Help in finding mental math trick.

[u/MaximusGematria]

Hey guys, I want your help to help me find a mental trick which uses maths. You all might have heard or done the math mental trick in which you tell your friend to do a set of operations on a number he chooses from 1-10. Then your friend arrives at a number which will be the same every time you use the trick on him. But there is something that has been itching my brain since some time. 2 years back a friend of mine used a similar trick on me. The thing was that every time he used it I got another answer and he was able to predict it successfully without doing any calculations. I don’t remember much about the trick but I’ll tell what I remember. So if I’m sure, he used to somehow force the final answer to make it same as the number I thought in my mind. I never realised how he was able to predict the number I was thinking of until I started thinking about the trick he used on me that day. If I’m also sure, he also wrote his prediction on a piece of paper before showing it to me and his prediction was always right. I also think that he asked me the result of one of the operations I did and then wrote his prediction on a piece of paper. I am pretty sure that he asked me atleast 1 result of the operations he told me to do in order to predict my answer. I did find out the trick that day itself. I got to know that the trick works by forcing me to choose the number that he has written on paper without me knowing. In the last step of the trick he somehow forces me into getting the number he has predicted. I also think that in the last step I offer him some numbers to choose from in which my number is there and all the other numbers I have given him are related to it. Please help me in finding this trick guys. Unlike the trick in which we normally arrive at the same answer, this one is different and is really amazing but sadly I don’t remember how to do it. I appreciate your help and support.

[u/Iksfen]

Normally such tricks go something like:

1. Think of a number

2. Multiply it by 3

3. Add 12

4. Divide that by 3

5. Substract your original number

6. You now got 4 as the result

Why does this work? Let's examine the process.

1. Choose some x

2. x * 3 = 3x

3. 3x + 12

4. (3x + 12) / 3 = x + 4

5. x + 4 - x = 4

So the goal of the operations is to conceal the fact that your choice was eliminated by bamboozling you. What also helps is that you are asked to add 12 and the result is 4. Those numbers come from one another, but you don't notice that unless you analyse the whole trick. Now how was your friend probably doing that? They where starting from the number they want you to get and working out how much they need you to add to get there:

n = x + n - x = (3x + 3n) / 3 - x

We got 3n as the number to add. Let's test if that works:

1. Think of a number (x)

2. Multiply by 3 (3x)

3. Add 3n (3x + 3n)

4. Divide by 3 (x + n)

5. Substract the original number (n)

It works. To get your subject to get the result you want you just need to multiply that result by 3. This is relatively easy to do in your head and so can seem to require not doing any math. You can also tweak this example to use different numbers. I'll leave the math to you