Permuted multiples: Difference between revisions
→{{header|Phix}}
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The smallest positive integer n for which the following
multiples contain exactly the same digits is:
n = 142857
2 x n = 285714
3 x n = 428571
4 x n = 571428
5 x n = 714285
6 x n = 857142
</pre>
=={{header|Phix}}==
Maintain a limit (n10) and bump the iteration whenever *6 increases the number of digits, which (as shown) cuts the number of iterations by a factor of nearly thirteen and a half times (as in eg 67 iterations instead of 900 to find nothing in 100..1,000).
<!--<lang Phix>(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">n10</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">10</span>
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</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;">n10</span> <span style="color: #008080;">then</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;">"Nothing less than %,d (%,d)\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">})</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n10</span>
<span style="color: #000000;">n10</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">10</span>
<span style="color: #008080;">else</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">ns</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">))</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">i</span> <span style="color: #000080;font-style:italic;">-- (for test after loop)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">6</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">ins</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">*</span><span style="color: #000000;">i</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">ins</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">ns</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</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;">if</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">7</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">fmt</span><span style="color: #0000FF;">=</span><span style="color: #008000;">"""
Smallest positive integer n for which (1..6)*n contain the same digits:
n = %d
2 x n = %d
3 x n = %d
4 x n = %d
5 x n = %d
6 x n = %d
"""</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: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">6</span><span style="color: #0000FF;">)))</span>
<!--</lang>-->
{{out}}
<pre>
Nothing less than 10 (2)
Nothing less than 100 (17)
Nothing less than 1,000 (167)
Nothing less than 10,000 (1,667)
Nothing less than 100,000 (16,667)
Smallest positive integer n for which (1..6)*n contain the same digits:
n = 142857
2 x n = 285714
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