Permuted multiples: Difference between revisions
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The smallest positive integer n for which the following |
The smallest positive integer n for which the following |
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multiples contain exactly the same digits is: |
multiples contain exactly the same digits is: |
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n = 142857 |
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2 x n = 285714 |
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3 x n = 428571 |
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4 x n = 571428 |
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5 x n = 714285 |
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6 x n = 857142 |
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</pre> |
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=={{header|Phix}}== |
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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). |
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<!--<lang Phix>(phixonline)--> |
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
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<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> |
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<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span> |
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<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> |
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<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> |
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<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n10</span> |
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<span style="color: #000000;">n10</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">10</span> |
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<span style="color: #008080;">else</span> |
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<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> |
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<span style="color: #004080;">integer</span> <span style="color: #000000;">i</span> <span style="color: #000080;font-style:italic;">-- (for test after loop)</span> |
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<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> |
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<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> |
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<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> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
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<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> |
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<span style="color: #000000;">n</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span> |
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<span style="color: #008080;">constant</span> <span style="color: #000000;">fmt</span><span style="color: #0000FF;">=</span><span style="color: #008000;">""" |
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Smallest positive integer n for which (1..6)*n contain the same digits: |
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n = %d |
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2 x n = %d |
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3 x n = %d |
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4 x n = %d |
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5 x n = %d |
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6 x n = %d |
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"""</span> |
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<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> |
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<!--</lang>--> |
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{{out}} |
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<pre> |
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Nothing less than 10 (2) |
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Nothing less than 100 (17) |
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Nothing less than 1,000 (167) |
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Nothing less than 10,000 (1,667) |
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Nothing less than 100,000 (16,667) |
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Smallest positive integer n for which (1..6)*n contain the same digits: |
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n = 142857 |
n = 142857 |
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2 x n = 285714 |
2 x n = 285714 |