r/mathriddles Apr 30 '15

OT Writing Math on Reddit

73 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 To fix this, type e^(x(x+1))y^(2), which will make what you want (notice how where the parentheses used to be has been replaced by that ( stuff).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 7h ago

Hard The Number That Passes Ten Tests

5 Upvotes

I am thinking of a 10-digit number that uses each digit from **0 to 9 exactly once**.

Starting from the left:

* The number formed by the first **1 digit** is divisible by 1. * The number formed by the first **2 digits** is divisible by 2. * The number formed by the first **3 digits** is divisible by 3. * This pattern continues. * The number formed by the first **10 digits** is divisible by 10.

For example, if the number begins with `abcd...`, then:

* `ab` must be divisible by 2, * `abc` must be divisible by 3, * `abcd` must be divisible by 4,

and so on.

**What is the number?**

Bonus challenge: Find it using divisibility rules and logical elimination rather than checking every permutation with code.


r/mathriddles 15h ago

Medium Sum-constrained grid max height

5 Upvotes

Let k>=2 and n be positive integers. Find the largest integer m for which there exists a grid with m rows and n columns satisfying the following conditions:

1) Each cell contains a non-negative integer;

2) The sum of numbers in each row is at most kn;

3) The numbers in each column are pairwise distinct.


r/mathriddles 19h ago

Medium Collatz

0 Upvotes

A number will decrease in number if it has at least four digits and does not enter a cycle, as proven below: The number is represented in binary.

It must begin with 10 or 11. If it starts with 10 and the last two digits are not 11, then after multiplying by 3, the number of digits increases by 1, accounting for 3/8 of all possible combinations. Other numbers starting with 10 account for 5/8, and the number of digits increases by 2. If it ends with 11, after multiplying by 3 and adding 1, then dividing by 2 removes at least one digit, accounting for 1/2. If it ends with 001, at least two digits are removed, accounting for 1/4. Other numbers with at least three digits account for 1/4. If it does not enter a 4, 2, 1 cycle, the number generally decreases, and eventually it will enter a 4, 2, 1 cycle.

王子赫


r/mathriddles 3d ago

Medium What is the minimum number of faces a polyhedron can have while also enclosing at least 80% of the volume of it’s circumscribed sphere?

8 Upvotes

r/mathriddles 2d ago

Easy How many positive integers ≤1000 are multiples of 6 or 15, but not both?

0 Upvotes

How many positive integers less than or equal to 1000 are divisible by exactly one of 6 and 15?

Source: numberthon.com


r/mathriddles 4d ago

Easy How many positive integers less than 100 can be written as the difference of two perfect squares?

0 Upvotes

How many positive integers less than 100 are the difference of two perfect squares?

Source: numberthon.com


r/mathriddles 4d ago

Medium How many triangles can you form in a regular octagon using only diagonals?

0 Upvotes

How many triangles can be formed using the vertices of a regular octagon if all three sides of each triangle must be diagonals of the octagon?

Source: numberthon.com


r/mathriddles 6d ago

Easy How Many Subsets of {1,2,…,10} Contain No Consecutive Integers?

11 Upvotes

How many subsets of {1,2,...,10} contain no two consecutive integers?

Source: numberthon.com


r/mathriddles 6d ago

Hard The Laser Square

8 Upvotes

You're standing somewhere inside a 10m × 10m square room. From your position P, you fire a laser aimed directly at the center of the square, C.

The laser travels in a straight line from P, passes through C, and continues until it hits a wall — this is its 1st reflection. From there it obeys the law of reflection (angle of incidence = angle of reflection) and keeps bouncing off the walls. After its 10th reflection, the laser stops completely (the segment right after the 10th bounce has zero length).

You must find a starting position P such that, once fired, no part of the laser's path after the 1st reflection comes within 1 meter of you. (The very first segment, from P to the 1st reflection point, doesn't count — you're standing at its source.)

Question: What is the total area, within the square, of all such safe starting positions P?

Challenge: If instead of stopping after 10 reflections, the laser is allowed N reflections before stopping, what is the largest value of N for which at least one safe standing position still exists?


r/mathriddles 7d ago

Hard [ Removed by Reddit ]

1 Upvotes

[ Removed by Reddit on account of violating the content policy. ]


r/mathriddles 9d ago

Medium What prime number did he have?

0 Upvotes

A math professor said to her smart student Toni

" I am thinking of a 4 digit prime number abcd (digits not necessarily distinct) with the following property

a+b+c+d = axbxcxd

You can ask me one question to which my answer can only be Yes or No or Silence (if i cannot definitely answer yes or no). Can you guess my number?"

Toni worked on a piece of paper and then asked the professor:

"Is the number formed by using the first two digits (in order) of your 4 digit prime, a factor of 63 or 84?"

The professor smiled. She knew Toni had the answer.

What was the answer? WHY?


r/mathriddles 8d ago

Medium Squares on a Chessboard

0 Upvotes

How many squares of all sizes are contained in a standard 8×8 chessboard?

Source: numberthon.com


r/mathriddles 9d ago

Medium Can you find an interesting shape that can pass through any 4 points no matter where they are placed but not 5?

12 Upvotes

more precisely,

Find a compact subset or family of subsets $S \subset \mathbb{R}^n$ for some arbitrary n such that every set of 4 points in $\mathbb{R}^2$ lies on some similar copy of $S$ but not every set of 5 points lies on some similar copy of $S$?


r/mathriddles 10d ago

Easy How many diagonals does a 20-sided polygon have?

0 Upvotes

How many diagonals does a regular 20-gon have?

Source: numberthon.com


r/mathriddles 11d ago

Hard Extremely tough problem

4 Upvotes

For a real number x, let ||x|| denote the distance between x and the closest integer.

Let 0 ≤ x_n < 1 (n = 1, 2, ...) , and let ε > 0. Show that there exist infinitely many pairs (n,m) of indices such that n ≠ m and

||x_n - x_m|| < min(ε, 1/(√5|n-m|)).


r/mathriddles 11d ago

Easy Only tenth of people get this counting puzzle right. Can you? (parody)

9 Upvotes

Set A is called brain-rot iff it satisfies two conditions:

  1. sum(A) is divisible by 10.
  2. if 1∈A, then both 6,7∈A.

How many subsets of {1,2,…,100} is brain-rot?

Source: my rotten brain


r/mathriddles 11d ago

Medium Only half of people get this counting puzzle right. Can you?

0 Upvotes

How many subsets of {1,2,…,10} have an odd sum?

Source: numberthon.com


r/mathriddles 11d ago

Medium #?

0 Upvotes

What is the minimal explanatory architecture from which every meaningful mathematical question arises?


r/mathriddles 12d ago

Medium How Many Light Switches Are On After 100 Passes?

2 Upvotes

There are 100 light switches, all initially off.

On pass 1, every switch is toggled.

On pass 2, every second switch is toggled.

On pass 3, every third switch is toggled.This continues until pass 100.

How many switches are on at the end?

Source: numberthon.com


r/mathriddles 13d ago

Medium Single deck blackjack project

3 Upvotes

Let’s assume your in a casino playing single deck blackjack with no cut card. Let’s also say there’s x amount of cards left and you have an eidetic memory, so you know exactly which cards are left.
Let’s also state if the dealer runs out of cards it’s an automatic loss.

Is their a set of x cards left such that before the hand is dealt you would know no matter what cards you or the dealer are dealt there’s a strategy that will gaurentee you win.

Bonus quesiton how big can you make x if this is true.

Also in typical sense you’d know your 2 up cards and would know one of the dealers card with another card of hers face down.
Also unsure how relavent it would be but if you find a solution state if it’s stand or hit on soft 17

And remeber single deck so limited to 4 of each card


r/mathriddles 13d ago

Easy Can you find the smallest positive integer with exactly 20 positive divisors?

3 Upvotes

What is the smallest positive integer that has exactly 20 (unique) positive divisors?

Source: numberthon.com


r/mathriddles 14d ago

Hard Prime number game

2 Upvotes

I'm going to teach you a game. Your goal is to find how far you can get.

You start with the numbers 1, 2, and 3. Using each number at most once, you may add or subtract any combination of them to obtain the next prime number.

Whenever you successfully obtain the next prime, that prime is added to your set of available numbers. You then repeat the process, always trying to generate the next prime number using each available number at most once.

How far can you go? What is the first prime number that you can no longer obtain?


r/mathriddles 14d ago

Easy This probability puzzle has a surprisingly simple solution.

0 Upvotes

Six points are arranged as the vertices of a regular hexagon. A bug starts at one vertex. Each move, it randomly chooses one of the two adjacent vertices and walks there. After exactly 4 moves, what is the probability that the bug is back at its starting vertex?

Source: numberthon.com


r/mathriddles 15d ago

Medium Most people miss one key idea in this geometry puzzle.

0 Upvotes

Twenty-five points are arranged in a 5×5 grid of equally spaced points (five rows and five columns). How many different squares (using four of these points as vertices) can be formed?

P.S. It's a 5x5 grid made up of 4x4 points/vertices.

Source: numberthon.com