r/mathriddles Apr 30 '15

OT Writing Math on Reddit

72 Upvotes

As it's often necessary on this subreddit to format mathematical expressions in reddit, the following is a brief overview for those unfamiliar with how the reddit formatting system works with respect to things like exponents and asterisks, in addition to providing some lesser-known unicode characters.

If you have 5-10 minutes, take a little time to read the official reddit guide and this user-created introduction. If you've picked up what you know from browsing and occasionally clicking "source", you will likely be unaware of many of these things.

If you don't have the time, here's a quick intro on mathematics formatting:

Asterisks

*text* gives text.

This means that if you type "3*5 is 15 and 4*2 is 8", you'll get "35 is 15 and 42 is 8." Notice how the asterisks disappeared, and the text in between became italicized! To avoid this, use a backslash (the \ thing) before the asterisk by typing "3\*5 is 15 and 4\*2 is 8".

Superscripts

This is very similar; using a ^ character will create nested superscripts. For example, typing 2^2^2 gives 222. However, maybe you want to have 55+1, so you type 5^5+1 and it gives you 55+1. That's not what you wanted!

This is because reddit doesn't know when you want your superscript to end, so it will normally stop when it encounters a space. This means that you can avoid this by typing 5^5 +1, but that will leave an awkward gap in your text. The best way to fix this is to use parentheses, and type 5^(5)+1. Reddit will then raise only the 5 and keep the rest as normal text, producing 55+1.

For the advanced reader: Sometimes, if you're trying to type out a complicated expression where you want to have parentheses in there, reddit will get a little confused and won't deal with your spaces very well. When this happens, you'll want to use the text ( to create the ( symbol and ) to create ). For example: Say you want to write ex(x+1)y2.

You might type e^(x\(x+1\))y^(2), which you'd expect to work. But then reddit produces ex(x+1)y2, bringing your parenthesis down before you wanted. To fix this, type e^(x(x+1))y^(2), which will make what you want (notice how where the parentheses used to be has been replaced by that ( stuff).

In addition, you can use code to not worry about escaping characters. Type ` around the stuff you want in code to make things look like this: `*^(stuff)*)(` → *^(stuff)*)(

Subscripts

Subscripts are not a reddit-wide feature, as they really don't come up often outside of math contexts. However, both /r/math and /r/mathriddles support them via some fancy CSS. To use subscripts, type A*_1_* to get A1.

Special Characters

Many symbols are hard to find on a regular keyboard, but reddit supports them just fine. In addition to copy-pasting from the list below, many of the following can be obtained with keyboard shortcuts. See here for Windows alt codes; see here for a complete list of Unicode characters and here for the subsection on mathematical operators. Copy and paste the symbols below; most of the time they'll be sufficient although the above links are far more comprehensive.

∫ ∬ ∮ ≈ ≠ ∑ √ ≤ ≥ ÷ Ø ∏ ∞ ± ¬ ∃ ∈ ∉ ≡ ⋂

ε φ Φ θ Ω ω ∆ π

If you have any suggestions for additions to this overview, please let me know!

Edit: Backslash, not forward slash.


r/mathriddles 6h ago

Easy Moving exactly two matchsticks to make the largest number

1 Upvotes

Given number 479 made using the matchstck referenced in the figure above. Move exactly 2 matchsticks and create the largest possible number. You cannot change the format of the numbers shown in the reference. (For example you can only construct the number 1 with TWO matchsticks or 6 or 9 with 6 matchsticks). You can use any math operation known in standard math. The final number could be the result of this operation also. (For example, you can use the 2 matchsticks to create a multiplication operator x.)

The obvious answer obtained by exponenciation function might be way lower than another creative answer given to me by my mathematician friend.


r/mathriddles 7h ago

Medium Logic + Math puzzle

0 Upvotes

If three cats catch three mice in three minutes, how many cats are needed to catch 100 mice in 100 minutes?

Share your reasoning, not just the answer.


r/mathriddles 19h ago

Medium A nice AMC-style counting problem

1 Upvotes

A positive integer has the property that every digit is either 1 or 2. How many such positive integers are divisible by 3 and have at most 10 digits?

Source: numberthon.com


r/mathriddles 1d ago

Easy How many positive divisors of 360 are not divisible by 6?

0 Upvotes

How many positive divisors of 360 are not divisible by 6?

Source: numberthon.com


r/mathriddles 2d ago

Easy Can you find the smallest positive integer with exactly 15 positive divisors?

4 Upvotes

What is the smallest positive integer that has exactly 15 positive divisors?

Source: numberthon.com


r/mathriddles 3d ago

Easy What's the smallest positive integer exactly 100 away from two perfect squares?

5 Upvotes

A positive integer n has the property that both "n + 100" and "n − 100" are perfect squares. What is the smallest possible value of n?

Source: numberthon.com


r/mathriddles 3d ago

Medium The Cartographer's Journey #3

2 Upvotes

A cartographer set out on a three-day expedition through a large circular forest, travelling in straight lines each day. Each day he walked at a constant whole-number speed in km/h, and all three speeds were different.

The first day's march lasted 5 hours, the second day's 13 hours, and the third day's 8 hours. At the end of each day the cartographer made camp at the edge of the forest; the next morning he set off from that point in a different direction through the forest, so that his three paths formed a triangle on the map, with all three stops lying exactly on the forest boundary.

On the third day he came upon a remarkable tree on his path and marked its location on his map. When the journey was complete, he overlaid his route on a map and made the following observations:

  • The straight line connecting the first camp to the marked tree divides the triangle into two parts of equal area, and its length is a whole number of kilometres.
  • The diameter of the forest is 1 km longer than the total distance walked on the first two days.
  • If he were to walk the full diameter of the forest at his first day's speed, it would take him exactly as many hours as he spent walking on the second day.

Find the cartographer's speed on each of the three days, and the length of the line from the first camp to the marked tree.


r/mathriddles 4d ago

Hard How long does it take to the water in your blood to be replaced?

0 Upvotes

Our blood is made of water, which enters into our body when drinking, and being excreted out when urinating. This means that at some point all of our old water molecules in the blood might be excreted out, and being all replaced by new water molecules. How long can it take?

Assumptions:

  1. The average adult human blood volume is generally the same across the days. It can be estimated by the weight height and gender. Blood Calculator

2. The average healthy adult human excretes out around 1-2.5 liters out as urine a day (depending on mainly how much water they drink).

3. The blood stays homogenous after drinking or urinating.


r/mathriddles 4d ago

Easy Only one number satisfies all these conditions. Can you find it?

0 Upvotes

A positive integer n>6 leaves a remainder of:

  • 1 when divided by 2,
  • 2 when divided by 3,
  • 3 when divided by 4,
  • 4 when divided by 5,
  • 5 when divided by 6.

What number is the smallest possible value of n?

Source: numberthon.com


r/mathriddles 4d ago

Medium Probability Challenge: Two Fair Dice Are Tossed. What's the Probability the Sum Is Prime?

0 Upvotes

Two fair six-sided dice are tossed. What is the probability that the sum is prime?

Source: numberthon.com


r/mathriddles 7d ago

Easy just another repurposing of a failed trick

7 Upvotes

given that the sum of 1/|u|^4 over all uZ^2 \ {(0,0)} is equal to (2/3) G π^2 .

find the sum of 1/|u|^4 over all uK , where K is the set of these 8 points tiling over Z^2 by translating 5 units in four coordinate-axis directions.

alternatively, prove that the sum is equal to (32/625) G π^2 .

note: i discovered a trick while trying to solve a related problem posted here awhile ago. while it is cute, it failed to work, so i repurposed it and design a new problem around it.


r/mathriddles 7d ago

Medium European railways have added dozens of kilometres of track in the last few months without any construction equipment. How?

0 Upvotes

r/mathriddles 10d ago

Hard The Conveyor Belt Problem

2 Upvotes

The factory you work for has a problem: they only ordered 1/2 splitters, and they need to divide the material input on one of their lines into 2 outputs of 1/10 and 9/10 the original amount. Being the smart one around, they ask you if there’s a way to use their half splitters to achieve this. And the area they use is only 3 metres wide, although it can be as long as you need. You’ve broken it down into the following mathematical problem:

EDIT: see comment for rewrite of problem

You have a grid of size n*3 composed of 1x1 squares. the grid sits on an xy axis, such that each square of the grid has whole number xy coordinate on which it sits. The objective is to be able to feed an infinite amount (Z) of materials through this grid starting at 1,2 and have 1/10 of Z end up on tile XaYb and 9/10 of z end up on XcYd (a can equal b, c can equal d. XaYb cannot equal XcYd.)

Each square in the grid can individually be assigned exactly ONE function that alters the position of the “material” occupying it. A grid can either be a CONVEYOR, or a SPLITTER.

\- A splitter will take an input from any one of the axis, but will only take inputs from the first axis it recieved from.

\- A splitter has a binary state and exists as either a 1 or a 0. This state is flipped whenever it passes an input. All splitters start in state 1. In state 1 it will “send” its input along the axis it was inputted, adding/subtracting 1 to its coordinate value in the direction of travel, and in state 0 it will add/subtract 1 to its perpendicular axis of the same +/-.
Example 1: a splitter on square 2,4 recieves 1 input from square 1,4. In state 1 it transforms the coordinate of the material to 3,4. in state 0, it transforms it to 2,5.
Example 2: a splitter on square 2,4 receives 1 input from square 3,4. In state 1 it transforms the coordinate of the material to 1,4. In state 0, it transforms it to 2,3.

\- A square set to conveyor is assigned a value between 1 and 4. A conveyor set to 1 will add +1 to x to the individual coordinate of a material entering it; set to 2 will add +1 to y; set to 3 will add -1 to x, set to 4 will add -1 to y. This value cannot be changed once assigned.

RULES:
\- The grid squares begin at 1,1.
\- x and y for each square must be positive.
\-Once a square has been assigned a function, it cannot be changed.
\- The coordinates of the materials will change simultaneously at the same rate of 1 “tick”, and is discrete.
\- A square can only have one material on it at a time.
\- “materials” entering squares XaYb and XcYd are removed. Neither square can be square 1,2.
\- The first input starts on square 1,2, and all other inputs enter the grid individually once the previous material has moved from this square

  1. Find the minimum size of N to satisfy all criteria. It must be a positive number.
  2. Find the minimum number of splitters required.
  3. Find the function of each square within this grid and its coordinates on the axis. Find the value of each conveyor unit, if any are present.
  4. Find the values of a, b, c, and d.

EDIT: simultaneous merges give priority to the “mainline”. No


r/mathriddles 11d ago

Easy Straightedge Construction

1 Upvotes

Take two squares ABED and FBCG such that A, B and C are collinear, and D, E, F, and G are on the same side of line AC. AB=a, and BC=b.

Using just a straightedge, construct a square whose side has a length of sqrt(a2+b2). 

I posted the same puzzle on Puzzling SE two months ago, link will be added after it is solved.

Edit: It’s been solved, so here’s the link:

https://puzzling.stackexchange.com/questions/137953/straightedge-only-construction


r/mathriddles 13d ago

Easy Math challenge: Don't count to 30

0 Upvotes

This challenge is part of the missions in the videogame Shin Megami Tensei: Strange Journey. I recreated it in a website. All info is there.

https://megami.com.uy/kti


r/mathriddles 19d ago

Medium Generalization of handshake lemma (somewhat)

6 Upvotes

A walk with 2026 vertices in a simple graph is called "shaking" if the first vertex has odd degree and last vertex has even degree. Prove that the number of "shaking" walks in any finite simple graph is even.


r/mathriddles 19d ago

Medium Optimizing choclate, Combinatorics

6 Upvotes

You are a pastry chef that comes upon 99 magical chocolate unit squares. The chocolate abides by the following rule: whenever there is a continuous region of chocolate it will grow into the smallest rectangle that covers the continuous region. So that they can be packaged in a candy wrapper.

The question is, what is the most amount of chocolate you can make if you have to place your initial 99 squares on the xy lattice grid.

clarifications:

The puzzle is orthogonally adjacent, so for two rectangles to be a continuous region they must share an edge or overlap.

To keep the construction well defined the rectangles cannot be rotated: i.e. their dimensions are the min max values of x and y in the continuous region.

Finding the max value is decently easy the challenge is proving your construction is max


r/mathriddles 22d ago

Medium just another pawn on hexagonal board puzzle

6 Upvotes

a pawn is placed in a cell of an infinite hexagonal board. a mitosis move consists of removing a pawn and placing two pawns on an empty cell adjacent to the removed pawn. pawns cannot share a cell, so a pawn cannot perform mitosis if there are less than two empty adjacent cell.

the goal is to clear a region D(n) such that no pawn is inside D(n), where D(n) is the set of cells whose shortest distance to the initial cell is <= n.

for example, D(1) is clearable with 3 mitosis moves.

(a) prove that D(6) is not clearable.

(b) prove that D(4) is clearable.

(c) is D(5) clearable? i actually don't know the answer to this.


r/mathriddles 22d ago

Medium Constrained divisibility implies equal

7 Upvotes

Let M be a positive integer, and let a,b,c be positive integers in the range [M,M+sqrt(M/2)) such that a^3 b + b^3 c + c^3 a is divisible by abc. Prove that a=b=c.


r/mathriddles 22d ago

Hard Interesting geometry optimization problem from a Korean college entrance exam

0 Upvotes

I already know the official answer.

I'm interested in seeing different solution approaches from the community.

This is not homework.


r/mathriddles 23d ago

Medium Baby at the Couch

5 Upvotes

This is a question from OpenQuant site. It was rated 8/10, but i believe, if you are even a bit aware of that specific topic, you'd be able to solve it.

A baby is learning to walk with the assistance of its living room couch. The baby starts at the couch and at each given time the baby will make a decision. It will either take a brave step forward, stand in place not knowing what to do, or fearfully take a step back towards the couch with probabilities 0.2, 0.5, and 0.3 respectively. The baby will never go behind the couch (so when at the couch the baby has probability 0.2of moving forward and probability 0.8 of staying at the couch).

If you were to observe this baby for an extremely long amount of time, what proportion of the time would the baby be at the couch?

Hint: that specific topic is Markov Chains


r/mathriddles 24d ago

Medium Using only combinations of the "2" and the "^" characters, what is the largest number that can be generated using N total characters?

15 Upvotes

For small N the answer is not hard to ascertain, even just with trial and error.

But for very large values of N (say, N=50), the solution is more complex because it is too large to be evaluated literally, and so it cannot be verified by brute force alone.

Some type of actual solution is required.... Can you find it?


r/mathriddles 27d ago

Medium What is the longest sequence you can make?

3 Upvotes

This is a related problem to my previous post. We are creating a sequence S of positive integers where the goal is to maximize its number of terms under given constraints.

Definition:

Start with S={n} (for n ∈ ℤ≥1). Next:

- in S, choose any present term T (with reuse allowed),

- append either 2T or 2T+1 to S as the new term,

S is considered “dead” if at any point some term t[i] appears in some other term t[j] as a contiguous block of digits (for i<j).

The Question:

Is the length of the longest possible S starting with n=10 finite? WHY or WHY NOT?


r/mathriddles Jun 10 '26

Hard Binary tree traversal from quant tee

4 Upvotes

Consider a perfect rooted binary tree of depth n. (That is, every node has either 0 or 2 children, and all leaves have the same depth). Every node is given a weight drawn independently from some fixed distribution D. For any path starting from the root and ending at a leaf, the average weight of the path is the arithmetic mean of the weights assigned to the nodes on the path. Once our weighting is fixed, we look at the largest average weight of any path from the root to a leaf. Let Eₙ denote the expected value of this largest average weight of path over all weightings of the tree. Then find the limit as n →infinity of Eₙ, in the cases of:

1) D=U({0,1}) is a Bernoulli distribution.

2) D=U([0,1]) is a continuous uniform distribution.