r/maths • • 1d ago

💬 Math Discussions Messed around with Gauss's 1–100 sum and solved it with calculus

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27 Upvotes

So I watched a YouTube Short about how Gauss found this arithmetic sum, and I decided to mess around, try some pattern matching, and ended up finding another way to solve it using calculus. Just a heads-up, I don't really pay much attention to symbols and notation, so my work might look a bit unorthodox. Are there any good books for learning how to express math properly?


r/maths • • 1d ago

❓ General Math Help Maths progression advice

1 Upvotes

I love maths and I’m currently in year 12 studying maths and further maths for my A levels. I want to learn higher level maths and I just don’t know where to start as it feels like everything needs prerequisites and then those aren’t interesting enough (or taught in an interesting enough way) that I have a bunch of motivation to self teach myself. I’m impatient to learn higher maths as I don’t want to have to wait for university. I was wondering if there was a book or something that could excite me and give me the same feeling I get when a great teacher explains a new concept. I don’t just want to grind through textbooks as I want it to be an enjoyable hobby, not just something I do for the sake of learning more maths. I also struggle on how to learn it because I don’t want to go too deep into one really niche part and miss out on the surrounding context or go too broad and get overwhelmed and never make significant progress. If anyone could help giving me a starting point, a checklist or the necessary prerequisites before I can move onto harder stuff (and maybe also ideas of what stuff to do after those) that would be much appreciated. Any helpful links or resources would also be greatly appreciated.
Thanks!


r/maths • • 1d ago

💬 Math Discussions How to remember the equations for long

1 Upvotes

Without forgetting them every time


r/maths • • 2d ago

❓ General Math Help can we prove for all int n>1 there is a distance between two primes exactly n ?

11 Upvotes

i mean there are infinite primes


r/maths • • 2d ago

Help: 📗 Advanced Math (16-18) I dont know what to do

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25 Upvotes

part 1,b seems in possible to get an answer when put back into the solution gets 2 and I'm really stuck ill really appreciate is i can get some help


r/maths • • 3d ago

💬 Math Discussions Book recommendations

4 Upvotes

So I’m in year 12 and I love maths. I’m doing further maths at sixth form and I’m almost growing impatient to wait to learn more interesting cool maths. I’ve tried to teach myself before but I can never do it successfully (always going to narrow and not really getting the context etc or going too broad and thinking ‘Oh now theres so many prerequisites I need to know’. I was hoping that theres a book that could help me with this. I don’t want something thats exactly like a textbook as I want to almost have a story to enjoy (not quite but I want the book to make me feel the pleasure of having a great teacher explain something). I’m open to books on most topics as I’m still unsure what I would like best. Any advice would be much appreciated. I’m sure many people have had similar troubles!
Thanks!


r/maths • • 3d ago

Help: 📘 Middle School (11-14) How do i find the amount of congruent triangles in these questions?

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4 Upvotes

I have only been able to make sense of area 1/2 which is 32 congruent triangles. I do not understand the rest of them. Area 1 is able to get 24 congruent triangles and you have to combine two of those little triangles to get an area of 1 according to other people, but the thing is when you combine two triangles there are only 16.


r/maths • • 3d ago

💬 Math Discussions A free story game that walks through the history of integration, 1675 onward. I'd love corrections on the math, the history, and the playability.

1 Upvotes

A Life in Slices is a math analogy game. Integirl's life mirrors the history of integral calculus, as accurately as I could make it while keeping the story in mind.

The story begins roughly with the birth of the integral sign (our heroine is the integral) and follows what came after: the struggle with Newton's dot notation, the problems the integral was used to solve, and the long road to rigor.

Integirl's story takes place in the same universe as my LinAlg Library story world: https://linalglibrary.com/

Play it free: https://yko79135.itch.io/a-life-in-slices


r/maths • • 4d ago

Help:🎓 College & University Trig and Geometry.

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38 Upvotes

Need help solving.


r/maths • • 3d ago

💬 Math Discussions I have solved basic math without being able to remember how to count on fingers.

0 Upvotes

Hello math people.
I have solved basic operation in math that was left like impossible, undefined, while working on my programming language, 'cause I want to build things on flawless fundamental rules and logic if possible for others and for the future, we need working things (especially math) that solve things for us properly and give us better and proper tools, so we don't have to do useless work and do it in bad ways.

I don't know if I even should tell what it is.

And I'm trying quickly to fix many fundamental math things, whilst I forgot how to write any math or what even is expression, 'cause I don't use almost anything math for 10years, but I was learning various concepts from various fields on YT and the things are connecting.

I don't understand how people do math when I figured out that nobody cares what even their basic equations are about. Almost no laws, rules, informations, just made up numerical space with operators that also barely have rules, just use whatever everything you want for whatever, mix it up literally for a century! Everything is silent assumptions about incompatible things and incomplete informations and frameworks.
Last thing I saw and why I get to this was division by 0. I looked at it and seen several problems, so I was like F do I have to solve also a math????? Wanted to do proper solution and explanation. Which I basically have but it's hard to complete it with overall math framework that make full sense. When you don't use any real basis and boundaries, please don't call it a "proof", almost everything goes to infinity if you allow it and don't care first want you are using.

Can I even get rewarded for my skills and what they did cost me, to be able to do it? I'm only really good in those things. Since my young age I wanted to use my self and talents to do things "for humanity", so basically anything I think about are things I don't even know how I can get paid for. I was gathering experiences and sacrificing things for this ability for more then 20y. Just to be able to get to this point, kinda late.. and standard work for someone is like impossible for me now.

I may need later some real matematician for both the math frameworks and the programming language concepts to check and try some things.

I have incredibly good things thought out, but can't do everything my self.


r/maths • • 3d ago

💬 Math Discussions Riemann Hypothesis, a Millenium Prize Problem, finally proven by Nuhash Badruzzaman (No AI was used in the making of this proof)

0 Upvotes

Conjecture: There exists a value of s where s = 0.

Answer: Incorrect/disproven.

PROOF: The Riemann Zeta function has no zeroes because the function is always additive (always results in a value greater than 0).The Riemann Zeta function has no zeroes because the function is always additive (always results in a value greater than 0). In fact, the function always at least equal to 1 because (the lowest value is 1) 1 to any exponent is only 1 itself. The function's values are always infinite in the positive y-direction for all values of x, with a minimum y-value of positive 1. The Riemann Zeta function has no negative y-value or zero. The same works for complex numbers in the complex plane, it is just the complex plane is LABELLED DIFFERENTLY from the real number plane.

The number of complex numbers equals the number of real numbers.

The value of the Riemann Zeta function is an infinite 2D plane where the lowest value in the plane is 1. Therefore the closed asymptote of the infinite 2D plane is y = 1.

For every value of s, the Riemann Zeta function returns infinite positive y-values infinity, where the maximum value is positive y-infinity and the minimum value is y = 1.

Proof that when s = 1/2, or when s = 1/4 or when s = 3/4, or for any value of s the Riemann Zeta function equals to infinity with an closed asymptote of x = 1. The asymptote is closed because for all values of s, the function has converged to 1 as the minimum value but DOES NOT APPROACH 1.

Example"

Starts with x = 1 and s = 1/2, the closed asymptote:

1/(1^1/2) = 1/1 = 1

1/(1^1/2) + 1/(2^1/2) + 1/(3^1/2) + 1/(4^1/2) + 1/(5^1/2) = 3.23

1/(1^1/2) + 1/(2^1/2) + 1/(3^1/2) + 1/(4^1/2) + 1/(6^1/2) = 3.64

Therefore, since 3.64 is greater than 3.23, the function has emerged to y-infinity for the maximum value when 6 terms were added together rather than the lower value of 5 terms. (The lowest value is 1 term or y = 1).


r/maths • • 3d ago

💬 Math Discussions There is a box ... BIG box.

2 Upvotes

Box in three-dimensional space. Box dimensions are integers. Surface diagonals are also integers. There is an inner diagonal for this very big box. The inner diagonal is also an integer. When you square these integers of dimensions of said big box and add them together, the value is equivalent to the square of the inner diagonal. Hmmm. artificial things #CannotCompute basic arithmetic - squaring and addition. Hmmmm.


r/maths • • 4d ago

💬 Math Discussions :3 i got curious about what would happen if you defined multiple number systems using seperate variables and saw how they interacted

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4 Upvotes

makes a rule for multiplying constants from systems with commutative and anticommutative multiplication

achievement unlocked: how in the everliving FUCK did we get here


r/maths • • 4d ago

Help:🎓 College & University Chuletas y pruebas matemáticas de acceso a la univesidad

1 Upvotes

HE creado un sitio web con tests y teoría matemática para las puebas de acceso a la universidad, echarle un vistazo en https://dailymathpuzzle.com/list.html, https://dailymathpuzzle.com/cheatsheets.html Estoy tratando de tener el mejor contenido en Internet en este sentido.


r/maths • • 4d ago

Help:🎓 College & University need help with linear algebra

3 Upvotes

i am pretty decent at maths, we got this course linear algebra for AI, i am not that good in this course, we are being taught normal things like SVD and then gradient descent , pca etc etc , basically the stanford course of linear algebra, what are the possible resources that would help me in grasping linear algebra in general as for the course part, its pretty simple to just do the questions asked lol


r/maths • • 5d ago

💬 Math Discussions The divisibility rules of 1 to 100 with examples and with attempts to explain why the rule works like that

14 Upvotes

For the 1st time I tried to make an effort in trying to explain why the rules work

NumberRuleExampleReason the rule works (or I think it works)
1Every number is a multiple of 112 is a multiple of 1Going 1 by 1 always gives you consecutive numbers
2It ends in 0, 2, 4, 6 or 8 (an even digit)10 is a multiple of 2 because it ends in 0Going 2 by 2 always gives you numbers that have the same 5 digits as the last digit
3The sum of the digits is a multiple of 312 is a multiple of 3 because 1 + 2 = 3, a multiple of 39 is the 1st multiple of 3 ending in 1 or 9 (in this case 9) and it's the number before 10
4The 2nd to last digit is even and the last digit is 0, 4 or 8 or the 2nd to last digit is odd and the last digit is 2 or 6100 is a multiple of 4 because the 2nd to last digit is 0 and the last digit is 0Going 4 by 4 gives you numbers that have the same 3 digits when the 2nd to last digit is either even or odd but when the 2nd to last digit changes its kind you get numbers that have the same 2 digits as the last digit
5It ends in 0 or 510 is a multiple of 5 because it ends in 0Going 5 by 5 always gives you numbers that have the same 2 digits as the last digit
6It's a multiple of both 2 and 312 is a multiple of 6 because it ends in 2, which means it's a multiple of 2, and 1 + 2 = 3, which means it's a multiple of 3The prime factorization of 6 is 2 * 3
7The subtraction of twice the last digit and the rest of the number is a multiple of 714 is a multiple of 7 because 4 * 2 - 1 = 7, a multiple of 721 is the 1st multiple of 7 that ends in 1 or 9 (in this case 1) and is the number after 20
8The 3rd to last digit is even and the last 2 digits are a multiple of 8 or the 3rd to last digit is odd and the last 2 digits are a multiple of 4 but not of 81000 is a multiple of 8 because the 3rd to last digit is 0 and the last 2 digits are 00, a multiple of 8Going 8 by 8 gives you numbers that have the same 13 combinations of last 2 digits when the 3rd to last digit is either even or odd but when the 3rd to last digit changes its kind you get numbers that have the same 12 combinations of last 2 digits
9The sum of the digits is a multiple of 918 is a multiple of 9 because 1 + 8 = 9, a multiple of 99 is the number before 10
10It ends in 0120 is a multiple of 10 because it ends in 0Going 10 by 10 always gives you numbers that end in the same digit
11The subtraction of the last digit and the rest of the number is a multiple of 11121 is a multiple of 11 because 12 - 1 = 11, a multiple of 1111 is the number after 10
12It's a multiple of both 3 and 4108 is a multiple of 12 because 1 + 8 = 9, which means it's a multiple of 3, and ends in 08, which means it's a multiple of 4The prime factorization of 12 is 3 * (22 = 4)
13The sum of 4 times the last digit and the rest of the number is a multiple of 13104 is a multiple of 13 because 10 + 4 * 4 = 26, a multiple of 1339 is the 1st multiple of 13 that ends in 1 or 9 (in this case 9) and is the number before 40
14It's a multiple of both 2 and 7112 is a multiple of 14 because it ends in 2, which means it's a multiple of 2, and 11 - 2 * 2 = 7, which means it's a multiple of 7The prime factorization of 14 is 2 * 7
15It's a multiple of both 3 and 5120 is a multiple of 15 because 1 + 2 = 3, which means it's a multiple of 3, and ends in 0, which means it's a multiple of 5The prime factorization of 15 is 3 * 5
16The 4th to last digit is even and the last 3 digits are a multiple of 16 or the 4th to last digit is odd and the last 3 digits are a multiple of 8 but not of 1610000 is a multiple of 16 because the 4th to last digit is 0 and the last 3 digits are 000, a multiple of 16Going 16 by 16 gives you numbers that have the same 63 combinations of last 3 digits when the 4th to last digit is either even or odd but when the 4th to last digit changes its kind you get numbers that have the same 62 combinations of last 3 digits
17The subtraction of 5 times the last digit and the rest of the number is a multiple of 17102 is a multiple of 17 because 10 - 2 * 5 = 0, a multiple of 1751 is the 1st multiple of 17 that ends in 1 or 9 (in this case 1) and is the number after 50
18It's a multiple of both 2 and 9126 is a multiple of 18 because it ends in 6, which means it's a multiple of 2, and 1 + 2 + 6 = 9, which means it's a multiple of 9The prime factorization of 18 is 2 * (32 = 9)
19The sum of twice the last digit and the rest of the number is a multiple of 19114 is a multiple of 19 because 11 + 4 * 2 = 19, a multiple of 1919 is the number before 20
20It ends in 00, 20, 40, 60 or 80100 is a multiple of 20 because it ends in 00Going 20 by 20 always gives you 5 different combinations of last 2 digits
21The subtraction of twice the last digit and the rest of the number is a multiple of 21105 is a multiple of 21 because 10 - 5 * 2 = 0, a multiple of 2121 is the number after 20
22It's a multiple of both 2 and 11132 is a multiple of 22 because it ends in 2, which means it's a multiple of 2, and 13 - 2 = 11, which means it's a multiple of 11The prime factorization of 22 is 2 * 11
23The sum of 7 times the last digit and the rest of the number is a multiple of 23115 is a multiple of 23 because 11 + 5 * 7 = 46, a multiple of 2369 is the 1st multiple of 23 that ends in 1 or 9 (in this case 9) and is the number before 70
24It's a multiple of both 3 and 81008 is a multiple of 24 because 1 + 8 = 9, which means it's a multiple of 3, and ends in 008, which means it's a multiple of 24The prime factorization of 24 is 3 * (23 = 8)
25It ends in 00, 25, 50 or 75100 is a multiple of 25 because it ends in 00Going 25 by 25 always gives you numbers that have the same 4 combinations of last 2 digits
26It's a multiple of both 2 and 13156 is a multiple of 26 because it ends in 6, which means it's a multiple of 2, and 15 + 6 * 4 = 39, which means it's a multiple of 13The prime factorization of 26 is 2 * 13
27The subtraction of 8 times the last digit and the rest of the number is a multiple of 27108 is a multiple of 27 because 8 * 8 - 10 = 54, a multiple of 2781 is the 1st multiple of 27 that ends in 1 or 9 (in this case 1) and is the number after 80
28It's a multiple of both 4 and 7112 is a multiple of 28 because it ends in 12, which means it's a multiple of 4, and 11 - 2 * 2 = 7, which means it's a multiple of 7The prime factorization of 28 is (22 = 4) * 7
29The sum of 3 times the last digit and the rest of the number is a multiple of 29116 is a multiple of 29 because 11 + 6 * 3 = 29, a multiple of 2929 is the number before 30
30It's a multiple of both 3 and 10120 is a multiple of 30 because 1 + 2 = 3, which means it's a multiple of 3, and ends in 0, which means it's a multiple of 10The prime factorization of 30 is 3 * (2 * 5 = 10)
31The subtraction of 3 times the last digit and the rest of the number is a multiple of 31124 is a multiple of 31 because 12 - 4 * 3 = 0, a multiple of 3131 is the number after 30
32The 5th to last digit is even and the last 4 digits are a multiple of 32 or the 5th to last digit is odd and the last 4 digits are a multiple of 16 but not of 32100,000 is a multiple of 32 because the 5th to last digit is 0 and the last 4 digits are 0000, a multiple of 32Going 32 by 32 gives you numbers that have the same 313 combinations of last 4 digits when the 5th to last digit is either even or odd but when the 5th to last digit changes its kind you get numbers that have the same 312 combinations of last 4 digits
33The sum of 10 times the last digit and the rest of the number is a multiple of 33132 is a multiple of 33 because 13 + 2 * 10 = 33, a multiple of 3399 is the 1st multiple of 33 that ends in 1 or 9 (in this case 9) and is the number before 100
34It's a multiple of both 2 and 17102 is a multiple of 34 because it ends in 2, which means it's a multiple of 2, and 10 - 2 * 5 = 0, which means it's a multiple of 21The prime factorization of 34 is 2 * 17
35It's a multiple of both 5 and 7105 is a multiple of 35 because it ends in 5, which means it's a multiple of 5, and 10 - 5 * 2 = 0, which means it's a multiple of 7The prime factorization of 35 is 5 * 7
36It's a multiple of both 4 and 9108 is a multiple of 36 because it ends in 08, which means it's a multiple of 4, and 1 + 8 = 9, which means it's a multiple of 9The prime factorization of 36 is (22 = 4) * (32 = 9)
37The subtraction of 11 times the last digit and the rest of the number is a multiple of 37148 is a multiple of 37 because 8 * 11 - 14 = 74, a multiple of 37111 is the 1st multiple of 37 that ends in 1 or 9 (1 in this case) and is the number after 110
38It's a multiple of both 2 and 19114 is a multiple of 38 because it ends in 8, which means it's a multiple of 2, and 11 + 4 * 2 = 19, which means it's a multiple of 19The prime factorization of 38 is 2 * 19
39The sum of 4 times the last digit and the rest of the number is a multiple of 39117 is a multiple of 39 because 11 + 7 * 4 = 39, a multiple of 3939 is the number before 40
40The 3rd to last digit is even and the last 2 digits are 00, 40 or 80, or the 3rd to last digit is odd and the last 2 digits are 20 or 601000 is a multiple of 40 because the 3rd to last digit is 0 and the last 2 digits are 00Going 40 by 40 gives you numbers that have the same 3 combinations of last 2 digits when the 3rd to last digit is either even or odd but when the 3rd to last digit changes its kind you get numbers that have the same 2 combinations of last 2 digits
41The subtraction of 4 times the last digit and the rest of the number is a multiple of 41123 is a multiple of 41 because 12 -3 * 4 = 0, a multiple of 4141 is the number after 40
42It's a multiple of both 2 and 21126 is a multiple of 42 because it ends in 6, which means it's a multiple of 2, and 12 - 6 * 2 = 0, which means it's a multiple of 21The prime factorization of 42 is 2 * (3 * 7 = 21)
43The sum of 13 times the last digit and the rest of the number is a multiple of 43172 is a multiple of 43 because 17 + 2 * 13 = 43, a multiple of 43129 is the 1st multiple of 43 that ends in 1 or 9 (in this case 9) and is the number before 130
44It's a multiple of both 4 and 11132 is a multiple of 44 because it ends in 32, which means it's a multiple of 4, and 13 - 2 = 11, which means it's a multiple of 11The prime factorization of 44 is (22 = 4) * 11
45It's a multiple of both 5 and 9135 is a multiple of 45 because it ends in 5, which means it's a multiple of 5, and 1 + 3 + 5 = 9, which means it's a multiple of 9The prime factorization of 45 is 5 * (32 = 9)
46It's a multiple of both 2 and 23138 is a multiple of 46 because it ends in 8, which means it's a multiple of 2, and 13 + 8 * 7 = 69, which means it's a multiple of 23The prime factorization of 46 is 2 * 23
47The subtraction of 14 times the last digit and the rest of the number is a multiple of 47188 is a multiple of 47 because 8 * 14 - 18 = 94, a multiple of 47141 is the 1st multiple of 47 that ends in 1 or 9 (in this case 1) and is the number after 140
48It's a multiple of both 3 and 1610032 is a multiple of 48 because 1 + 3 + 2 = 6, which means it's a multiple of 3, and ends in 0032, which means it's a multiple of 16The prime factorization of 48 is 3 * (24 = 16)
49The sum of 5 times the last digit and the rest of the number is a multiple of 49147 is a multiple of 49 because 14 + 7 * 5 = 49, a multiple of 4949 is the number before 50
50It ends in 00 or 50100 is a multiple of 50 because it ends in 00Going 50 by 50 always gives you numbers that have the same 2 combinations of last 2 digits
51The subtraction of 5 times the last digit and the rest of the number is a multiple of 51102 is a multiple of 51 because 10 - 2 * 5 = 0, a multiple of 5151 is the number after 50
52It's a multiple of both 4 and 13104 is a multiple of 52 because it ends in 04, which means it's a multiple of 4, and 10 + 4 * 4 = 26, which means it's a multiple of 13The prime factorization of 52 is (22 = 4) * 13
53The sum of 16 times the last digit and the rest of the number is a multiple of 53212 is a multiple of 53 because 21 + 2 * 16 = 53, a multiple of 53159 is the 1st multiple of 53 that ends in 1 or 9 (in this case 9) and is the number before 160
54It's a multiple of both 2 and 27162 is a multiple of 54 because it ends in 2, which means it's a multiple of 2, and 16 - 2 * 8 = 0, which means it's a multiple of 27The prime factorization of 54 is 2 * (33 = 27)
55It's a multiple of both 5 and 11165 is a multiple of 55 because it ends in 5, which means it's a multiple of 5, and 16 - 5 = 11, which means it's a multiple of 11The prime factorization of 55 is 5 * 11
56It's a multiple of both 7 and 81008 is a multiple of 56 because 100 - 8 * 2 = 84, which means it's a multiple of 7, and ends in 008, which means it's a multiple of 8The prime factorization of 56 is 7 * (23 = 8)
57The subtraction of 17 times the last digit and the rest of the number is a multiple of 57114 is a multiple of 57 because 4 * 17 - 11 = 57, a multiple of 57171 is the 1st multiple of 57 that ends in 1 or 9 (in this case 1) and is the number after 170
58It's a multiple of both 2 and 29116 is a multiple of 58 because it ends in 6, which means it's a multiple of 2, and 11 + 6 * 3 = 29, which means it's a multiple of 29The prime factorization of 58 is 2 * 29
59The sum of 6 times the last digit and the rest of the number is a multiple of 59118 is a multiple of 59 because 11 + 8 * 6 = 59, a multiple of 5959 is the number before 60
60It's a multiple of both 3 and 20120 is a multiple of 20 because 1 + 2 = 3, which means it's a multiple of 3, and ends in 20, which means it's a multiple of 20The prime factorization of 60 is 3 * (22 * 5 = 20)
61The subtraction of 6 times the last digit and the rest of the number is a multiple of 61122 is a multiple of 61 because 12 - 2 * 6 = 0, a multiple of 6161 is the number after 60
62It's a multiple of both 2 and 31124 is a multiple of 62 because it ends in 4, which means it's a multiple of 2, and 12 - 4 * 3 = 0, which means it's a multiple of 31The prime factorization of 62 is 2 * 31
63The sum of 19 times the last digit and the rest of the number is a multiple of 63252 is a multiple of 63 because 25 + 2 * 19 = 63, a multiple of 63189 is the 1st multiple of 63 that ends in 1 or 9 (in this case 9) and is the number before 190
64The 6th to last digit is even and the last 5 digits are a multiple of 64 and the 6th to last digit is odd and the last 5 digits are a multiple of 32 but not of 641,000,000 is a multiple of 64 because the 6th to last digit is 0 and the last 5 digits are 00,000, a multiple of 64Going 64 by 64 gives you numbers that have the same 1563 combinations of last 5 digits when the 6th to last digit is either even or odd but when the 6th to last digit changes its kind you get numbers that have the same 1562 combinations of last 5 digits
65It's a multiple of both 5 and 13195 is a multiple of 65 because it ends in 5, which means it's a multiple of 5, and 19 + 5 * 4 = 39, which means it's a multiple of 13The prime factorization of 65 is 5 * 13
66It's a multiple of both 2 and 33132 is a multiple of 66 because it ends in 2, which means it's a multiple of 2, and 13 + 2 * 10 = 33, which means it's a multiple of 33The prime factorization of 66 is 2 * (3 * 11 = 33)
67The subtraction of 20 times the last digit and the rest of the number is a multiple of 67134 is a multiple of 67 because 4 * 20 - 13 = 67, a multiple of 67201 is the 1st multiple of 67 that ends in 1 or 9 (in this case 1) and is the number after 200
68It's a multiple of both 4 and 17136 is a multiple of 68 because it ends in 36, which means it's a multiple of 4, and 6 * 5 - 13 = 17, which means it's a multiple of 17The prime factorization of 68 is (22 = 4) * 17
69The sum of 7 times the last digit and the rest of the number is a multiple of 69138 is a multiple of 69 because 13 + 8 * 7 = 69, a multiple of 6969 is the number before 70
70It's a multiple of both 7 and 10140 is a multiple of 70 because 4 * 2 - 1 = 7, which means it's a multiple of 7, and ends in 0, which means it's a multiple of 10The prime factorization of 70 is 7 * (2 * 5 = 10)
71The subtraction of 7 times the last digit and the rest of the number is a multiple of 71142 is a multiple of 71 because 14 - 2 * 7 = 0, a multiple of 7171 is the number after 70
72It's a multiple of both 8 and 91008 is a multiple of 72 because it ends in 008, which means it's a multiple of 8, and 1 + 8 = 9, which means it's a multiple of 9The prime factorization of 72 is (23 = 8) * (32 = 9)
73The sum of 22 times the last digit and the rest of the number is a multiple of 73292 is a multiple of 73 because 29 + 2 * 22 = 73, a multiple of 73219 is the 1st multiple of 73 that ends in 1 or 9 (in this case 9) and is the number before 220
74It's a multiple of both 2 and 37222 is a multiple of 74 because it ends in 2, which means it's a multiple of 2, and 22 - 2 * 11 = 0, which means it's a multiple of 37The prime factorization of 74 is 2 * 37
75It's a multiple of both 3 and 25150 is a multiple of 75 because 1 + 5 = 6, which means it's a multiple of 3, and ends in 50, which means it's a multiple of 25The prime factorization of 75 is 3 * (52 = 25)
76It's a multiple of both 4 and 19152 is a multiple of 76 because it ends in 52, which means it's a multiple of 4, and 15 + 2 * 2 = 19, which means it's a multiple of 19The prime factorization of 76 is (22 = 4) * 19
77The subtraction of 23 times the last digit and the rest of the number is a multiple of 77154 is a multiple of 77 because 4 * 23 - 15 = 77, a multiple of 77231 is the 1st multiple of 77 that ends in 1 or 9 (in this case 1) and is the number after 230
78It's a multiple of both 2 and 39156 is a multiple of 78 because it ends in 6, which means it's a multiple of 2, and 15 + 6 * 4 = 39, which means it's a multiple of 39The prime factorization of 78 is 2 * (3 * 13 = 39)
79The sum of 8 times the last digit and the rest of the number is a multiple of 79158 is a multiple of 79 because 15 + 8 * 8 = 79, a multiple of 7979 is the number before 80
80The 4th to last digit is even and the last 3 digits are a multiple of 80 or the 4th to last digit is odd and the last 3 digits are a multiple of 40 but not of 8010000 is a multiple of 80 because the 4th to last digit is 0 and the last 3 digits are 000, a multiple of 80Going 80 by 80 gives you numbers that have the same 13 combinations of last 3 digits when the 4th to last digit is either even or odd but when the 4th to last digit changes its kind you get numbers that have the same 12 combinations of last 3 digits
81The subtraction of 8 times the last digit and the rest of the number is a multiple of 81162 is a multiple of 81 because 16 - 2 * 8 = 0, a multiple of 8181 is the number after 80
82It's a multiple of both 2 and 41164 is a multiple of 82 because it ends in 4, which means it's a multiple of 2, and 16 - 4 * 4 = 0, which means it's a multiple of 41The prime factorization of 82 is 2 * 41
83The sum of 25 times the last digit and the rest of the number is a multiple of 83332 is a multiple of 83 because 33 + 2 * 25 = 83, a multiple of 83249 is the 1st multiple of 83 that ends in 1 or 9 (in this case 9) and 249 is the number before 250
84It's a multiple of both 4 and 21168 is a multiple of 84 because it ends in 68, which means it's a multiple of 4, and 16 - 8 * 2 = 0, which means it's a multiple of 21The prime factorization of 84 is (22 = 4) * (3 * 7 = 21)
85It's a multiple of both 5 and 17255 is a multiple of 85 because it ends in 5, which means it's a multiple of 5, and 25 - 5 * 5 = 0, which means it's a multiple of 17The prime factorization of 85 is 5 * 17
86It's a multiple of both 2 and 43172 is a multiple of 86 because it ends in 6, which means it's a multiple of 2, and 17 + 2 * 13 = 43, which means it's a multiple of 43The prime factorization of 86 is 2 * 43
87The subtraction of 26 times the last digit and the rest of the number is a multiple of 87174 is a multiple of 87 because 4 * 26 - 17 = 87, a multiple of 87261 is the 1st multiple of 87 that ends in 1 or 9 (in this case 1) and is the number after 260
88It's a multiple of both 8 and 111056 is a multiple of 88 because it ends in 056, which means it's a multiple of 8, and 105 - 6 = 99, which means it's a multiple of 99The prime factorization of 88 is (23 = 8) * 11
89The sum of 9 times the last digit and the rest of the number is a multiple of 89178 is a multiple of 89 because 17 + 8 * 9 = 89, a multiple of 8989 is the number before 90
90It's a multiple of both 9 and 10180 is a multiple of 90 because 1 + 8 = 9, which means it's a multiple of 9, and ends in 0, which means it's a multiple of 10The prime factorization of 90 is (32 = 9) * (2 * 5 = 10)
91The subtraction of 9 times the last digit and the rest of the number is a multiple of 91182 is a multiple of 91 because 18 - 2 * 9 = 0, a multiple of 9191 is the number after 90
92It's a multiple of both 4 and 23184 is a multiple of 92 because it ends in 84, which means it's a multiple of 4, and 18 + 4 * 7 = 46, which means it's a multiple of 23The prime factorization of 92 is (22 = 4) * 23
93The sum of 28 times the last digit and the rest of the number is a multiple of 93372 is a multiple of 93 because 37 + 2 * 28 = 93, a multiple of 93279 is the 1st multiple of 93 that ends in 1 or 9 (in this case 9) and is the number before 280
94It's a multiple of both 2 and 47282 is a multiple of 94 because it ends in 2, which means it's a multiple of 2, and 28 - 2 * 14 = 0, which means it's a multiple of 47The prime factorization of 94 is 2 * 47
95It's a multiple of both 5 and 19285 is a multiple of 95 because it ends in 5, which means it's a multiple of 5, and 28 + 5 * 2 = 38, which means it's a multiple of 19The prime factorization of 95 is 5 * 19
96It's a multiple of both 3 and 32100,032 is a multiple of 96 because 1 + 3 + 2 = 6, which means it's a multiple of 3, and ends in 00,032, which means it's a multiple of 32The prime factorization of 96 is 3 * (25 = 32)
97The subtraction of 29 times the last digit and the rest of the number is a multiple of 97194 is a multiple of 97 because 4 * 29 - 19 = 97, a multiple of 97291 is the 1st multiple of 97 that ends in 1 or 9 (in this case 1) and is the number after 290
98It's a multiple of both 2 and 49196 is a multiple of 98 because it ends in 6, which means it's a multiple of 2, and 19 + 6 * 5 = 49, which means it's a multiple of 49The prime factorization of 98 is 2 * (72 = 49)
99The sum of 10 times the last digit and the rest of the number is a multiple of 99198 is a multiple of 99 because 19 + 8 * 10 = 99, a multiple of 9999 is the number before 100
100It ends in 001200 is a multiple of 100 because it ends in 00Going 100 by 100 always gives you numbers that end in the same last 2 digits

r/maths • • 4d ago

❓ General Math Help Math books

1 Upvotes

Hi, is there any book I can read that will make maths interesting for me? Like for physics, there's Six Easy Pieces by Feynmann, I know maths is pretty abstract but I just want to read something that will bring back my spark for mathematics.


r/maths • • 4d ago

💬 Math Discussions 5 of the 7 Millenium Prize Problems solved and verified by Nuhash Badruzzaman and submitted on one day, many years of private work, no AI was used here in the making of these proofs

0 Upvotes

r/maths • • 4d ago

💬 Math Discussions What's the answer?

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0 Upvotes

r/maths • • 5d ago

💬 Math Discussions Heres an interesting variation of the Monty Hall problem I thought of: Misinformed Monty

3 Upvotes

So in the classic Monty hall problem, Monty knows which door has the car and always reveals a goat. This creates a 1/3 chance to win by staying and a 2/3 chance to win by switching (since the your initial pick is a 1 in 3 guess).

Theres also the version where he doesn't know and sometimes reveals the car, which ends the game immediately. This version is 50/50 since him being able to reveal the car weakens the chance to win by switching.

But now lets imagine a version where Monty is misinformed about where the car is, but still trys to avoid revealing it. For example: Monty thinks the car is behind door #2, buts its actually behind door #3.

If you picked door #1, Monty would think he now has to open door #3, so he would do that and end the game immediately by revealing the car.

If you picked door #2 (the door Monty thinks has the car), then he would freely choose ethier door #1 or #3 to open. If he opens door #1, switching to door #3 wins. If he opens door #3, the game ends immediately.

And lastly, if you pick door #3 (the door that actually has the car), then Monty now thinks he has to open door #1, after which, you'd win by staying with door #3

So in total, the odds for this version are:

Staying wins: 1/3

Switching wins: 1/6

Car revealed:1/2

This means that staying is twice as good as switching overall, the exact opposite of the regular problem funnily enough!


r/maths • • 5d ago

💬 Math Discussions hot take long division is easy it just isn't taught correctly in schools

7 Upvotes

lol


r/maths • • 5d ago

💡 Puzzle & Riddles Magic the Gathering Hypothetical

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1 Upvotes

I created a hypothetical board state in Magic the Gathering that in order to resolve the addition properly could take hours to resolve, and want to instead create an equation/formula that would allow me to plug in values to figure out the result rather than have everyone wait for me to finish going through the cycle. It is a non-infinite loop, that has multiple variables that can be different from game to game, but as it is what the deck intends to push towards in a game, it is likely that some iteration of this state occurs in a game.

I have linked a document in which I attempted to explain the hypothetical. If anybody is interested in helping me figure this out I would greatly appreciate it, as well as any input in making the explanation clearer.

If you have any questions regarding the hypothetical, I will try to respond if any rules need explaining etc.

Sorry if I'm formatting this wrong, this is my first post here and I'm not sure as to the exact nature of what the answer to my question would be, so I'm labeling it as a function.


r/maths • • 5d ago

💬 Math Discussions What's the answer?

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0 Upvotes

r/maths • • 6d ago

💡 Puzzle & Riddles Finished: 3=10 (base-3)

0 Upvotes

If this formula is a suppose formula
So I can suppose t=3 and 10=3 now!

So altogether is:
3+3+3=9

Then: t++t+t/t=3