fix(challenges): Added blockquote to department numbers and fixed fractions in fractran
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@ -20,20 +20,13 @@ The Chief of the Police doesn't like odd numbers and wants to have an even numbe
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## Instructions
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<section id='instructions'>
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Write a program which outputs all valid combinations:
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[2, 3, 7]
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[2, 4, 6]
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[2, 6, 4]
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[2, 7, 3]
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[4, 1, 7]
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[4, 2, 6]
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[4, 3, 5]
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[4, 5, 3]
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[4, 6, 2]
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[4, 7, 1]
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[6, 1, 5]
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[6, 2, 4]
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[6, 4, 2]
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[6, 5, 1]
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<blockquote>
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[2, 3, 7] [2, 4, 6] [2, 6, 4]<br>
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[2, 7, 3] [4, 1, 7] [4, 2, 6]<br>
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[4, 3, 5] [4, 5, 3] [4, 6, 2]<br>
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[4, 7, 1] [6, 1, 5] [6, 2, 4]<br>
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[6, 4, 2] [6, 5, 1]
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</blockquote>
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</section>
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## Tests
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@ -14,11 +14,11 @@ The program is run by updating the integer $n$ as follows:
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<li>repeat this rule until no fraction in the list produces an integer when multiplied by $n$, then halt.</li>
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</ul>
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Conway gave a program for primes in FRACTRAN:
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<span style="margin-left: 2em;">$17/91$, $78/85$, $19/51$, $23/38$, $29/33$, $77/29$, $95/23$, $77/19$, $1/17$, $11/13$, $13/11$, $15/14$, $15/2$, $55/1$</span>
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Starting with $n=2$, this FRACTRAN program will change $n$ to $15=2\times (15/2)$, then $825=15\times (55/1)$, generating the following sequence of integers:
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<span style="margin-left: 2em;">$2$, $15$, $825$, $725$, $1925$, $2275$, $425$, $390$, $330$, $290$, $770$, $\ldots$</span>
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<span style="margin-left: 1em;">$\dfrac{17}{91}$, $\dfrac{78}{85}$, $\dfrac{19}{51}$, $\dfrac{23}{38}$, $\dfrac{29}{33}$, $\dfrac{77}{29}$, $\dfrac{95}{23}$, $\dfrac{77}{19}$, $\dfrac{1}{17}$, $\dfrac{11}{13}$, $\dfrac{13}{11}$, $\dfrac{15}{14}$, $\dfrac{15}{2}$, $\dfrac{55}{1}$</span>
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Starting with $n=2$, this FRACTRAN program will change $n$ to $15=2\times (\frac{15}{2})$, then $825=15\times (\frac{55}{1})$, generating the following sequence of integers:
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<span style="margin-left: 1em;">$2$, $15$, $825$, $725$, $1925$, $2275$, $425$, $390$, $330$, $290$, $770$, $\ldots$</span>
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After 2, this sequence contains the following powers of 2:
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<span style="margin-left: 2em;">$2^2=4$, $2^3=8$, $2^5=32$, $2^7=128$, $2^{11}=2048$, $2^{13}=8192$, $2^{17}=131072$, $2^{19}=524288$, $\ldots$</span>
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<span style="margin-left: 1em;">$2^2=4$, $2^3=8$, $2^5=32$, $2^7=128$, $2^{11}=2048$, $2^{13}=8192$, $2^{17}=131072$, $2^{19}=524288$, $\ldots$</span>
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which are the prime powers of 2.
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</section>
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