[MATH]{n}[/MATH]
Double it
[MATH]{2n}[/MATH]
Add 7
[MATH]{2n}+{7}[/MATH]
Double the result
[MATH]{2}({2n+7})={4n}+{7}[/MATH]
Add 6
[MATH]{4n}+{14}+{6}={4n}+{20}[/MATH]
Divide by 4
[MATH]\frac{4n+20}{4}=\frac{4n}{4}+\frac{20}{4}={n}+{5}[/MATH]
Take away the number first thought of;

[MATH]{n}+{5}-{n}={5}[/MATH]
The way I'm understanding this at the moment is that you end up with their number by using your own number but not your own thoughts of the number you thought of!

Look at my think of a number above, which is (10). That is the number I thought of. Enter that into the algebra and see the result, which will be their number (5), which is not the number I thought of!

I am perplexed with your confusion:

Think of a number...10 ........................................... n
Multiply it by 3..........30........................................... 3n
Add 2............................32........................................... 3n+2
Double the result.....64........................................... 6n+4
Add 2............................66........................................... 6n + 6
Divide by 6.................11........................................... n + 1
Take away first number thought of (n)............1

It will happen every time - as sun will come out to-morrow

 

[JeffM]

I am perplexed with your confusion:

Think of a number...10 ........................................... n
Multiply it by 3..........30........................................... 3n
Add 2............................32........................................... 3n+2
Double the result.....64........................................... 6n+4
Add 2............................66........................................... 6n + 6
Divide by 6.................11........................................... n + 1
Take away first number thought of (n)............1

It will happen every time - as sun will come out to-morrow

He did not follow the directions.

He did not multiply by 3 at the first step. Instead, he multiplied by 2.

He did not add 2 in the second step. Instead he added 7.

He did not multiply by 3 in the third step. Instead he multiplied by 2.

It as though someone gave him directions to LIverpool: drive north and then west. But he drove east and then south and is perplexed why he is in Dover.

 

[Probability]

I am perplexed with your confusion:

Think of a number...10 ........................................... n
Multiply it by 3..........30........................................... 3n
Add 2............................32........................................... 3n+2
Double the result.....64........................................... 6n+4
Add 2............................66........................................... 6n + 6
Divide by 6.................11........................................... n + 1
Take away first number thought of (n)............1

It will happen every time - as sun will come out to-morrow

This is the part I don't get;

Take away first number thought of (n)....1 No my first number is 10. The activity said think of a number, it did not say a number between 1 and 9 say!

I'am I misunderstanding the trick or is the trick misunderstanding me!

You see how I see it the trick says, think of a number, so only I know that number, but when I enter my number into their trick I end up with their answer (5). That is not the number I thought of but they are using my number to find their solution. The way the trick was told to me implied they could know what number I was thinking, but clearly that is not possible, which is the message I'm trying to get across.

 

[JeffM]

This is the part I don't get;

Take away first number thought of (n)....1 No my first number is 10. The activity said think of a number, it did not say a number between 1 and 9 say!

I'am I misunderstanding the trick or is the trick misunderstanding me!

You see how I see it the trick says, think of a number, so only I know that number, but when I enter my number into their trick I end up with their answer (5). That is not the number I thought of but they are using my number to find their solution. The way the trick was told to me implied they could know what number I was thinking, but clearly that is not possible, which is the message I'm trying to get across.

My goodness. How many times do I have to say it? They told you what to do and YOU DID NOT DO IT.

 

[Deleted member 4993]

This is the part I don't get;

Take away first number thought of (n)....1 No my first number is 10. The activity said think of a number, it did not say a number between 1 and 9 say!

I'am I misunderstanding the trick or is the trick misunderstanding me!

You see how I see it the trick says, think of a number, so only I know that number, but when I enter my number into their trick I end up with their answer (5). That is not the number I thought of but they are using my number to find their solution. The way the trick was told to me implied they could know what number I was thinking, but clearly that is not possible, which is the message I'm trying to get across.

You did not say - what did the trickster tell you (whether

"I can tell you the number you thought of" or

wrote 1 in a piece of paper and handed you the piece of paper saying " the answer is 1" or something else....)

 

[Probability]

You did not say - what did the trickster tell you (whether

"I can tell you the number you thought of" or

wrote 1 in a piece of paper and handed you the piece of paper saying " the answer is 1" or something else....)

OK so let me see if I understand you correctly. You are saying "I can tell you the number you thought of"???

I don't believe that and here is my proof.

Think of a number [MATH]{n}[/MATH]
My number I've chosen ranges between (2) or (3) or (4) All these numbers will provide the same result.

Multiply that number by (3)
Add(2)
Double the result
Add(2)
Divide by(6)
Take away the first number I thought of, either (2), (3) or (4)

I've now got [MATH]{n}+{5}-{n}=5[/MATH]
If you put any of my numbers (2) or (3) or (4) into the expression you will end up with (5). If you change the value of (5) in the expression for any other number you choose, then enter any of my numbers above, you'll still end up with the same answer from each one of the numbers I chose above. So by example;

[MATH]{n}+{7}-{n}={7}[/MATH]
[MATH]{2}+{7}-{2}={7}[/MATH]
Do the same for other numbers will provide the same answer (7)

There noway can you tell me which of the numbers I used to calculate (5) above. I've given three examples of numbers that provide the same answer, you cannot know which number I chose.

Please prove me wrong.

 

[JeffM]

OK so let me see if I understand you correctly. You are saying "I can tell you the number you thought of"???

I don't believe that and here is my proof.

Think of a number [MATH]{n}[/MATH]
My number I've chosen ranges between (2) or (3) or (4) All these numbers will provide the same result.

Multiply that number by (3)
Add(2)
Double the result
Add(2)
Divide by(6)
Take away the first number I thought of, either (2), (3) or (4)

I've now got [MATH]{n}+{5}-{n}=5[/MATH]
If you put any of my numbers (2) or (3) or (4) into the expression you will end up with (5). If you change the value of (5) in the expression for any other number you choose, then enter any of my numbers above, you'll still end up with the same answer from each one of the numbers I chose above. So by example;

[MATH]{n}+{7}-{n}={7}[/MATH]
[MATH]{2}+{7}-{2}={7}[/MATH]
Do the same for other numbers will provide the same answer (7)

There noway can you tell me which of the numbers I used to calculate (5) above. I've given three examples of numbers that provide the same answer, you cannot know which number I chose.

Please prove me wrong.

No. The trick is psychological.

You choose your number. You follow the directions. The trickster gives you a piece of paper with the result of 1 on it, which of course matches what you get if you follow the directions. Now one of two things happens. The trickster allows you to deduce that therefore the trickster must have figured out your number to get the same result, which is an invalid inference on your part. Or the trickster says that he (for some reason the people who do this sort of thing are invariably male) got the correct result because he can read your mind, which is pure nonsense.

The trickster got the correct result because it makes no difference what number you choose; the result of the process will always be 1 if you follow the directions. You would have figured out the psychological trick played on you if you had followed the directions because you would have seen that 1 is always the result. Instead, you did a completely different process and confused yourself even more.

DO THE ALGEBRA STRICTLY ACCORDING TO THE INSTRUCTIONS.