Fraction reduction: Difference between revisions
Content deleted Content added
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351 have 8's omitted
2988 have 9's omitted</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<lang Mathematica>ClearAll[AnomalousCancellationQ2]
AnomalousCancellationQ2[frac : {i_?Positive, j_?Positive}] :=
Module[{\[Beta], samedigits, idig, jdig, candidates, ff, p, q, r, tmp},
idig = IntegerDigits[i];
jdig = IntegerDigits[j];
samedigits = Intersection[idig, jdig];
ff = i/j;
If[samedigits != {},
r = {};
Do[
p = Flatten[Position[idig, s]];
q = Flatten[Position[jdig, s]];
p = FromDigits[Delete[idig, #]] & /@ p;
q = FromDigits[Delete[jdig, #]] & /@ q;
tmp = Select[Tuples[{p, q}], #[[1]]/#[[2]] == ff &];
If[Length[tmp] > 0,
r = Join[r, Join[#, {i, j, s}] & /@ tmp];
];
,
{s, samedigits}
];
r
,
{}
]
]
c = 0;
Dynamic[{j, Length[ijs], c}]
ijs = Select[Select[Range[1, 9999], IntegerDigits /* FreeQ[0]], IntegerDigits /* DuplicateFreeQ];
res = Reap[
Do[
Do[
num = ijs[[i]];
den = ijs[[j]];
out = AnomalousCancellationQ2[{num, den}];
If[Length[out] > 0,
c += Length[out];
Sow[out]
]
,
{i, 1, j - 1}
]
,
{j, Length[ijs]}
]
][[2, 1]];
tmp = Catenate[res];
sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 2 &];
Length[sel]
t = Take[sel, UpTo[12]];
Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t]
SortBy[Tally[sel[[All, -1]]], First]
sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 3 &];
Length[sel]
t = Take[sel, UpTo[12]];
Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t]
SortBy[Tally[sel[[All, -1]]], First]
sel = Sort@Select[tmp, IntegerLength[#[[3]]] == IntegerLength[#[[4]]] == 4 &];
Length[sel]
t = Take[sel, UpTo[12]];
Column[Row[{#3, "/", #4, " = ", #1, "/", #2, " by removing ", #5}] & @@@ t]
SortBy[Tally[sel[[All, -1]]], First]</lang>
{{out}}
<pre>4
16/64 = 1/4 by removing 6
19/95 = 1/5 by removing 9
26/65 = 2/5 by removing 6
49/98 = 4/8 by removing 9
{{6,2},{9,2}}
122
132/231 = 12/21 by removing 3
162/648 = 12/48 by removing 6
143/341 = 13/31 by removing 4
163/652 = 13/52 by removing 6
139/695 = 13/65 by removing 9
193/965 = 13/65 by removing 9
194/291 = 14/21 by removing 9
154/253 = 14/23 by removing 5
149/298 = 14/28 by removing 9
154/352 = 14/32 by removing 5
146/365 = 14/35 by removing 6
154/451 = 14/41 by removing 5
{{3,9},{4,1},{5,6},{6,15},{7,16},{8,15},{9,60}}
660
1623/6492 = 123/492 by removing 6
1239/6195 = 123/615 by removing 9
1923/9615 = 123/615 by removing 9
1324/2317 = 124/217 by removing 3
1249/2498 = 124/248 by removing 9
1234/4936 = 124/496 by removing 3
1259/6295 = 125/625 by removing 9
1925/9625 = 125/625 by removing 9
1246/3649 = 126/369 by removing 4
1297/2594 = 127/254 by removing 9
1297/3891 = 127/381 by removing 9
1279/6395 = 127/635 by removing 9
{{1,14},{2,25},{3,92},{4,14},{5,29},{6,63},{7,16},{8,17},{9,390}}</pre>
=={{header|MiniZinc}}==
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