chore: fix typos in spelling (#38100)
* spelling: accidentally * spelling: announce * spelling: assembly * spelling: avoid * spelling: backend * spelling: because * spelling: claimed * spelling: candidate * spelling: certification * spelling: certified * spelling: challenge * spelling: circular * spelling: it isn't * spelling: coins * spelling: combination * spelling: compliant * spelling: containers * spelling: concise * spelling: deprecated * spelling: development * spelling: donor * spelling: error * spelling: everything * spelling: exceed * spelling: exist * spelling: falsy * spelling: faulty * spelling: forward * spelling: handle * spelling: indicates * spelling: initial * spelling: integers * spelling: issealed * spelling: javascript * spelling: length * spelling: maximum * spelling: minimum * spelling: mutable * spelling: notifier * spelling: coordinate * spelling: passport * spelling: perform * spelling: permuter * spelling: placeholder * spelling: progressively * spelling: semantic * spelling: submission * spelling: submit * spelling: translations * spelling: turquoise * spelling: visualization * spelling: without * spelling: registration * spelling: representation
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@ -12,7 +12,7 @@ Consider the following two triangles:
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A(-340,495), B(-153,-910), C(835,-947)
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X(-175,41), Y(-421,-714), Z(574,-645)
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It can be verified that triangle ABC contains the origin, whereas triangle XYZ does not.
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Using triangles.txt (right click and 'Save Link/Target As...'), a 27K text file containing the co-ordinates of one thousand "random" triangles, find the number of triangles for which the interior contains the origin.
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Using triangles.txt (right click and 'Save Link/Target As...'), a 27K text file containing the coordinates of one thousand "random" triangles, find the number of triangles for which the interior contains the origin.
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NOTE: The first two examples in the file represent the triangles in the example given above.
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</section>
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@ -7,7 +7,7 @@ forumTopicId: 301820
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## Description
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<section id='description'>
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Consider the set Ir of points (x,y) with integer co-ordinates in the interior of the circle with radius r, centered at the origin, i.e. x2 + y2 < r2.
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Consider the set Ir of points (x,y) with integer coordinates in the interior of the circle with radius r, centered at the origin, i.e. x2 + y2 < r2.
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For a radius of 2, I2 contains the nine points (0,0), (1,0), (1,1), (0,1), (-1,1), (-1,0), (-1,-1), (0,-1) and (1,-1). There are eight triangles having all three vertices in I2 which contain the origin in the interior. Two of them are shown below, the others are obtained from these by rotation.
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@ -7,7 +7,7 @@ forumTopicId: 301928
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## Description
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<section id='description'>
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Given the values of integers 1 < a1 < a2 <... < an, consider the linear combinationq1a1 + q2a2 + ... + qnan = b, using only integer values qk ≥ 0.
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Given the values of integers 1 < a1 < a2 <... < an, consider the linear combination q1a1 + q2a2 + ... + qnan = b, using only integer values qk ≥ 0.
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Note that for a given set of ak, it may be that not all values of b are possible.
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@ -12,7 +12,7 @@ There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73
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How many circular primes are there below n, whereas 100 <= n <= 1000000?
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<br><strong>Note:</strong><br>
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Circular primes individual rotation can exceeed `n`.
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Circular primes individual rotation can exceed `n`.
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</section>
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## Instructions
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@ -106,7 +106,7 @@ function circularPrimes(n) {
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continue;
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}
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else if (!primes[x]) {
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// If the rotated value is 0 then its not a ciruclar prime, break the loop
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// If the rotated value is 0 then it isn't a circular prime, break the loop
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tmp = 0;
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break;
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}
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@ -15,7 +15,7 @@ Let C<sub>out</sub> be the circle having the diameter WZ.
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The triplet (<var>a</var>, <var>b</var>, <var>c</var>) is called a <em>necklace triplet</em> if you can place <var>k</var> ≥ 3 distinct circles C<sub>1</sub>, C<sub>2</sub>, ..., C<sub><var>k</var></sub> such that:
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<ul><li>C<sub><var>i</var></sub> has no common interior points with any C<sub><var>j</var></sub> for 1 ≤ <var>i</var>, <var>j</var> ≤ <var>k</var> and <var>i</var> ≠ <var>j</var>,</li><li>C<sub><var>i</var></sub> is tangent to both C<sub>in</sub> and C<sub>out</sub> for 1 ≤ <var>i</var> ≤ <var>k</var>,</li><li>C<sub><var>i</var></sub> is tangent to C<sub><var>i</var>+1</sub> for 1 ≤ <var>i</var> < <var>k</var>, and</li><li>C<sub><var>k</var></sub> is tangent to C<sub>1</sub>.</li></ul>
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For example, (5, 5, 5) and (4, 3, 21) are necklace triplets, while it can be shown that (2, 2, 5) is not.
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<img src="https://projecteuler.net/project/images/p428_necklace.png" alt="a visual reresentation of a necklace triplet">
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<img src="https://projecteuler.net/project/images/p428_necklace.png" alt="a visual representation of a necklace triplet">
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Let T(<var>n</var>) be the number of necklace triplets (<var>a</var>, <var>b</var>, <var>c</var>) such that <var>a</var>, <var>b</var> and <var>c</var> are positive integers, and <var>b</var> ≤ <var>n</var>.
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For example, T(1) = 9, T(20) = 732 and T(3000) = 438106.
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@ -7,12 +7,12 @@ forumTopicId: 302208
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## Description
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<section id='description'>
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The points P (x1, y1) and Q (x2, y2) are plotted at integer co-ordinates and are joined to the origin, O(0,0), to form ΔOPQ.
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The points P (x1, y1) and Q (x2, y2) are plotted at integer coordinates and are joined to the origin, O(0,0), to form ΔOPQ.
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There are exactly fourteen triangles containing a right angle that can be formed when each co-ordinate lies between 0 and 2 inclusive; that is,0 ≤ x1, y1, x2, y2 ≤ 2.
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There are exactly fourteen triangles containing a right angle that can be formed when each coordinate lies between 0 and 2 inclusive; that is,0 ≤ x1, y1, x2, y2 ≤ 2.
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