Here's a much better party/bar trick:

  1. Point to the drink glass in front of you
  2. Ask friend if they think the circumference or height of the glass is larger
  3. Friend will invariably think that height is larger
  4. Wager for a drink that that's not the case
  5. Use a straw to measure the circumference and then height
  6. Enjoy your free drink

Unless you've picked an a Champaigne flute you'll always win. To make it even more fun, for (4) wager that the circumference will be two times the height to make it sound more incredulous. For typical glasses you may go up to three!

I learned this trick from Things to Make and Do in the Fourth Dimension (https://www.amazon.com/Things-Make-Fourth-Dimension-Mathemat...), overall good book.

How this goes in real life:

"Was your number... 3741?"

"No."

"Heh, I'm afraid that's impossible based on number theory. You must have made a mistake in the step where I asked you to choose a second 4-digit number by scrambling the four digits of the first number and subtracting the larger number from the smaller. Try it again, I'll wait."

"No."

Yeah, I donno. Even if I were able to convince someone at a party to go along with this "trick", I don't think they'd be especially impressed when after scrambling and subtracting 4 digit numbers, I'm able to wow them with a single digit.

𝙸̶ ̶𝚙̶𝚒̶𝚌̶𝚔̶𝚎̶𝚍̶ ̶𝟻̶𝟶̶𝟶̶𝟶̶.̶ ̶ ̶𝚃̶𝚑̶𝚎̶ ̶𝚝̶𝚛̶𝚒̶𝚌̶𝚔̶ ̶𝚍̶𝚘̶𝚎̶𝚜̶𝚗̶'̶𝚝̶ ̶𝚠̶𝚘̶𝚛̶𝚔̶ ̶𝚊̶𝚗̶𝚍̶ ̶𝚍̶𝚎̶𝚖̶𝚘̶𝚗̶𝚜̶𝚝̶𝚛̶𝚊̶𝚋̶𝚕̶𝚢̶,̶ ̶𝚝̶𝚑̶𝚎̶ ̶𝚊̶𝚞̶𝚝̶𝚘̶𝚖̶𝚊̶𝚝̶𝚎̶𝚍̶ ̶𝚟̶𝚎̶𝚛̶𝚜̶𝚒̶𝚘̶𝚗̶ ̶𝚍̶𝚘̶𝚎̶𝚜̶𝚗̶'̶𝚝̶ ̶𝚔̶𝚗̶𝚘̶𝚠̶ ̶𝚠̶𝚑̶𝚊̶𝚝̶ ̶𝚗̶𝚞̶𝚖̶𝚋̶𝚎̶𝚛̶ ̶𝙸̶ ̶𝚙̶𝚒̶𝚌̶𝚔̶𝚎̶𝚍̶.̶

A different issue by picking 2222 (anything that ends up with all 0s or 9s ofc)

Not something I would bring up at a party because people are drinking and not really interested in doing addition/subtraction and will DEFINITELY pick simple numbers. By the time you get into "it has to be non-zero digits" they have already become bored.

It feels like my little brother running up to me and screaming "What's 729 squared?" and without a beat "531,441" , "I'm smarter than you!"

I would bet a decent chunk of money the author has never successfully tried this at a party.

Asking people to subtract two 4 digit numbers and picking digits that are not 0 and 9 is absolutely not a “party trick”.

I'm being honest here. Reading along I randomly picked 987 from my brain. I scrambled that to 897. Subtracting the smaller from the larger I got 90, per the instructions. So I am unable to tell you the remaining digits starting with a number that isn't 9 or 0.... Maybe I'm a "you must be fun to talk to at parties" kind of guy.

Actual Math Party tricks are standard affairs: just jokes about Math.

* "Hey Babe, would you like to be my derivative and lie tangent to my curves?"

* Question: What did Euler discover while sitting on the toilet?

-- Answer: A natural log.

* Question: Why do programmers mix up Christmas and Halloween?

-- Answer: Because Dec(imal) 25 == Oct(al) 31.

* Once upon a time, a big, evil derivative was approaching town. All the polynomials ran away in terror, expecting themselves to be derived away. Suddenly, the local Sheriff appeared, and rode out to parley with the derivative.

The Sheriff and Derivative meet up, and a showdown was about to occur. Knowing that it will all be over soon, they exchanged pleasantries before the final showdown.

The Sheriff introduces himself: "I'm e^x, the Sheriff of this town. You can't dare to derive me!"

Upon hearing the name: the evil derivative gives a toothy grin and says "My name is d/dy".

Etc. etc. Assuming you're comfortable telling these kinds of jokes of course. As usual, you need to read the room and see if the jokes would fly in the company you're in.

some python to do this trick and find counterexamples that won't work

    import random as r
    def fnc(b):
        bstr = list(str(b))
        if bstr.count(bstr[0]) == len(bstr): 
            return "can't shuffle"
        max_ct = len(bstr)*10
         
        # do while
        r.shuffle(bstr)
        b_shuf = int(''.join(bstr))
        diff = abs(b-b_shuf)
        bstr = list(str(diff))
        i = r.randint(0,len(bstr)-1)

        while bstr[i] == '0' or bstr[i] == '9':
            i = r.randint(0,len(bstr)-1)
            bstr = list(str(b))
            r.shuffle(bstr)
            b_shuf = int(''.join(bstr))
            diff = abs(b-b_shuf)
            bstr = list(str(diff))
            max_ct -=1
            if max_ct == 0: 
                return "bollocks!"
        
        del(bstr[i])
        s = sum(map(int,bstr))
        i =0
        while (i+s) % 9 != 0:
            i+=1
        return bstr,i,diff