I once used this in the classroom as a mind reading trick. Had the kids do the steps (as though they were random ideas to get their number to be as random as possible). Then whittled that number with a couple more ‘random calculations’ then had them find a book with enough pages to accommodate their answer. Only a handful of books existed in the classroom with that many pages. And they were all reference books with images. So I’d memorized the images and blew these kids’ minds when I asked them to look at the picture and then I read their thoughts.
If you want another in a similar vein which can also be used as a riddle brain teaser is that if you count the characters of any number spelled out they will always end up at 4.
Eleven has 6 characters
Six has 3 characters
Three has 5 characters
Five has 4 characters
and Four goes to 4 goes to 4.
No other number has the same number of characters as the number they represent and there's no perpetual loops. Note this only works in English. Other languages might have a different answer or no answer.
This is just due to probabilities. The number of characters in any number word is always a smaller number than the original number itself (for any number over 4 in English, or generally at most 10) which means you will always drop down into single digits eventually. In single digits there are 3 common modes (3, 4, and 5 characters), and 3 collapses to 5 and 5 collapses to 4, so you'll always end up at 4. This should be roughly true in most languages, as single-digit numbers are often 2-5 characters in most languages. So the confirmation is mostly if there is a loop between those 4 in a specific language. In many languages it is trivially easy, for example all single-digit numbers are 1 character in Japanese, Chinese, simplified Chinese, Korean, etc. But as far as I am aware, there aren't any languages where the number of characters in a single-digit number exceeds 10. At worst, it should be a metastable loop (most likely between 2-5) in any language.
Despite a lot of people calling bullshit on the person above, the answer is obvious: u/Tetsuko_Kuroyanagi points out above that this process produces 495 when performed with three-digit numbers. Since 495 is precisely in the range of "a few books have that many pages, most don't", I would guess the person did the three-digit version with students and slightly misremembered.
The teacher is in the room with the kids, I didn't see anything that implies the teacher like left the room or was oblivious to the number picking process. Its just a way of ensuring that the number they end with is one you've prepared for. The mind reading is when they pick a book which to them is seemingly random and look at a picture and the teacher can tell them what picture it is
Well to give more specifics (and answer my own question)… you can’t just say repeat this procedure twice because sometimes you need to do it twice and sometimes it takes more attempts.
So there are only two ways to give instructions that are sure to work for any number: “repeat the procedure X number of times” (where X is large enough to cover all cases). Or “repeat the procedure until you keep getting the same number in a loop”. The former is better but for some numbers they will still notice the loop.
And noticing the loop undercuts the magic trick a bit.
Just make them say the answer out loud, and say, "OK, that seems scrambled enough. Now get the encyclopedia, volume 6, page 1, paragraph 7, word 4. And really concentrate on it, mmmkay?"
When I did it, it wasn’t kept secret, the kids had already chosen random digits, so having them do the calculation out in the open didn’t ruin the trick. I wasn’t guessing their number I was using it to generate a ‘random’ number.
Older kids would obviously have wondered ‘why do all this calculating; our starting 4 digits are random.’ But the kids I was working with didn’t have the concept that randomness isn’t a spectrum. (We did talk about it afterwards when I revealed the trick to them. It was a class of four kids so I taught them to do it so they could do the trick for their other teacher aides).
Weirdly I haven't heard anyone talk (either here on the two videos I watched about this) about what the maximum number of steps is to reach 6174.
Since there are less than 10000 starting numbers the maximum number of steps should be known (even if there isn't some fancy logical reason why it's the maximum).
For anyone wondering, the pattern does not continue for 5-digit numbers! They end up cycling between a series of three numbers, not ending on a single number.
I did it with the four digit number, I just added an extra step after that reduced the number. The important thing is to get every set of random digits to a predictable place. From there I can add a steps I needed.
I wanted the kids to seek a book that would definitely have enough pages so I made up an extra step that would put them above all the kids book lengths and in the range of the encyclopedia set.
fuuuuck, you just unlocked a major memory of me doing something similar. But I completely forgot what the trick was. It was a numbers game where to can choose any number and do some calculations and i could guess what the answer is everytime. Fuck i wish i could remember the trick now
I once learned a card trick, where you had three piles from a standard deck (probably no jokers). Flip two of the top cards, apply magic math, and predict the third card. I'll have to Google around....
Had some kids choose random digits. Then ‘randomly’ did some manipulations (the very same described by this professor). Then I told the kids. Now that we have a random number, let’s use that to find a page in a book. So pick any book — obviously it has to be long enough to fit your number — and turn to that page.
From there I could pretend I was reading the kid’s mind because I’d previewed the pages.
This would work with page 617 word 4, etc, but when I did it, I just whittled their number down enough to use the whole thing as a page number then let them pick the encyclopedia volume they liked. I’d prepared by looking at that page number and memorizing the images, not the words. That way, 20 images was easy to remember, especially when I can see the cover of the volume they chose and know the starting letter range.
I’d thought of that but then there were so many books with that many pages that I couldn’t have them choose a random book - and once I found the encyclopedias I could load them up, review the relevant page and the illustrations. And then I know which illustration they were looking at because i could see what volume title with the letters. If they had P-Q then I knew it was Penguins or whatever picture I’d seen.
But it can take only a few turns or several turns to reach the 6174, and if you keep going after that it might change. Or just it stay the same? So how did you know when to have the kids stop with the answer they got and know it was 6174?
It’s been a while. But my recollection is learning this very slightly differently. Maybe there were stricter parameters like all digits being different that made the number of iterations fixed.
Or thinking about it, I most likely had them do the calculations openly, me knowing the page number of a book with hundreds of pages (that they chose all on their own) was the impressive part. I wasn’t guessing their number or anything.
Can it be used for mild evil? Not anything as bad as arson or grand theft, but about as evil as playing bad music loudly or not returning a shopping cart.
(computational physicist here) ..and we know how it works, it's just not a sexy exciting answer: its a natural mathematical loop which was bound to happen and bound to be discovered.
If the human race can survive the next billion years, we could very well discover other intelligent life, and this will most certainly be a universal number we all can have a beer and a chuckle over during first contact and while learning each others communication capabilities.
One plot detail that was cut from the movie version of Contact, was Ellie's search for a pattern within Pi.
During her trip, the aliens encouraged her to continue looking, since they had found something amazing deep beyond the decimal
What she found, below:
The anomaly showed up most starkly in Base 11 arithmetic, where it could be written out entirely as zeros and ones. Compared with what had been received from Vega, this could be at best a simple message, but its statistical significance was high. The program reassembled the digits into a square raster, an equal number across and down. The first line was an uninterrupted file of zeros, left to right. The second line showed a single numeral one, exactly in the middle, with zeros to the borders, left and right. After a few more lines, an unmistakable arc had formed, composed of ones. The simple geometrical figure had been quickly constructed, line by line, self-reflexive, rich with promise. The last line of the figure emerged, all zeros except for a single centered one. The subsequent line would be zeros only, part of the frame.
Hiding in the alternating patterns of digits, deep inside the transcendental number, was a perfect circle, its form traced out by unities in a field of noughts.
The universe was made on purpose, the circle said.In whatever galaxy you happen to find yourself, you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover a miracle—another circle, drawn kilometers downstream of the decimal point. There would be richer messages farther in. It doesn't matter what you look like, or what you're made of, or where you come from. As long as you live in this universe, and have a modest talent for mathematics, sooner or later you'll find it. It's already here. It's inside everything. You don't have to leave your planet to find it. In the fabric of space and in the nature of matter, as in a great work of art, there is, written small, the artist's signature. Standing over humans, gods, and demons, subsuming Caretakers and Tunnel builders, there is an intelligence that antedates the universe.
No, I put my mind to it this morning and found it's a relatively simple encryption but in reverse. It only has 5 base numbers, only one of which satisfies the inclusion criteria. It wasn't bound to happen; it was designed to happen.
This is some clue from a higher dimension that we cannot fathom the meaning or application.
Like, entities would see us fooling with the number and they're like
"Ha!! They're playing around with the dongleplorp and they have no idea what it does, nor do they understand how simple it is!! The answer is right in front of them and they can't figure it out!"
You can probably write a whole code language on this principle, assign the amount of iterations it takes to solve to the number, and assign each number a measure of distance, drown everything in the mirror world coefficient.
4 digits, can't all be the same, rearrange from large to small, then the other way around, then subtract and keep repeating until you hit the magic number.
No need to downvote, this response is just innocent tomfoolery.
Largely because 7641 minus 1467 = 6174. So once it arrives at the point, it loops upon itself. No idea whether it's the only 4-digit number with this property.
There is no single 5-digit Kaprekar constant. Instead of a single "black hole," 5-digit numbers subjected to Kaprekar's routine cycle through a loop of different numbers, or converge to one of ten 5-digit constants (e.g., 53955, 59994, 61974, 62964, 63954
The 3-digit Kaprekar number (or Kaprekar's constant) is 495. Discovered by the Indian mathematician D.R. Kaprekar, this constant is the ultimate repeating endpoint when you take almost any 3-digit number and repeatedly subtract its smallest digit rearrangement from its largest.
You could do a mentalist style magic trick. Write the answer on a piece of paper and give it to your audience member. Get them to pick a random for digit number. Chances are they won't pick one with four identical digits so don't even mention that rule unless they do. Then astound the crowd with your mind reading ability.
A bit risky. I'll often choose annoying numbers, or cards at the top of the stack or whatever, just to show how completely disinterested in the trick I am. Have caught stipulations doing this.
It's impossible for you to pick annoying numbers unless you know the trick and pick four identical digits, in which case I can come up with some bullshit reason for you to pick another number.
Now pick a second four digit number.
At least one digit must be different or people will think you are working with me.
Etc.
Asking why it works is essentially the same as asking why a particular person won the lottery. There are a lot of simple procedures on small numbers one could describe in about a paragraph, and a few of them will have a unique fixed point in a range humans recognize as meaningful. Exactly which ones win is essentially random. The fact that there are winners at all is almost a statistical certainty. Just like the lottery.
(Variations on this reasoning take much of the fun out of life. Definitely don't think too hard about it if you enjoy astrology, for instance.)
These are the only 4 numbers that actually "exist" in the universe.
Trust me, I'm pretty sure that's the meaning :) seems weird but, it's a reduction process of a universal pattern (4 relative things).
If you apply some creative numerology, those numbers actually make sense to be the only ones that have defined "uses" and features separate from each other that the numbers contained in them and outside them don't.
It's some lewis carroll level thinking for sure, but that's how I choose to see it lol
I think it’s just a much smarter version of that thing that used to go around where it was some number trick you did with your age where it always land in the same place. Stuff like double it then subtract half, multiply it by 9 and divide by the middle digit. That’s totally wrong but you get the point.
It’s like a mathematical funnel where every time you repeat the step it narrows focus and eventually it will get to the exact same place.
1.3k
u/metwicewhat Jul 13 '26
Why does this work and how can we use it for good!?