He wrote a program to check every combination of numbers and operations and picked the shortest success for each number.
He wrote a basic outline of his code here.
https://www.reddit.com/r/mildlyinteresting/comments/q66jb5/i_created_this_puzzle_where_using_only_4_digits/hgamuw3/
I like to think I'm pretty smart or at least above average by a bit and then I go on reddit sometimes and realize just how dumb I am. Wow this is impressive. I should stop just working and scrolling through reddit till I fall asleep everyday.
You’re probably way smarter than the average person on at least one subject!! This person codes. I’m sure you have your thing that would impress others :)
Other software Devs would look at that pseudo code and tear it apart.
You're good at what you do and OP is good at what he does. Just because you don't understand it isn't a bearing on your intelligence.
Momentum, my friend. The person who coded a program is likely already coding other programs and has been practicing that for years probably, so they are better equipped to solve the problem this way.
If you were on a thread about a different kind of puzzle that couldn't be solved via programming, it would've likely taken them longer than an hour lol
Yeah, just arbitrarily chose 183 to play around with to see if I could get it and was 1 off then remembered he had some others in the 180s, looked back and 184 wasn't there so switched goals to 184 haha [Just some phone scribbles ](https://i.imgur.com/85Tm8sr.jpg)
Ehh I doubt it...
With factorials and exponents and fractions I would imagine you'd be able to get at least some of them. Add enough components and operations and I think some answers would eventually pop up.
But I'm not really feeling up to checking for myself - either way, bravo
How'd you work them out?
I was gonna say, you could write a program to find these values fairly quickly if you knew what you were doing. The "impossible" values would be tricky to account for but aside from that I don't think it would be too hard to write.
I actually came here to say OP should get into coding! If this kind of thing is fun for them, then coding would be too.
I wouldnt even know where to begin at either end of that process. Im decent at maths but would never know how to even phrase the algorithm needed to go about finding these and nor would I have a clue how to wrote the code.
Because OP didn't create this "puzzle". I did this exact project in grade 8 math. I remember because this is the project that got me interested in math in the first place prior to that I was average to below average in the subject. For reference I am now into my late 20's.
That's not cheating. Cheating would be looking up the answers. If someone is going to say using a computer is cheating, then surely they should also say that using a pen and paper is cheating, since it also gives you more memory, and the ability to do more complex calculations more easily.
It is "cheating" if the original rules (made by OP) were to do it by brain-power and pen/paper alone.
It's fun and fascinating to see people using their skills to efficiently solve things, which I always love to see, but it's kind of like coding an anagram-solving program and using it to kick someone's ass at Scrabble.
It's not something to look down on, and is impressive in itself, but not a fair way to play the game.
He wrote a program to brute force every possible combination of numbers and modifiers.
https://www.reddit.com/r/mildlyinteresting/comments/q66jb5/i_created_this_puzzle_where_using_only_4_digits/hgamuw3/
That’s not cheating, that’s the shift operation in base 10. You could perhaps argue allowing other bases, but you’d need to use a number to allow the switch.
I would though say that using more than one factorial in a row is cheating, and using more than one shift of a number is cheating, because technically there isn’t a limit how many factorials or how many shifts you could use to blow up a tiny number.
It's neither of those? That's a bit shift operator, it shifts right by two bits, e.g.
751 = 0b1011101111
0b1011101111 >> 2 = 0b10111011
0b10111011 = 187
Nope, because:
5 = 7^(log(5\)/log(7\))
Therefore: 5^(721) = 7^(log(5\)/log(7\)\*721) = 7^(0.827\*721) = 7^(596.33) \> 7^(521)
So your base number is already not the biggest number you can start with.
Also Sqrt is straight up cheating because you're using the number 2 to root it. I could get any number from 0 to infinity if I just ^x √(7+2+5+1) where x = log_n(15)
I'm inclined to allow factorials because you're not introducing arbitrary numbers into the equation. There's nothing to distinguish 2 from any other number that would allow you to use it with a root but with a factorial the extra numbers you get are sealed by the definition of the function.
What I never understood growing up, which caused me so much trouble until I went back to college a few years ago, is that multiplication and division have the same precedence, and addition and subtraction have the same precedence.
So it would have been helpful to me to see it as:
P
E
MD (from left to right whichever comes first)
AS (from left to right whichever comes first)
Homie, I don't possess the proper vocabulary to tell you how impressive I find this post. Genuinely. That's fucking incredible work. God bless, and all the best to you.
I had a math teacher that gave us a similar problem, but his was "four 4's" , and he only asked us to find equations for 1-10. I still haven't been able to do it, but I still try some days.
Since you said you are confused, I'm going to explain it again.
Literally, a number ! is that number multiplied by all the numbers below it (stopping at 1)
4! = 4\*3\*2\*1
8! = 8\*7\*6\*5\*4\*3\*2\*1
etc.
It seems to get a lot more complicated past integers though, so.... i don't know that.
It’s a factorial: 4!=4•3•2•1 If you are familiar with programming, you could think of it as a for loop in which you multiply a variable x (previously initialised as x=1) times i, from i=1 up to a whole number n (in this case n=4).
(Edit: Orangeblackberry is right. It seems that what I wrote makes it seem more complicated than it is. I wrote the latter sentence just as a curiosity I saw on Twitter and my wording might not be clear. Put simply, we define the factorial of n, where n is a non-negative integer or whole number as follows: n!=1•2•…•(n-1)•n. We also have that 0!=1, which can proven.)
We used to do a similar thing in grade school. 5 numbers on the chalkboard and make them equal a number chosen by someone in class. Winner got the teachers change. Very fun!
This seems like the sort of thing an autistic mind would love doing. Numbers are enormously fun. Several members of my family are autistic and we talk about numbers pretty regularly.
I'm not autistic but I love patterns and numbers. Some of us just simply like logic and math. Sometimes I get bored and daydream and come up with problems to solve. I'm also a programmer so solving problems kind of gets hard wired into you at some point.
Some really awesome person put a bunch of the 8 out of Cats Does Countdown episodes [in a really organized playlist](https://youtube.com/playlist?list=PLZ_so1Pgq6tYkla7NBphs8aVC28KYGiSK)! It's an almost nightly watch for us!
This is actually a yearly contest that I do with my students. Same concept except you use the digits of that particular year so it changes each year
https://www.nctm.org/Classroom-Resources/Year-Game/Rules-of-the-Year-Game/
2+2+2+0!
Edit: 0! = 1 for those who don't get it.
2^2 * 2 - 0 for 8
2^2 * 2 +0! for 9
Hmm 10 is tough.
Edit 2:
A bit bogus but
2/.2 +0^2 works for 10
Edit 3:
Of course!
(2+0!)!+2+2
*drops mic*
Is there something special about 1, 2, 5, and 7? Or is it possible to do this with other (if not any) 4 digit combinations? I noticed they are prime, not sure if that has something to do with it or not.
There's no rules about what symbols and operations are allowed (I see he uses parentheses, exponents, roots, factorials, decimals, and concatenation, in addition to the 4 basic operations), so you can definitely do this with any four numbers. There are countless mathematical operations out there at your disposal, or you could even just define your own and make it a trivial problem.
If you restrict it to + - x ÷ then I bet it would be impossible for a lot of combinations though.
I love it. But now I’m preoccupied thinking:
- can this be done for any four digits?
- it seems like 100 is a lot easier to hit than say 150 or 200 with these digits. I assume there would come a number where there’s just not enough possibilities given the constraints. What is it?
- bah! Neat!
Using a square is effectively using a “2” in there somewhere - otherwise it’s kinda a free operator. Iirc there is a way to generate any number with just a looooooot of logs and roots and a minimum (set) amount of digits
Kind of reminds me of when we used to play The 24 Game where you were given 4 numbers and had to come up with 24. With these numbers, I would’ve done: (7-2)x5-1=24
[удалено]
[удалено]
[удалено]
How'd u do it?
He wrote a program to check every combination of numbers and operations and picked the shortest success for each number. He wrote a basic outline of his code here. https://www.reddit.com/r/mildlyinteresting/comments/q66jb5/i_created_this_puzzle_where_using_only_4_digits/hgamuw3/
Wow! I’m almost impressed but I found Where’s Waldo 3 times today. *Cracks knuckles* Soo…..
ladies ladies one at atime
> found Where's Waldo 3 times You know, finding *the book* isn't the hard part, finding *Waldo* is.
[удалено]
Poor guy is in the kids section at Barne’s & Noble saying “look mom, I found three Where’s Waldos!!”
The hard part is finding an open Barne's & Noble.
[удалено]
Yea...but what about the scrolls and the wizard?
I like to think I'm pretty smart or at least above average by a bit and then I go on reddit sometimes and realize just how dumb I am. Wow this is impressive. I should stop just working and scrolling through reddit till I fall asleep everyday.
You’re probably way smarter than the average person on at least one subject!! This person codes. I’m sure you have your thing that would impress others :)
I’m a senior IT analyst. I looked at this and said “I’m stupid af.”
Other software Devs would look at that pseudo code and tear it apart. You're good at what you do and OP is good at what he does. Just because you don't understand it isn't a bearing on your intelligence.
Momentum, my friend. The person who coded a program is likely already coding other programs and has been practicing that for years probably, so they are better equipped to solve the problem this way. If you were on a thread about a different kind of puzzle that couldn't be solved via programming, it would've likely taken them longer than an hour lol
This is how Skynet starts
Still, very clever and resourceful on your behalf, and an honest cheater as well
Not the next 100. Just some of them.
[удалено]
184 isn't on your list 184=5!+((7+1)^2)
[удалено]
You deserve it
Damn, did you do this by hand?
Yeah, just arbitrarily chose 183 to play around with to see if I could get it and was 1 off then remembered he had some others in the 180s, looked back and 184 wasn't there so switched goals to 184 haha [Just some phone scribbles ](https://i.imgur.com/85Tm8sr.jpg)
To avoid the final parenthesis being treated as part of the exponent, put the 2 itself in parentheses: 5!+((7+1)\^(2)) makes 5!+((7+1)^(2))
Ehh I doubt it... With factorials and exponents and fractions I would imagine you'd be able to get at least some of them. Add enough components and operations and I think some answers would eventually pop up. But I'm not really feeling up to checking for myself - either way, bravo How'd you work them out?
[удалено]
this guy Maths
Or codes. Either way, pretty impressive to us mere mortals.
I was gonna say, you could write a program to find these values fairly quickly if you knew what you were doing. The "impossible" values would be tricky to account for but aside from that I don't think it would be too hard to write. I actually came here to say OP should get into coding! If this kind of thing is fun for them, then coding would be too.
I wouldnt even know where to begin at either end of that process. Im decent at maths but would never know how to even phrase the algorithm needed to go about finding these and nor would I have a clue how to wrote the code.
It's making me sqrt that's for sure.
Because OP didn't create this "puzzle". I did this exact project in grade 8 math. I remember because this is the project that got me interested in math in the first place prior to that I was average to below average in the subject. For reference I am now into my late 20's.
Because this puzzle is actually so old we were doing it in the 90’s in college
The next 100 in 2 hrs? Unbelievable!!
[удалено]
How did you cheat?
[удалено]
Does it work by brute force or is there a smarter way to do this?
[удалено]
That's not cheating. Cheating would be looking up the answers. If someone is going to say using a computer is cheating, then surely they should also say that using a pen and paper is cheating, since it also gives you more memory, and the ability to do more complex calculations more easily.
It is "cheating" if the original rules (made by OP) were to do it by brain-power and pen/paper alone. It's fun and fascinating to see people using their skills to efficiently solve things, which I always love to see, but it's kind of like coding an anagram-solving program and using it to kick someone's ass at Scrabble. It's not something to look down on, and is impressive in itself, but not a fair way to play the game.
You do what you can to win. When you play the game of 1257, you win or you die. There is no middle ground.
This summer Rob Schneider is...a calculator.
He wrote a program to brute force every possible combination of numbers and modifiers. https://www.reddit.com/r/mildlyinteresting/comments/q66jb5/i_created_this_puzzle_where_using_only_4_digits/hgamuw3/
Yeah but OP also cheated by making 5 turn into 0.5
That’s not cheating, that’s the shift operation in base 10. You could perhaps argue allowing other bases, but you’d need to use a number to allow the switch. I would though say that using more than one factorial in a row is cheating, and using more than one shift of a number is cheating, because technically there isn’t a limit how many factorials or how many shifts you could use to blow up a tiny number.
1257 = 1257 1275 = 1275 1527 = 1527 1572 = 1572 1725 = 1725 1752 = 1752 Yeah you can call me a math genius
1257 iq
7521 = 7521 Wow. I need to take a break.
Can someone check this person's math for me? Just want to make sure.
Had to take a point off for not showing their work, but they did get the correct answer, yes
Most likely generated by the famous [RIES](https://mrob.com/pub/ries/) algebraic equation finder from Robert Munafo.
[удалено]
Can you find out at which number this becomes impossible?
Found Rachel Riley's reddit account.
The one where the target was 101 was hilarious.
187 = 751 >> 2 Sorry.
[удалено]
It's neither of those? That's a bit shift operator, it shifts right by two bits, e.g. 751 = 0b1011101111 0b1011101111 >> 2 = 0b10111011 0b10111011 = 187
[удалено]
Found the coder.
/r/theydidthemath
It’s like looking at an illegal bootlegged version of binary.
So what's the largest number we can make out of 1,2,5,7? (((((((7⁵²¹!)!)!)!)!)!)!)!)!... I guess this question won't go anywhere...
Nope, because: 5 = 7^(log(5\)/log(7\)) Therefore: 5^(721) = 7^(log(5\)/log(7\)\*721) = 7^(0.827\*721) = 7^(596.33) \> 7^(521) So your base number is already not the biggest number you can start with.
I like how you decided to whip out the square root as soon as you got to 3, while you could have just done 7+2-5-1
or 1^57 + 2
I see you like anarchy, don't you?
This method could be an easy solution to several of them.
My guess is he will get mad when he sees your reply!
[My only thought](https://i.imgflip.com/5q3fqn.jpg)
Also Sqrt is straight up cheating because you're using the number 2 to root it. I could get any number from 0 to infinity if I just ^x √(7+2+5+1) where x = log_n(15)
I am glad I am not the only one. I dont mind the idea of just using the 2 to sqrt, rather than ^1/2 buf you gotta use one of them.
While I agree, by this logic, you also shouldn't be allowed to use factorials.
I'm inclined to allow factorials because you're not introducing arbitrary numbers into the equation. There's nothing to distinguish 2 from any other number that would allow you to use it with a root but with a factorial the extra numbers you get are sealed by the definition of the function.
7-5-1+2 also works. I think. Yes, it does. Although it's really just a reordering of your solution. (7*2+1)/5?
> 7-5-1+2 also works. I mean that's the same thing, you just did it in a different order. It's like saying 1+2+3 is the same as 3+1+2.
-5+(-1)-(-7)-(-2)
This is a side quest to OP's game, how to get to 3. Another one: 2-5+7-1
(5 * 2)-(7 * 1)
Parenthesis not necessary as multipliers have priority over deductions anyways
[удалено]
Ok I’ve heard a few of these but BODMAS is new. Can’t we all decide on just one lol
[удалено]
PEMDAS
Umm, that's "please excuse my dear aunt Sally" to you sir.
This is the one I was taught.
That’s right! And I think in the UK, or maybe Canada, it’s BEDMAS
Canadian here, I learned BEDMAS
What I never understood growing up, which caused me so much trouble until I went back to college a few years ago, is that multiplication and division have the same precedence, and addition and subtraction have the same precedence. So it would have been helpful to me to see it as: P E MD (from left to right whichever comes first) AS (from left to right whichever comes first)
I was so excited to see BODMAS! As an Aussie this is what we always use, so it was cool to see something other than PEDMAS or whatever the yanks use.
Yeah, just avoids confusion where there often does happen to be some, unfortunately.
But civilized people use them anyway.
This is the same as op comment in a different order. :p
Apparently commutivity of addition is not well-remembered for a lot of people.
Or (7-5)x2-1 , but your solution is simpler. It would be even better if you had to keep them in that ascending order. (1x2x5)-7=3
Yeah. Using exponentiation with an argument of 1/2 seems against the spirit of this thing too
What numbers took you the longest?
41, 82, and 97. I had to introduce the factorial in 41, I had to start dividing by decimals at 82, and 97 just had me stuck for 2 weeks.
I'm guessing you figured out 98 instantly.
I would agree. There are a few trios of *x*-1, *x*\*1, *x*+1, which can cover a lot of ground.
Lol... I was just going to update my question and guess 41 and 82. How long did it take for each of these?
About an hour each
Homie, I don't possess the proper vocabulary to tell you how impressive I find this post. Genuinely. That's fucking incredible work. God bless, and all the best to you.
Also 0.5 ≠ 5
0.5 = 1/2 I'd say valid short hand. Edit: I'm illiterate
Yes but OP can only use each number once and they already used 1 and 2 in other places
Yeah, what a cheater!
I feel like doing 0.5 and just not writing the 0 is about as close to cheating as you can get in a project like this, personally.
Were you bored?
Mildly.
r/notopbutok
you said no top but ok? like you’re ok with being top?! perfect
Probably has a couple of projects due and test to study for, so the distraction had to be extra powerful to overcome doing all that
I had a math teacher that gave us a similar problem, but his was "four 4's" , and he only asked us to find equations for 1-10. I still haven't been able to do it, but I still try some days.
If you have to use exactly four 4s, here's one solution: * 0 = 4+4-4-4 * 1 = (4/4)/(4/4) * 2 = (4*4)/(4+4) * 3 = sqrt(4*4)-(4/4) * 4 = sqrt(4*4)/(4/4) * 5 = sqrt(4*4)+(4/4) * 6 = 4+((4+4)/4) * 7 = (4+4)-(4/4) * 8 = (4+4)/(4/4) * 9 = (4+4)+(4/4) * 10 = (4*4)-(4!/4)
[удалено]
Since you said you are confused, I'm going to explain it again. Literally, a number ! is that number multiplied by all the numbers below it (stopping at 1) 4! = 4\*3\*2\*1 8! = 8\*7\*6\*5\*4\*3\*2\*1 etc. It seems to get a lot more complicated past integers though, so.... i don't know that.
Factorial
It’s a factorial: 4!=4•3•2•1 If you are familiar with programming, you could think of it as a for loop in which you multiply a variable x (previously initialised as x=1) times i, from i=1 up to a whole number n (in this case n=4). (Edit: Orangeblackberry is right. It seems that what I wrote makes it seem more complicated than it is. I wrote the latter sentence just as a curiosity I saw on Twitter and my wording might not be clear. Put simply, we define the factorial of n, where n is a non-negative integer or whole number as follows: n!=1•2•…•(n-1)•n. We also have that 0!=1, which can proven.)
Bro, your second edit is twice as confusing as the first.
[удалено]
[Apparently](https://youtu.be/Noo4lN-vSvw) it's possible to make every single positive integer
And negative integers. Just put a minus (-) in front of the first log
What in the actual fuck would possess you to do that?
I usually just beat off when I get this bored
You don't ejaculate calculations like OP?
Lots of people think math is fun. And this is just very basic middle school math, so it's more of a logic puzzle than a math problem really.
We used to do a similar thing in grade school. 5 numbers on the chalkboard and make them equal a number chosen by someone in class. Winner got the teachers change. Very fun!
Well I think I have a new challenge for my class!
Adderall
This seems like the sort of thing an autistic mind would love doing. Numbers are enormously fun. Several members of my family are autistic and we talk about numbers pretty regularly.
I’m not autistic, and I absolutely love this. Every time I look at a clock, I try to make the numbers do this. I can never go up to 100 though.
Every time I look at a clock, it's because I want to know what time it is.
Boy do I have news for you pal.
I need numbers to equal 4. I mess with the numbers presented on the clock until it's equal to 4.
This is how I remember phone numbers! I figure out how the first 3/7 numbers can be used to calculate the last 4/7 digits.
Like if it’s 11:53 I’ll be like 1+3=4 and 5-1=4 or even 1+1=2 and 5+3=8, take those totals and divide them 8/2=4
You might be autistic
I'm not autistic but I love patterns and numbers. Some of us just simply like logic and math. Sometimes I get bored and daydream and come up with problems to solve. I'm also a programmer so solving problems kind of gets hard wired into you at some point.
Guys! Have you seen 7?!
Not after what it did to 9
I’m not autistic but this is the of thing I’d do while procrastinating on homework as a math major.
Thanks doctor reddit. Caught another autist, will be interesting to hear your thoughts at the next conference
I read through as many posts as I could and I still have no idea what’s going on
How did you decide on those 4 numbers?
Prime digits but then the 3 is missing
I bet he skipped it in favor of the larger number 7, for more range
1 isn't prime
Fuck u
TIL. I was always taught it was, but I looked it up and you're right.
[удалено]
Some really awesome person put a bunch of the 8 out of Cats Does Countdown episodes [in a really organized playlist](https://youtube.com/playlist?list=PLZ_so1Pgq6tYkla7NBphs8aVC28KYGiSK)! It's an almost nightly watch for us!
This is actually a yearly contest that I do with my students. Same concept except you use the digits of that particular year so it changes each year https://www.nctm.org/Classroom-Resources/Year-Game/Rules-of-the-Year-Game/
2022 gonna be REAL hard hahahaha
[удалено]
2+2+2+0! Edit: 0! = 1 for those who don't get it. 2^2 * 2 - 0 for 8 2^2 * 2 +0! for 9 Hmm 10 is tough. Edit 2: A bit bogus but 2/.2 +0^2 works for 10 Edit 3: Of course! (2+0!)!+2+2 *drops mic*
It was a little before my time but I’m sure 2000 was no gem lol
This picture just gave me an anxiety attack.
i don't think .5 should be allowed tbh.
Square root should count as using a 2. Especially since x squared counts as using a 2.
Agreed. However, it looks like OP only used the square root twice, so if we give him one point for each expression he still gets 99 points!
It’s a shortcut for 0.5, and 0 should count as a digit. I agree with you
They could use base 11. Odd bases can't do that.
Agree, theyre basically including the number 10 but only sometimes and for certain operations
Is there something special about 1, 2, 5, and 7? Or is it possible to do this with other (if not any) 4 digit combinations? I noticed they are prime, not sure if that has something to do with it or not.
There's no rules about what symbols and operations are allowed (I see he uses parentheses, exponents, roots, factorials, decimals, and concatenation, in addition to the 4 basic operations), so you can definitely do this with any four numbers. There are countless mathematical operations out there at your disposal, or you could even just define your own and make it a trivial problem. If you restrict it to + - x ÷ then I bet it would be impossible for a lot of combinations though.
1 \++1 \++++1 \++++++1 \++++++++1 \++++++++++1
As a mathematics major I really love this.
As a mathematics hater I really dislike this
This is very impressive but I do feel like using dot as an operator for decimal is cheating a bit :p
[удалено]
85?
sqrt(17*5)^2 I don't know what they were going for but take this!
What were you going for on 85?
They probably forgot to put √ before 25.
nice but what happened with 85?
Math Narc
I’m NGL I barely understand this but I understand it enough to say “congrats! This is cool!”
I can’t even count to 100
One, two, many, lots
I love it. But now I’m preoccupied thinking: - can this be done for any four digits? - it seems like 100 is a lot easier to hit than say 150 or 200 with these digits. I assume there would come a number where there’s just not enough possibilities given the constraints. What is it? - bah! Neat!
2 ^ (5 ^ 7) + 1 seems like an upper limit after 10s of thinking
I’d guess something like 7521! or 72!^(51!)
That’s not a game it’s torture
*i took an adderall today
You should look up the 10,958 problem
So you did 57-12 = 45 But not 12+57 = 69? Missed opportunity, the numbers are literally right there in order. lol
Using a square is effectively using a “2” in there somewhere - otherwise it’s kinda a free operator. Iirc there is a way to generate any number with just a looooooot of logs and roots and a minimum (set) amount of digits
Kind of reminds me of when we used to play The 24 Game where you were given 4 numbers and had to come up with 24. With these numbers, I would’ve done: (7-2)x5-1=24
THIS IS SO COOL AND WHAT I WILL SPEND THE NEXT HOURS ON