Rosetta Code

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Countdown (view source)

Revision as of 07:29, 8 October 2022

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The brute force algorithm is quite obvious. What is more interesting is to find some optimisation heuristics to reduce the number of calculations. For example, a rather interesting computational challenge is to calculate, as fast as possible, all existing solutions (that means 2'764'800 operations) for all possible games (with all the 13'243 combinations of six numbers out of twenty-four for all 898 possible targets between 101 and 999).
 
 
=={{header|Phix}}==
Here's one I already had, cleaned up a bit:
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #000080;font-style:italic;">--
-- demo/Countdown.exw
--
-- solves the numbers game from countdown.
--</span>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">6</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">ops</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"+-*/"</span>
<span style="color: #008080;">enum</span> <span style="color: #000000;">ADD</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">SUB</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">MUL</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">DIV</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">chosen</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- original numbers &lt;-&gt; partial sums</span>
<span style="color: #000000;">expression</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- the operations tried so far</span>
<span style="color: #000000;">solution</span> <span style="color: #000080;font-style:italic;">-- (a/best snapshot of expression)</span>
<span style="color: #004080;">int</span> <span style="color: #000000;">len</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- n+1 means no solution yet found</span>
<span style="color: #000000;">maxlev</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- recursion limit (5, drops as solns found)</span>
<span style="color: #000000;">near</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- nearest answer (in solution) out by this</span>
<span style="color: #000000;">lenn</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- length of "" ""</span>
<span style="color: #000000;">target</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">countdown</span><span style="color: #0000FF;">(</span><span style="color: #004080;">int</span> <span style="color: #000000;">level</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">--
-- Recursive search - takes two numbers, performs an op (storing result), checks
-- for target value, and calls itself. All solutions are stored, to find shortest,
-- so that, for example, 100+1 is chosen instead of 100+(75/25)-1-1.
-- Optimizations are made to ensure commutative operations are only performed one
-- way round, division is only performed when no remainder, and */1 are skipped.
--</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">sti</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">chosen</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #000080;font-style:italic;">-- speedwise/save</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">sti</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">stj</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">chosen</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #000080;font-style:italic;">-- ""</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">j</span> <span style="color: #008080;">and</span> <span style="color: #000000;">stj</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">operation</span><span style="color: #0000FF;">=</span><span style="color: #000000;">ADD</span> <span style="color: #008080;">to</span> <span style="color: #000000;">DIV</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">operation</span><span style="color: #0000FF;"><</span><span style="color: #000000;">DIV</span> <span style="color: #008080;">or</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sti</span><span style="color: #0000FF;">,</span><span style="color: #000000;">stj</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">and</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">operation</span><span style="color: #0000FF;"><</span><span style="color: #000000;">MUL</span> <span style="color: #008080;">or</span> <span style="color: #000000;">stj</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">and</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">sti</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">stj</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- worth doing...</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">ci</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sti</span>
<span style="color: #008080;">switch</span> <span style="color: #000000;">operation</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">case</span> <span style="color: #000000;">ADD</span><span style="color: #0000FF;">:</span> <span style="color: #000000;">ci</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">stj</span>
<span style="color: #008080;">case</span> <span style="color: #000000;">SUB</span><span style="color: #0000FF;">:</span> <span style="color: #000000;">ci</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">stj</span>
<span style="color: #008080;">case</span> <span style="color: #000000;">MUL</span><span style="color: #0000FF;">:</span> <span style="color: #000000;">ci</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">stj</span>
<span style="color: #008080;">case</span> <span style="color: #000000;">DIV</span><span style="color: #0000FF;">:</span> <span style="color: #000000;">ci</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">stj</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">switch</span>
<span style="color: #000000;">chosen</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ci</span>
<span style="color: #000000;">chosen</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000080;font-style:italic;">/* store operands and operator */</span>
<span style="color: #000000;">expression</span><span style="color: #0000FF;">[</span><span style="color: #000000;">level</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">sti</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ops</span><span style="color: #0000FF;">[</span><span style="color: #000000;">operation</span><span style="color: #0000FF;">],</span><span style="color: #000000;">stj</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ci</span><span style="color: #0000FF;">}</span>
<span style="color: #000080;font-style:italic;">-- check for solution</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">ci</span><span style="color: #0000FF;">==</span><span style="color: #000000;">target</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">level</span><span style="color: #0000FF;"><</span><span style="color: #000000;">len</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">/* solution is shortest so far - store it */</span>
<span style="color: #000000;">len</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">level</span>
<span style="color: #000000;">maxlev</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">level</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span>
<span style="color: #000000;">near</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">solution</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">expression</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">else</span>
<span style="color: #000080;font-style:italic;">--store closest?</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">offby</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">target</span><span style="color: #0000FF;">-</span><span style="color: #000000;">ci</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">offby</span><span style="color: #0000FF;"><</span><span style="color: #000000;">near</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">near</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">offby</span>
<span style="color: #000000;">lenn</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">level</span>
<span style="color: #000000;">solution</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">expression</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">-- if not at required level, recurse</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">level</span><span style="color: #0000FF;"><</span><span style="color: #000000;">maxlev</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">countdown</span><span style="color: #0000FF;">(</span><span style="color: #000000;">level</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">-- undo</span>
<span style="color: #000000;">chosen</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sti</span>
<span style="color: #000000;">chosen</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">stj</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">list</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">int</span> <span style="color: #000000;">dest</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">len</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span>
<span style="color: #000000;">maxlev</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">5</span>
<span style="color: #000000;">near</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dest</span>
<span style="color: #000000;">target</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dest</span>
<span style="color: #000000;">chosen</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">list</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">countdown</span><span style="color: #0000FF;">()</span>
<span style="color: #000080;font-style:italic;">/* process solution into printable form */</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">off</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"exact"</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">len</span><span style="color: #0000FF;">=</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">off</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"off by %d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">near</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">len</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lenn</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">soln</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">,{{</span><span style="color: #008000;">"%d%c%d=%d"</span><span style="color: #0000FF;">},</span><span style="color: #000000;">solution</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">len</span><span style="color: #0000FF;">]}),</span><span style="color: #008000;">", "</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Target %d from %18v: %s (%s)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">dest</span><span style="color: #0000FF;">,</span><span style="color: #000000;">list</span><span style="color: #0000FF;">,</span><span style="color: #000000;">soln</span><span style="color: #0000FF;">,</span><span style="color: #000000;">off</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">t0</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">time</span><span style="color: #0000FF;">()</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">({</span><span style="color: #000000;">75</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">25</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},</span><span style="color: #000000;">737</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- Target 737 from {75,50,25,100,8,2}: 75/25=3, 50-3=47, 100-2=98, 98*8=784, 784-47=737 (exact)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">({</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">25</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">75</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">},</span><span style="color: #000000;">952</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- Target 952 from {3,6,25,50,75,100}: 75*3=225, 100+6=106, 225*106=23850, 23850-50=23800, 23800/25=952 (exact)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">({</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">75</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">25</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">},</span><span style="color: #000000;">952</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- Target 952 from {100,75,50,25,6,3}: 100+6=106, 106*75=7950, 7950*3=23850, 23850-50=23800, 23800/25=952 (exact)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">({</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">},</span><span style="color: #000000;">203</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- Target 203 from {50,100,4,2,2,4}: 50*4=200, 200+4=204, 2/2=1, 204-1=203 (exact)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">({</span><span style="color: #000000;">25</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">},</span><span style="color: #000000;">465</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- Target 465 from {25,4,9,2,3,10}: 25-10=15, 9*3=27, 27+4=31, 31*15=465 (exact)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">({</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">},</span><span style="color: #000000;">241</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- Target 241 from {9,8,10,5,9,7}: 9+9=18, 8+5=13, 18*13=234, 234+7=241 (exact)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">({</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">},</span><span style="color: #000000;">824</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- Target 824 from {3,7,6,2,1,7}: 7+3=10, 10*6=60, 60-1=59, 59*2=118, 118*7=826 (off by 2)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">({</span><span style="color: #000000;">75</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">25</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},</span><span style="color: #000000;">125</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- Target 125 from {75,50,25,100,8,2}: 75+50=125 (exact)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">({</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">},</span><span style="color: #000000;">594</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- Target 594 from {8,4,4,6,8,9}: 8*8=64, 64-4=60, 60+6=66, 66*9=594 (exact)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">({</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">},</span><span style="color: #000000;">363</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- Target 363 from {2,4,9,10,3,5}: 9*4=36, 36*10=360, 360+3=363 (exact)
--test(shuffle(tagset(10)&tagset(10)&tagstart(25,4,25))[1..6],100+rand(899))</span>
<span style="color: #0000FF;">?</span><span style="color: #7060A8;">time</span><span style="color: #0000FF;">()-</span><span style="color: #000000;">t0</span> <span style="color: #000080;font-style:italic;">-- 1.797</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Target 737 from {75,50,25,100,8,2}: 75/25=3, 50-3=47, 100-2=98, 98*8=784, 784-47=737 (exact)
Target 952 from {3,6,25,50,75,100}: 75*3=225, 100+6=106, 225*106=23850, 23850-50=23800, 23800/25=952 (exact)
Target 952 from {100,75,50,25,6,3}: 100+6=106, 106*75=7950, 7950*3=23850, 23850-50=23800, 23800/25=952 (exact)
Target 203 from {50,100,4,2,2,4}: 50*4=200, 200+4=204, 2/2=1, 204-1=203 (exact)
Target 465 from {25,4,9,2,3,10}: 25-10=15, 9*3=27, 27+4=31, 31*15=465 (exact)
Target 241 from {9,8,10,5,9,7}: 9+9=18, 8+5=13, 18*13=234, 234+7=241 (exact)
Target 824 from {3,7,6,2,1,7}: 7+3=10, 10*6=60, 60-1=59, 59*2=118, 118*7=826 (off by 2)
Target 125 from {75,50,25,100,8,2}: 75+50=125 (exact)
Target 594 from {8,4,4,6,8,9}: 8*8=64, 64-4=60, 60+6=66, 66*9=594 (exact)
Target 363 from {2,4,9,10,3,5}: 9*4=36, 36*10=360, 360+3=363 (exact)
1.797
</pre>
 
=={{header|Quorum}}==
Petelomax
7,818

edits

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