fix(curriculum): clean-up Project Euler 281-300 (#42922)

* fix: clean-up Project Euler 281-300

* fix: missing image extension

* fix: missing power

Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>

* fix: missing subscript

Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>

Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-281-pizza-toppings.md

@@ -8,20 +8,22 @@ dashedName: problem-281-pizza-toppings
 
 # --description--
 
-You are given a pizza (perfect circle) that has been cut into m·n equal pieces and you want to have exactly one topping on each slice.
+You are given a pizza (perfect circle) that has been cut into $m·n$ equal pieces and you want to have exactly one topping on each slice.
 
-Let f(m,n) denote the number of ways you can have toppings on the pizza with m different toppings (m ≥ 2), using each topping on exactly n slices (n ≥ 1). Reflections are considered distinct, rotations are not.
+Let $f(m,n)$ denote the number of ways you can have toppings on the pizza with $m$ different toppings ($m ≥ 2$), using each topping on exactly $n$ slices ($n ≥ 1$). Reflections are considered distinct, rotations are not.
 
-Thus, for instance, f(2,1) = 1, f(2,2) = f(3,1) = 2 and f(3,2) = 16. f(3,2) is shown below:
+Thus, for instance, $f(2,1) = 1$, $f(2,2) = f(3,1) = 2$ and $f(3,2) = 16$. $f(3,2)$ is shown below:
 
-Find the sum of all f(m,n) such that f(m,n) ≤ 1015.
+<img class="img-responsive center-block" alt="animation with 16 ways to have 3 different toppings on 2 slices each" src="https://cdn.freecodecamp.org/curriculum/project-euler/pizza-toppings.gif" style="background-color: white; padding: 10px;">
+
+Find the sum of all $f(m,n)$ such that $f(m,n) ≤ {10}^{15}$.
 
 # --hints--
 
-`euler281()` should return 1485776387445623.
+`pizzaToppings()` should return `1485776387445623`.
 
 ```js
-assert.strictEqual(euler281(), 1485776387445623);
+assert.strictEqual(pizzaToppings(), 1485776387445623);
 ```
 
 # --seed--
@@ -29,12 +31,12 @@ assert.strictEqual(euler281(), 1485776387445623);
 ## --seed-contents--
 
 ```js
-function euler281() {
+function pizzaToppings() {
 
   return true;
 }
 
-euler281();
+pizzaToppings();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-282-the-ackermann-function.md

@@ -8,18 +8,25 @@ dashedName: problem-282-the-ackermann-function
 
 # --description--
 
-For non-negative integers m, n, the Ackermann function A(m, n) is defined as follows:
+For non-negative integers $m$, $n$, the Ackermann function $A(m, n)$ is defined as follows:
 
-For example A(1, 0) = 2, A(2, 2) = 7 and A(3, 4) = 125.
+$$A(m, n) =
+\begin{cases}
+n + 1                 & \text{if $m = 0$}             \\\\
+A(m - 1, 1)           & \text{if $m > 0$ and $n = 0$} \\\\
+A(m - 1, A(m, n - 1)) & \text{if $m > 0$ and $n > 0$}
+\end{cases}$$
 
-Find A(n, n) and give your answer mod 148.
+For example $A(1, 0) = 2$, $A(2, 2) = 7$ and $A(3, 4) = 125$.
+
+Find $\displaystyle\sum_{n = 0}^6 A(n, n)$ and give your answer mod ${14}^8$.
 
 # --hints--
 
-`euler282()` should return 1098988351.
+`ackermanFunction()` should return `1098988351`.
 
 ```js
-assert.strictEqual(euler282(), 1098988351);
+assert.strictEqual(ackermanFunction(), 1098988351);
 ```
 
 # --seed--
@@ -27,12 +34,12 @@ assert.strictEqual(euler282(), 1098988351);
 ## --seed-contents--
 
 ```js
-function euler282() {
+function ackermanFunction() {
 
   return true;
 }
 
-euler282();
+ackermanFunction();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-283-integer-sided-triangles-for-which-the-area--perimeter-ratio-is-integral.md

@@ -13,20 +13,20 @@ dashedName: >-
 
 Consider the triangle with sides 6, 8 and 10. It can be seen that the perimeter and the area are both equal to 24.
 
-So the area/perimeter ratio is equal to 1.
+So the $\frac{\text{area}}{\text{perimeter}}$ ratio is equal to 1.
 
 Consider also the triangle with sides 13, 14 and 15. The perimeter equals 42 while the area is equal to 84.
 
-So for this triangle the area/perimeter ratio is equal to 2.
+So for this triangle the $\frac{\text{area}}{\text{perimeter}}$ ratio is equal to 2.
 
 Find the sum of the perimeters of all integer sided triangles for which the area/perimeter ratios are equal to positive integers not exceeding 1000.
 
 # --hints--
 
-`euler283()` should return 28038042525570324.
+`integralAreaPerimeterRatio()` should return `28038042525570324`.
 
 ```js
-assert.strictEqual(euler283(), 28038042525570324);
+assert.strictEqual(integralAreaPerimeterRatio(), 28038042525570324);
 ```
 
 # --seed--
@@ -34,12 +34,12 @@ assert.strictEqual(euler283(), 28038042525570324);
 ## --seed-contents--
 
 ```js
-function euler283() {
+function integralAreaPerimeterRatio() {
 
   return true;
 }
 
-euler283();
+integralAreaPerimeterRatio();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-284-steady-squares.md

@@ -8,20 +8,26 @@ dashedName: problem-284-steady-squares
 
 # --description--
 
-The 3-digit number 376 in the decimal numbering system is an example of numbers with the special property that its square ends with the same digits: 3762 = 141376. Let's call a number with this property a steady square.
+The 3-digit number 376 in the decimal numbering system is an example of numbers with the special property that its square ends with the same digits: ${376}^2 = 141376$. Let's call a number with this property a steady square.
 
-Steady squares can also be observed in other numbering systems. In the base 14 numbering system, the 3-digit number c37 is also a steady square: c372 = aa0c37, and the sum of its digits is c+3+7=18 in the same numbering system. The letters a, b, c and d are used for the 10, 11, 12 and 13 digits respectively, in a manner similar to the hexadecimal numbering system.
+Steady squares can also be observed in other numbering systems. In the base 14 numbering system, the 3-digit number $c37$ is also a steady square: $c37^2 = aa0c37$, and the sum of its digits is $c+3+7=18$ in the same numbering system. The letters $a$, $b$, $c$ and $d$ are used for the 10, 11, 12 and 13 digits respectively, in a manner similar to the hexadecimal numbering system.
 
-For 1 ≤ n ≤ 9, the sum of the digits of all the n-digit steady squares in the base 14 numbering system is 2d8 (582 decimal). Steady squares with leading 0's are not allowed.
+For $1 ≤ n ≤ 9$, the sum of the digits of all the $n$-digit steady squares in the base 14 numbering system is $2d8$ (582 decimal). Steady squares with leading 0's are not allowed.
 
-Find the sum of the digits of all the n-digit steady squares in the base 14 numbering system for 1 ≤ n ≤ 10000 (decimal) and give your answer in the base 14 system using lower case letters where necessary.
+Find the sum of the digits of all the $n$-digit steady squares in the base 14 numbering system for $1 ≤ n ≤ 10000$ (decimal) and give your answer as a string in the base 14 system using lower case letters where necessary.
 
 # --hints--
 
-`euler284()` should return 5a411d7b.
+`steadySquares()` should return a string.
 
 ```js
-assert.strictEqual(euler284(), '5a411d7b');
+assert(typeof steadySquares() === 'string');
+```
+
+`steadySquares()` should return the string `5a411d7b`.
+
+```js
+assert.strictEqual(steadySquares(), '5a411d7b');
 ```
 
 # --seed--
@@ -29,12 +35,12 @@ assert.strictEqual(euler284(), '5a411d7b');
 ## --seed-contents--
 
 ```js
-function euler284() {
+function steadySquares() {
 
   return true;
 }
 
-euler284();
+steadySquares();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-285-pythagorean-odds.md

@@ -8,22 +8,22 @@ dashedName: problem-285-pythagorean-odds
 
 # --description--
 
-Albert chooses a positive integer k, then two real numbers a, b are randomly chosen in the interval \[0,1] with uniform distribution.
+Albert chooses a positive integer $k$, then two real numbers $a$, $b$ are randomly chosen in the interval [0,1] with uniform distribution.
 
-The square root of the sum (k·a+1)2 + (k·b+1)2 is then computed and rounded to the nearest integer. If the result is equal to k, he scores k points; otherwise he scores nothing.
+The square root of the sum ${(ka + 1)}^2 + {(kb + 1)}^2$ is then computed and rounded to the nearest integer. If the result is equal to $k$, he scores $k$ points; otherwise he scores nothing.
 
-For example, if k = 6, a = 0.2 and b = 0.85, then (k·a+1)2 + (k·b+1)2 = 42.05. The square root of 42.05 is 6.484... and when rounded to the nearest integer, it becomes 6. This is equal to k, so he scores 6 points.
+For example, if $k = 6$, $a = 0.2$ and $b = 0.85$, then ${(ka + 1)}^2 + {(kb + 1)}^2 = 42.05$. The square root of 42.05 is 6.484... and when rounded to the nearest integer, it becomes 6. This is equal to $k$, so he scores 6 points.
 
-It can be shown that if he plays 10 turns with k = 1, k = 2, ..., k = 10, the expected value of his total score, rounded to five decimal places, is 10.20914.
+It can be shown that if he plays 10 turns with $k = 1, k = 2, \ldots, k = 10$, the expected value of his total score, rounded to five decimal places, is 10.20914.
 
-If he plays 105 turns with k = 1, k = 2, k = 3, ..., k = 105, what is the expected value of his total score, rounded to five decimal places?
+If he plays ${10}^5$ turns with $k = 1, k = 2, k = 3, \ldots, k = {10}^5$, what is the expected value of his total score, rounded to five decimal places?
 
 # --hints--
 
-`euler285()` should return 157055.80999.
+`pythagoreanOdds()` should return `157055.80999`.
 
 ```js
-assert.strictEqual(euler285(), 157055.80999);
+assert.strictEqual(pythagoreanOdds(), 157055.80999);
 ```
 
 # --seed--
@@ -31,12 +31,12 @@ assert.strictEqual(euler285(), 157055.80999);
 ## --seed-contents--
 
 ```js
-function euler285() {
+function pythagoreanOdds() {
 
   return true;
 }
 
-euler285();
+pythagoreanOdds();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-286-scoring-probabilities.md

@@ -8,18 +8,18 @@ dashedName: problem-286-scoring-probabilities
 
 # --description--
 
-Barbara is a mathematician and a basketball player. She has found that the probability of scoring a point when shooting from a distance x is exactly (1 - x/q), where q is a real constant greater than 50.
+Barbara is a mathematician and a basketball player. She has found that the probability of scoring a point when shooting from a distance $x$ is exactly ($1 - \frac{x}{q}$), where $q$ is a real constant greater than 50.
 
-During each practice run, she takes shots from distances x = 1, x = 2, ..., x = 50 and, according to her records, she has precisely a 2 % chance to score a total of exactly 20 points.
+During each practice run, she takes shots from distances $x = 1, x = 2, \ldots, x = 50$ and, according to her records, she has precisely a 2 % chance to score a total of exactly 20 points.
 
-Find q and give your answer rounded to 10 decimal places.
+Find $q$ and give your answer rounded to 10 decimal places.
 
 # --hints--
 
-`euler286()` should return 52.6494571953.
+`scoringProbabilities()` should return `52.6494571953`.
 
 ```js
-assert.strictEqual(euler286(), 52.6494571953);
+assert.strictEqual(scoringProbabilities(), 52.6494571953);
 ```
 
 # --seed--
@@ -27,12 +27,12 @@ assert.strictEqual(euler286(), 52.6494571953);
 ## --seed-contents--
 
 ```js
-function euler286() {
+function scoringProbabilities() {
 
   return true;
 }
 
-euler286();
+scoringProbabilities();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-287-quadtree-encoding-a-simple-compression-algorithm.md

@@ -8,30 +8,35 @@ dashedName: problem-287-quadtree-encoding-a-simple-compression-algorithm
 
 # --description--
 
-The quadtree encoding allows us to describe a 2N×2N black and white image as a sequence of bits (0 and 1). Those sequences are to be read from left to right like this:
+The quadtree encoding allows us to describe a $2^N×2^N$ black and white image as a sequence of bits (0 and 1). Those sequences are to be read from left to right like this:
 
-the first bit deals with the complete 2N×2N region;
+- the first bit deals with the complete $2^N×2^N$ region;
+- "0" denotes a split:
+  - the current $2^n×2^n$ region is divided into 4 sub-regions of dimension $2^{n - 1}×2^{n - 1}$,
+  - the next bits contains the description of the top left, top right, bottom left and bottom right sub-regions - in that order;
+- "10" indicates that the current region contains only black pixels;
+- "11" indicates that the current region contains only white pixels.
 
-"0" denotes a split:
+Consider the following 4×4 image (colored marks denote places where a split can occur):
 
-the current 2n×2n region is divided into 4 sub-regions of dimension 2n-1×2n-1,
+<img class="img-responsive center-block" alt="4x4 image with colored marks denoting place where split can occur" src="https://cdn.freecodecamp.org/curriculum/project-euler/quadtree-encoding-a-simple-compression-algorithm.gif" style="background-color: white; padding: 10px;">
 
-the next bits contains the description of the top left, top right, bottom left and bottom right sub-regions - in that order;
+This image can be described by several sequences, for example : "<strong><span style="color: red">0</span></strong><strong><span style="color: blue">0</span></strong>10101010<strong><span style="color: green">0</span></strong>1011111011<strong><span style="color: orange">0</span></strong>10101010", of length 30, or "<strong><span style="color: red">0</span></strong>10<strong><span style="color: green">0</span></strong>101111101110", of length 16, which is the minimal sequence for this image.
 
-"10" indicates that the current region contains only black pixels;
+For a positive integer $N$, define $D_N$ as the $2^N×2^N$ image with the following coloring scheme:
 
-"11" indicates that the current region contains only white pixels.Consider the following 4×4 image (colored marks denote places where a split can occur):
+- the pixel with coordinates $x = 0$, $y = 0$ corresponds to the bottom left pixel,
+- if ${(x - 2^{N - 1})}^2 + {(y - 2^{N - 1})}^2 ≤ 2^{2N - 2}$ then the pixel is black,
+- otherwise the pixel is white.
 
-This image can be described by several sequences, for example : "001010101001011111011010101010", of length 30, or "0100101111101110", of length 16, which is the minimal sequence for this image.
+What is the length of the minimal sequence describing $D_{24}$?
-
-For a positive integer N, define DN as the 2N×2N image with the following coloring scheme: the pixel with coordinates x = 0, y = 0 corresponds to the bottom left pixel, if (x - 2N-1)2 + (y - 2N-1)2 ≤ 22N-2 then the pixel is black, otherwise the pixel is white.What is the length of the minimal sequence describing D24 ?
 
 # --hints--
 
-`euler287()` should return 313135496.
+`quadtreeEncoding()` should return `313135496`.
 
 ```js
-assert.strictEqual(euler287(), 313135496);
+assert.strictEqual(quadtreeEncoding(), 313135496);
 ```
 
 # --seed--
@@ -39,12 +44,12 @@ assert.strictEqual(euler287(), 313135496);
 ## --seed-contents--
 
 ```js
-function euler287() {
+function quadtreeEncoding() {
 
   return true;
 }
 
-euler287();
+quadtreeEncoding();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-288-an-enormous-factorial.md

@@ -8,24 +8,28 @@ dashedName: problem-288-an-enormous-factorial
 
 # --description--
 
-For any prime p the number N(p,q) is defined by
+For any prime $p$ the number $N(p,q)$ is defined by $N(p,q) = \sum_{n=0}^q T_n \times p^n$ with $T_n$ generated by the following random number generator:
 
-N(p,q) = ∑n=0 to q Tn\*pn with Tn generated by the following random number generator:
+$$\begin{align}
+  & S_0 = 290797 \\\\
+  & S_{n + 1} = {S_n}^2\bmod 50\\,515\\,093 \\\\
+  & T_n = S_n\bmod p
+\end{align}$$
 
-S0 = 290797 Sn+1 = Sn2 mod 50515093 Tn = Sn mod p
+Let $Nfac(p,q)$ be the factorial of $N(p,q)$.
 
-Let Nfac(p,q) be the factorial of N(p,q). Let NF(p,q) be the number of factors p in Nfac(p,q).
+Let $NF(p,q)$ be the number of factors $p$ in $Nfac(p,q)$.
 
-You are given that NF(3,10000) mod 320=624955285.
+You are given that $NF(3,10000) \bmod 3^{20} = 624\\,955\\,285$.
 
-Find NF(61,107) mod 6110
+Find $NF(61,{10}^7)\bmod {61}^{10}$.
 
 # --hints--
 
-`euler288()` should return 605857431263982000.
+`enormousFactorial()` should return `605857431263982000`.
 
 ```js
-assert.strictEqual(euler288(), 605857431263982000);
+assert.strictEqual(enormousFactorial(), 605857431263982000);
 ```
 
 # --seed--
@@ -33,12 +37,12 @@ assert.strictEqual(euler288(), 605857431263982000);
 ## --seed-contents--
 
 ```js
-function euler288() {
+function enormousFactorial() {
 
   return true;
 }
 
-euler288();
+enormousFactorial();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-289-eulerian-cycles.md

@@ -8,24 +8,26 @@ dashedName: problem-289-eulerian-cycles
 
 # --description--
 
-Let C(x,y) be a circle passing through the points (x, y), (x, y+1), (x+1, y) and (x+1, y+1).
+Let $C(x,y)$ be a circle passing through the points ($x$, $y$), ($x$, $y + 1$), ($x + 1$, $y$) and ($x + 1$, $y + 1$).
 
-For positive integers m and n, let E(m,n) be a configuration which consists of the m·n circles: { C(x,y): 0 ≤ x < m, 0 ≤ y < n, x and y are integers }
+For positive integers $m$ and $n$, let $E(m,n)$ be a configuration which consists of the $m·n$ circles: { $C(x,y)$: $0 ≤ x < m$, $0 ≤ y < n$, $x$ and $y$ are integers }
 
-An Eulerian cycle on E(m,n) is a closed path that passes through each arc exactly once. Many such paths are possible on E(m,n), but we are only interested in those which are not self-crossing: A non-crossing path just touches itself at lattice points, but it never crosses itself.
+An Eulerian cycle on $E(m,n)$ is a closed path that passes through each arc exactly once. Many such paths are possible on $E(m,n)$, but we are only interested in those which are not self-crossing: A non-crossing path just touches itself at lattice points, but it never crosses itself.
 
-The image below shows E(3,3) and an example of an Eulerian non-crossing path.
+The image below shows $E(3,3)$ and an example of an Eulerian non-crossing path.
 
-Let L(m,n) be the number of Eulerian non-crossing paths on E(m,n). For example, L(1,2) = 2, L(2,2) = 37 and L(3,3) = 104290.
+<img class="img-responsive center-block" alt="Eulerian cycle E(3, 3) and Eulerian non-crossing path" src="https://cdn.freecodecamp.org/curriculum/project-euler/eulerian-cycles.gif" style="background-color: white; padding: 10px;">
 
-Find L(6,10) mod 1010.
+Let $L(m,n)$ be the number of Eulerian non-crossing paths on $E(m,n)$. For example, $L(1,2) = 2$, $L(2,2) = 37$ and $L(3,3) = 104290$.
+
+Find $L(6,10)\bmod {10}^{10}$.
 
 # --hints--
 
-`euler289()` should return 6567944538.
+`eulerianCycles()` should return `6567944538`.
 
 ```js
-assert.strictEqual(euler289(), 6567944538);
+assert.strictEqual(eulerianCycles(), 6567944538);
 ```
 
 # --seed--
@@ -33,12 +35,12 @@ assert.strictEqual(euler289(), 6567944538);
 ## --seed-contents--
 
 ```js
-function euler289() {
+function eulerianCycles() {
 
   return true;
 }
 
-euler289();
+eulerianCycles();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-290-digital-signature.md

@@ -8,14 +8,14 @@ dashedName: problem-290-digital-signature
 
 # --description--
 
-How many integers 0 ≤ n < 1018 have the property that the sum of the digits of n equals the sum of digits of 137n?
+How many integers $0 ≤ n < {10}^{18}$ have the property that the sum of the digits of $n$ equals the sum of digits of $137n$?
 
 # --hints--
 
-`euler290()` should return 20444710234716470.
+`digitalSignature()` should return `20444710234716470`.
 
 ```js
-assert.strictEqual(euler290(), 20444710234716470);
+assert.strictEqual(digitalSignature(), 20444710234716470);
 ```
 
 # --seed--
@@ -23,12 +23,12 @@ assert.strictEqual(euler290(), 20444710234716470);
 ## --seed-contents--
 
 ```js
-function euler290() {
+function digitalSignature() {
 
   return true;
 }
 
-euler290();
+digitalSignature();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-291-panaitopol-primes.md

@@ -8,16 +8,16 @@ dashedName: problem-291-panaitopol-primes
 
 # --description--
 
-A prime number p is called a Panaitopol prime if for some positive integersx and y.
+A prime number $p$ is called a Panaitopol prime if $p = \frac{x^4 - y^4}{x^3 + y^3}$ for some positive integers $x$ and $y$.
 
-Find how many Panaitopol primes are less than 5×1015.
+Find how many Panaitopol primes are less than $5 × {10}^{15}$.
 
 # --hints--
 
-`euler291()` should return 4037526.
+`panaitopolPrimes()` should return `4037526`.
 
 ```js
-assert.strictEqual(euler291(), 4037526);
+assert.strictEqual(panaitopolPrimes(), 4037526);
 ```
 
 # --seed--
@@ -25,12 +25,12 @@ assert.strictEqual(euler291(), 4037526);
 ## --seed-contents--
 
 ```js
-function euler291() {
+function panaitopolPrimes() {
 
   return true;
 }
 
-euler291();
+panaitopolPrimes();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-292-pythagorean-polygons.md

@@ -8,24 +8,27 @@ dashedName: problem-292-pythagorean-polygons
 
 # --description--
 
-We shall define a pythagorean polygon to be a convex polygon with the following properties:there are at least three vertices,
+We shall define a pythagorean polygon to be a convex polygon with the following properties:
 
-no three vertices are aligned,
+- there are at least three vertices,
+- no three vertices are aligned,
+- each vertex has integer coordinates,
+- each edge has integer length.
 
-each vertex has integer coordinates,
+For a given integer $n$, define $P(n)$ as the number of distinct pythagorean polygons for which the perimeter is $≤ n$.
-
-each edge has integer length.For a given integer n, define P(n) as the number of distinct pythagorean polygons for which the perimeter is ≤ n.
 
 Pythagorean polygons should be considered distinct as long as none is a translation of another.
 
-You are given that P(4) = 1, P(30) = 3655 and P(60) = 891045. Find P(120).
+You are given that $P(4) = 1$, $P(30) = 3655$ and $P(60) = 891045$.
+
+Find $P(120)$.
 
 # --hints--
 
-`euler292()` should return 3600060866.
+`pythagoreanPolygons()` should return `3600060866`.
 
 ```js
-assert.strictEqual(euler292(), 3600060866);
+assert.strictEqual(pythagoreanPolygons(), 3600060866);
 ```
 
 # --seed--
@@ -33,12 +36,12 @@ assert.strictEqual(euler292(), 3600060866);
 ## --seed-contents--
 
 ```js
-function euler292() {
+function pythagoreanPolygons() {
 
   return true;
 }
 
-euler292();
+pythagoreanPolygons();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-293-pseudo-fortunate-numbers.md

@@ -8,22 +8,22 @@ dashedName: problem-293-pseudo-fortunate-numbers
 
 # --description--
 
-An even positive integer N will be called admissible, if it is a power of 2 or its distinct prime factors are consecutive primes.
+An even positive integer $N$ will be called admissible, if it is a power of 2 or its distinct prime factors are consecutive primes.
 
-The first twelve admissible numbers are 2,4,6,8,12,16,18,24,30,32,36,48.
+The first twelve admissible numbers are 2, 4, 6, 8, 12, 16, 18, 24, 30, 32, 36, 48.
 
-If N is admissible, the smallest integer M > 1 such that N+M is prime, will be called the pseudo-Fortunate number for N.
+If $N$ is admissible, the smallest integer $M > 1$ such that $N + M$ is prime, will be called the pseudo-Fortunate number for $N$.
 
-For example, N=630 is admissible since it is even and its distinct prime factors are the consecutive primes 2,3,5 and 7. The next prime number after 631 is 641; hence, the pseudo-Fortunate number for 630 is M=11. It can also be seen that the pseudo-Fortunate number for 16 is 3.
+For example, $N = 630$ is admissible since it is even and its distinct prime factors are the consecutive primes 2, 3, 5 and 7. The next prime number after 631 is 641; hence, the pseudo-Fortunate number for 630 is $M = 11$. It can also be seen that the pseudo-Fortunate number for 16 is 3.
 
-Find the sum of all distinct pseudo-Fortunate numbers for admissible numbers N less than 109.
+Find the sum of all distinct pseudo-Fortunate numbers for admissible numbers $N$ less than ${10}^9$.
 
 # --hints--
 
-`euler293()` should return 2209.
+`pseudoFortunateNumbers()` should return `2209`.
 
 ```js
-assert.strictEqual(euler293(), 2209);
+assert.strictEqual(pseudoFortunateNumbers(), 2209);
 ```
 
 # --seed--
@@ -31,12 +31,12 @@ assert.strictEqual(euler293(), 2209);
 ## --seed-contents--
 
 ```js
-function euler293() {
+function pseudoFortunateNumbers() {
 
   return true;
 }
 
-euler293();
+pseudoFortunateNumbers();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-294-sum-of-digits---experience-23.md

@@ -8,22 +8,23 @@ dashedName: problem-294-sum-of-digits---experience-23
 
 # --description--
 
-For a positive integer k, define d(k) as the sum of the digits of k in its usual decimal representation.
+For a positive integer $k$, define $d(k)$ as the sum of the digits of $k$ in its usual decimal representation. Thus $d(42) = 4 + 2 = 6$.
 
-Thus d(42) = 4+2 = 6.
+For a positive integer $n$, define $S(n)$ as the number of positive integers $k < {10}^n$ with the following properties:
 
-For a positive integer n, define S(n) as the number of positive integers k < 10n with the following properties : k is divisible by 23 and d(k) = 23.
+- $k$ is divisible by 23 and,
+- $d(k) = 23$.
 
-You are given that S(9) = 263626 and S(42) = 6377168878570056.
+You are given that $S(9) = 263\\,626$ and $S(42) = 6\\,377\\,168\\,878\\,570\\,056$.
 
-Find S(1112) and give your answer mod 109.
+Find $S({11}^{12})$ and give your answer $\bmod {10}^9$.
 
 # --hints--
 
-`euler294()` should return 789184709.
+`experience23()` should return `789184709`.
 
 ```js
-assert.strictEqual(euler294(), 789184709);
+assert.strictEqual(experience23(), 789184709);
 ```
 
 # --seed--
@@ -31,12 +32,12 @@ assert.strictEqual(euler294(), 789184709);
 ## --seed-contents--
 
 ```js
-function euler294() {
+function experience23() {
 
   return true;
 }
 
-euler294();
+experience23();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-295-lenticular-holes.md

@@ -10,30 +10,36 @@ dashedName: problem-295-lenticular-holes
 
 We call the convex area enclosed by two circles a lenticular hole if:
 
-The centres of both circles are on lattice points.
+- The centres of both circles are on lattice points.
+- The two circles intersect at two distinct lattice points.
+- The interior of the convex area enclosed by both circles does not contain any lattice points.
 
-The two circles intersect at two distinct lattice points.
+Consider the circles:
 
-The interior of the convex area enclosed by both circles does not contain any lattice points.
+$$\begin{align}
+  & C_0: x^2 + y^2 = 25 \\\\
+  & C_1: {(x + 4)}^2 + {(y - 4)}^2 = 1 \\\\
+  & C_2: {(x - 12)}^2 + {(y - 4)}^2 = 65
+\end{align}$$
 
-Consider the circles: C0: x2+y2=25 C1: (x+4)2+(y-4)2=1 C2: (x-12)2+(y-4)2=65
+The circles $C_0$, $C_1$ and $C_2$ are drawn in the picture below.
 
-The circles C0, C1 and C2 are drawn in the picture below.
+<img class="img-responsive center-block" alt="C_0, C_1 and C_2 circles" src="https://cdn.freecodecamp.org/curriculum/project-euler/lenticular-holes.gif" style="background-color: white; padding: 10px;">
 
-C0 and C1 form a lenticular hole, as well as C0 and C2.
+$C_0$ and $C_1$ form a lenticular hole, as well as $C_0$ and $C_2$.
 
-We call an ordered pair of positive real numbers (r1, r2) a lenticular pair if there exist two circles with radii r1 and r2 that form a lenticular hole. We can verify that (1, 5) and (5, √65) are the lenticular pairs of the example above.
+We call an ordered pair of positive real numbers ($r_1$, $r_2$) a lenticular pair if there exist two circles with radii $r_1$ and $r_2$ that form a lenticular hole. We can verify that ($1$, $5$) and ($5$, $\sqrt{65}$) are the lenticular pairs of the example above.
 
-Let L(N) be the number of distinct lenticular pairs (r1, r2) for which 0 &lt; r1 ≤ r2 ≤ N. We can verify that L(10) = 30 and L(100) = 3442.
+Let $L(N)$ be the number of distinct lenticular pairs ($r_1$, $r_2$) for which $0 &lt; r_1 ≤ r_2 ≤ N$. We can verify that $L(10) = 30$ and $L(100) = 3442$.
 
-Find L(100 000).
+Find $L(100\\,000)$.
 
 # --hints--
 
-`euler295()` should return 4884650818.
+`lenticularHoles()` should return `4884650818`.
 
 ```js
-assert.strictEqual(euler295(), 4884650818);
+assert.strictEqual(lenticularHoles(), 4884650818);
 ```
 
 # --seed--
@@ -41,12 +47,12 @@ assert.strictEqual(euler295(), 4884650818);
 ## --seed-contents--
 
 ```js
-function euler295() {
+function lenticularHoles() {
 
   return true;
 }
 
-euler295();
+lenticularHoles();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-296-angular-bisector-and-tangent.md

@@ -8,18 +8,20 @@ dashedName: problem-296-angular-bisector-and-tangent
 
 # --description--
 
-Given is an integer sided triangle ABC with BC ≤ AC ≤ AB.k is the angular bisector of angle ACB.m is the tangent at C to the circumscribed circle of ABC.n is a line parallel to m through B.
+Given is an integer sided triangle $ABC$ with $BC ≤ AC ≤ AB$. $k$ is the angular bisector of angle $ACB$. $m$ is the tangent at $C$ to the circumscribed circle of $ABC$. $n$ is a line parallel to $m$ through $B$.
 
-The intersection of n and k is called E.
+The intersection of $n$ and $k$ is called $E$.
 
-How many triangles ABC with a perimeter not exceeding 100 000 exist such that BE has integral length?
+<img class="img-responsive center-block" alt="triangle ABC, with k - the angular bisector of angle ACB, m - tangent at point C, n - line parallel to m through B, and point E - intersection of k and n" src="https://cdn.freecodecamp.org/curriculum/project-euler/angular-bisector-and-tangent.gif" style="background-color: white; padding: 10px;">
+
+How many triangles $ABC$ with a perimeter not exceeding $100\\,000$ exist such that $BE$ has integral length?
 
 # --hints--
 
-`euler296()` should return 1137208419.
+`angularBisectorAndTangent()` should return `1137208419`.
 
 ```js
-assert.strictEqual(euler296(), 1137208419);
+assert.strictEqual(angularBisectorAndTangent(), 1137208419);
 ```
 
 # --seed--
@@ -27,12 +29,12 @@ assert.strictEqual(euler296(), 1137208419);
 ## --seed-contents--
 
 ```js
-function euler296() {
+function angularBisectorAndTangent() {
 
   return true;
 }
 
-euler296();
+angularBisectorAndTangent();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-297-zeckendorf-representation.md

@@ -12,18 +12,24 @@ Each new term in the Fibonacci sequence is generated by adding the previous two
 
 Starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89.
 
-Every positive integer can be uniquely written as a sum of nonconsecutive terms of the Fibonacci sequence. For example, 100 = 3 + 8 + 89. Such a sum is called the Zeckendorf representation of the number.
+Every positive integer can be uniquely written as a sum of nonconsecutive terms of the Fibonacci sequence. For example, 100 = 3 + 8 + 89.
 
-For any integer n>0, let z(n) be the number of terms in the Zeckendorf representation of n. Thus, z(5) = 1, z(14) = 2, z(100) = 3 etc. Also, for 0<n<106, ∑ z(n) = 7894453.
+Such a sum is called the Zeckendorf representation of the number.
 
-Find ∑ z(n) for 0<n<1017.
+For any integer $n>0$, let $z(n)$ be the number of terms in the Zeckendorf representation of $n$.
+
+Thus, $z(5) = 1$, $z(14) = 2$, $z(100) = 3$ etc.
+
+Also, for $0 < n < {10}^6$, $\sum z(n) = 7\\,894\\,453$.
+
+Find $\sum z(n)$ for $0 < n < {10}^{17}$.
 
 # --hints--
 
-`euler297()` should return 2252639041804718000.
+`zeckendorfRepresentation()` should return `2252639041804718000`.
 
 ```js
-assert.strictEqual(euler297(), 2252639041804718000);
+assert.strictEqual(zeckendorfRepresentation(), 2252639041804718000);
 ```
 
 # --seed--
@@ -31,12 +37,12 @@ assert.strictEqual(euler297(), 2252639041804718000);
 ## --seed-contents--
 
 ```js
-function euler297() {
+function zeckendorfRepresentation() {
 
   return true;
 }
 
-euler297();
+zeckendorfRepresentation();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-298-selective-amnesia.md

@@ -12,16 +12,29 @@ Larry and Robin play a memory game involving of a sequence of random numbers bet
 
 Both players start with empty memories. Both players always add new missed numbers to their memory but use a different strategy in deciding which number to remove: Larry's strategy is to remove the number that hasn't been called in the longest time. Robin's strategy is to remove the number that's been in the memory the longest time.
 
-Example game:Turn Callednumber Larry'smemory Larry'sscore Robin'smemory Robin'sscore 1 1 1 0 1 0 2 2 1,2 0 1,2 0 3 4 1,2,4 0 1,2,4 0 4 6 1,2,4,6 0 1,2,4,6 0 5 1 1,2,4,6 1 1,2,4,6 1 6 8 1,2,4,6,8 1 1,2,4,6,8 1 7 10 1,4,6,8,10 1 2,4,6,8,10 1 8 2 1,2,6,8,10 1 2,4,6,8,10 2 9 4 1,2,4,8,10 1 2,4,6,8,10 3 10 1 1,2,4,8,10 2 1,4,6,8,10 3
+Example game:
 
-Denoting Larry's score by L and Robin's score by R, what is the expected value of |L-R| after 50 turns? Give your answer rounded to eight decimal places using the format x.xxxxxxxx .
+| Turn | Called number | Larry's memory | Larry's score | Robin's memory | Robin's score |
+|------|---------------|---------------:|---------------|----------------|---------------|
+|   1  |       1       |              1 |       0       |              1 |       0       |
+|   2  |       2       |            1,2 |       0       |            1,2 |       0       |
+|   3  |       4       |          1,2,4 |       0       |          1,2,4 |       0       |
+|   4  |       6       |        1,2,4,6 |       0       |        1,2,4,6 |       0       |
+|   5  |       1       |        1,2,4,6 |       1       |        1,2,4,6 |       1       |
+|   6  |       8       |      1,2,4,6,8 |       1       |      1,2,4,6,8 |       1       |
+|   7  |      10       |     1,4,6,8,10 |       1       |     2,4,6,8,10 |       1       |
+|   8  |       2       |     1,2,6,8,10 |       1       |     2,4,6,8,10 |       2       |
+|   9  |       4       |     1,2,4,8,10 |       1       |     2,4,6,8,10 |       3       |
+|  10  |       1       |     1,2,4,8,10 |       2       |     1,4,6,8,10 |       3       |
+
+Denoting Larry's score by $L$ and Robin's score by $R$, what is the expected value of $|L - R|$ after 50 turns? Give your answer rounded to eight decimal places using the format x.xxxxxxxx .
 
 # --hints--
 
-`euler298()` should return 1.76882294.
+`selectiveAmnesia()` should return `1.76882294`.
 
 ```js
-assert.strictEqual(euler298(), 1.76882294);
+assert.strictEqual(selectiveAmnesia(), 1.76882294);
 ```
 
 # --seed--
@@ -29,12 +42,12 @@ assert.strictEqual(euler298(), 1.76882294);
 ## --seed-contents--
 
 ```js
-function euler298() {
+function selectiveAmnesia() {
 
   return true;
 }
 
-euler298();
+selectiveAmnesia();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-299-three-similar-triangles.md

@@ -8,26 +8,32 @@ dashedName: problem-299-three-similar-triangles
 
 # --description--
 
-Four points with integer coordinates are selected:A(a, 0), B(b, 0), C(0, c) and D(0, d),
+Four points with integer coordinates are selected:
 
-with 0 < a < b and 0 < c < d.
+$A(a, 0)$, $B(b, 0)$, $C(0, c)$ and $D(0, d)$, with $0 < a < b$ and $0 < c < d$.
 
-Point P, also with integer coordinates, is chosen on the line AC so that the three triangles ABP, CDP and BDP are all similar.
+Point $P$, also with integer coordinates, is chosen on the line $AC$ so that the three triangles $ABP$, $CDP$ and $BDP$ are all similar.
 
-It is easy to prove that the three triangles can be similar, only if a=c.
+<img class="img-responsive center-block" alt="points A, B, C, D and P creating three triangles: ABP, CDP, and BDP" src="https://cdn.freecodecamp.org/curriculum/project-euler/three-similar-triangles.gif" style="background-color: white; padding: 10px;">
 
-So, given that a=c, we are looking for triplets (a,b,d) such that at least one point P (with integer coordinates) exists on AC, making the three triangles ABP, CDP and BDP all similar.
+It is easy to prove that the three triangles can be similar, only if $a = c$.
 
-For example, if (a,b,d)=(2,3,4), it can be easily verified that point P(1,1) satisfies the above condition. Note that the triplets (2,3,4) and (2,4,3) are considered as distinct, although point P(1,1) is common for both.
+So, given that $a = c$, we are looking for triplets ($a$, $b$, $d$) such that at least one point $P$ (with integer coordinates) exists on $AC$, making the three triangles $ABP$, $CDP$ and $BDP$ all similar.
 
-If b+d &lt; 100, there are 92 distinct triplets (a,b,d) such that point P exists. If b+d &lt; 100 000, there are 320471 distinct triplets (a,b,d) such that point P exists. If b+d &lt; 100 000 000, how many distinct triplets (a,b,d) are there such that point P exists?
+For example, if $(a, b, d) = (2, 3, 4)$, it can be easily verified that point $P(1, 1)$ satisfies the above condition. Note that the triplets (2,3,4) and (2,4,3) are considered as distinct, although point $P(1, 1)$ is common for both.
+
+If $b + d &lt; 100$, there are 92 distinct triplets ($a$, $b$, $d$) such that point $P$ exists.
+
+If $b + d &lt; 100\\,000$, there are 320471 distinct triplets ($a$, $b$, $d$) such that point $P$ exists.
+
+If $b + d &lt; 100\\,000\\,000$, how many distinct triplets ($a$, $b$, $d$) are there such that point $P$ exists?
 
 # --hints--
 
-`euler299()` should return 549936643.
+`threeSimilarTriangles()` should return `549936643`.
 
 ```js
-assert.strictEqual(euler299(), 549936643);
+assert.strictEqual(threeSimilarTriangles(), 549936643);
 ```
 
 # --seed--
@@ -35,12 +41,12 @@ assert.strictEqual(euler299(), 549936643);
 ## --seed-contents--
 
 ```js
-function euler299() {
+function threeSimilarTriangles() {
 
   return true;
 }
 
-euler299();
+threeSimilarTriangles();
 ```
 
 # --solutions--

curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-300-protein-folding.md

@@ -10,24 +10,30 @@ dashedName: problem-300-protein-folding
 
 In a very simplified form, we can consider proteins as strings consisting of hydrophobic (H) and polar (P) elements, e.g. HHPPHHHPHHPH.
 
-For this problem, the orientation of a protein is important; e.g. HPP is considered distinct from PPH. Thus, there are 2n distinct proteins consisting of n elements.
+For this problem, the orientation of a protein is important; e.g. HPP is considered distinct from PPH. Thus, there are $2^n$ distinct proteins consisting of $n$ elements.
 
-When one encounters these strings in nature, they are always folded in such a way that the number of H-H contact points is as large as possible, since this is energetically advantageous. As a result, the H-elements tend to accumulate in the inner part, with the P-elements on the outside. Natural proteins are folded in three dimensions of course, but we will only consider protein folding in two dimensions.
+When one encounters these strings in nature, they are always folded in such a way that the number of H-H contact points is as large as possible, since this is energetically advantageous.
+
+As a result, the H-elements tend to accumulate in the inner part, with the P-elements on the outside.
+
+Natural proteins are folded in three dimensions of course, but we will only consider protein folding in <u>two dimensions</u>.
 
 The figure below shows two possible ways that our example protein could be folded (H-H contact points are shown with red dots).
 
+<img class="img-responsive center-block" alt="two possible ways to fold example protein" src="https://cdn.freecodecamp.org/curriculum/project-euler/protein-folding.gif" style="background-color: white; padding: 10px;">
+
 The folding on the left has only six H-H contact points, thus it would never occur naturally. On the other hand, the folding on the right has nine H-H contact points, which is optimal for this string.
 
-Assuming that H and P elements are equally likely to occur in any position along the string, the average number of H-H contact points in an optimal folding of a random protein string of length 8 turns out to be 850 / 28=3.3203125.
+Assuming that H and P elements are equally likely to occur in any position along the string, the average number of H-H contact points in an optimal folding of a random protein string of length 8 turns out to be $\frac{850}{2^8} = 3.3203125$.
 
 What is the average number of H-H contact points in an optimal folding of a random protein string of length 15? Give your answer using as many decimal places as necessary for an exact result.
 
 # --hints--
 
-`euler300()` should return 8.0540771484375.
+`proteinFolding()` should return `8.0540771484375`.
 
 ```js
-assert.strictEqual(euler300(), 8.0540771484375);
+assert.strictEqual(proteinFolding(), 8.0540771484375);
 ```
 
 # --seed--
@@ -35,12 +41,12 @@ assert.strictEqual(euler300(), 8.0540771484375);
 ## --seed-contents--
 
 ```js
-function euler300() {
+function proteinFolding() {
 
   return true;
 }
 
-euler300();
+proteinFolding();
 ```
 
 # --solutions--