Fraction reduction: Difference between revisions
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For 5-digit fractions, there are 2988 with crossed-out 9's. |
For 5-digit fractions, there are 2988 with crossed-out 9's. |
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</pre> |
</pre> |
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=={{header|Ruby}}== |
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{{trans|Python}} |
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<lang Ruby>def indexOf(haystack, needle) |
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idx = 0 |
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for straw in haystack |
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if straw == needle then |
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return idx |
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else |
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idx = idx + 1 |
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end |
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end |
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return -1 |
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end |
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def getDigits(n, le, digits) |
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while n > 0 |
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r = n % 10 |
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if r == 0 or indexOf(digits, r) >= 0 then |
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return false |
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end |
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le = le - 1 |
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digits[le] = r |
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n = (n / 10).floor |
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end |
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return true |
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end |
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POWS = [1, 10, 100, 1000, 10000] |
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def removeDigit(digits, le, idx) |
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sum = 0 |
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pow = POWS[le - 2] |
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i = 0 |
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while i < le |
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if i == idx then |
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i = i + 1 |
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next |
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end |
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sum = sum + digits[i] * pow |
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pow = (pow / 10).floor |
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i = i + 1 |
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end |
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return sum |
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end |
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def main |
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lims = [ [ 12, 97 ], [ 123, 986 ], [ 1234, 9875 ], [ 12345, 98764 ] ] |
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count = Array.new(5, 0) |
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omitted = Array.new(5) { Array.new(10, 0) } |
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i = 0 |
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for lim in lims |
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n = lim[0] |
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while n < lim[1] |
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nDigits = [0] * (i + 2) |
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nOk = getDigits(n, i + 2, nDigits) |
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if not nOk then |
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n = n + 1 |
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next |
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end |
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d = n + 1 |
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while d <= lim[1] + 1 |
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dDigits = [0] * (i + 2) |
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dOk = getDigits(d, i + 2, dDigits) |
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if not dOk then |
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d = d + 1 |
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next |
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end |
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nix = 0 |
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while nix < nDigits.length |
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digit = nDigits[nix] |
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dix = indexOf(dDigits, digit) |
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if dix >= 0 then |
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rn = removeDigit(nDigits, i + 2, nix) |
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rd = removeDigit(dDigits, i + 2, dix) |
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if (1.0 * n / d) == (1.0 * rn / rd) then |
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count[i] = count[i] + 1 |
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omitted[i][digit] = omitted[i][digit] + 1 |
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if count[i] <= 12 then |
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print "%d/%d = %d/%d by omitting %d's\n" % [n, d, rn, rd, digit] |
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end |
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end |
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end |
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nix = nix + 1 |
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end |
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d = d + 1 |
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end |
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n = n + 1 |
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end |
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print "\n" |
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i = i + 1 |
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end |
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i = 2 |
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while i <= 5 |
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print "There are %d %d-digit fractions of which:\n" % [count[i - 2], i] |
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j = 1 |
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while j <= 9 |
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if omitted[i - 2][j] == 0 then |
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j = j + 1 |
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next |
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end |
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print "%6s have %d's omitted\n" % [omitted[i - 2][j], j] |
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j = j + 1 |
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end |
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print "\n" |
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i = i + 1 |
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end |
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end |
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main()</lang> |
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{{out}} |
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<pre>16/64 = 1/4 by omitting 6's |
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19/95 = 1/5 by omitting 9's |
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26/65 = 2/5 by omitting 6's |
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49/98 = 4/8 by omitting 9's |
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132/231 = 12/21 by omitting 3's |
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134/536 = 14/56 by omitting 3's |
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134/938 = 14/98 by omitting 3's |
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136/238 = 16/28 by omitting 3's |
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138/345 = 18/45 by omitting 3's |
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139/695 = 13/65 by omitting 9's |
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143/341 = 13/31 by omitting 4's |
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146/365 = 14/35 by omitting 6's |
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149/298 = 14/28 by omitting 9's |
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149/596 = 14/56 by omitting 9's |
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149/894 = 14/84 by omitting 9's |
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154/253 = 14/23 by omitting 5's |
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1234/4936 = 124/496 by omitting 3's |
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1239/6195 = 123/615 by omitting 9's |
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1246/3649 = 126/369 by omitting 4's |
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1249/2498 = 124/248 by omitting 9's |
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1259/6295 = 125/625 by omitting 9's |
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1279/6395 = 127/635 by omitting 9's |
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1283/5132 = 128/512 by omitting 3's |
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1297/2594 = 127/254 by omitting 9's |
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1297/3891 = 127/381 by omitting 9's |
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1298/2596 = 128/256 by omitting 9's |
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1298/3894 = 128/384 by omitting 9's |
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1298/5192 = 128/512 by omitting 9's |
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12349/24698 = 1234/2468 by omitting 9's |
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12356/67958 = 1236/6798 by omitting 5's |
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12358/14362 = 1258/1462 by omitting 3's |
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12358/15364 = 1258/1564 by omitting 3's |
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12358/17368 = 1258/1768 by omitting 3's |
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12358/19372 = 1258/1972 by omitting 3's |
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12358/21376 = 1258/2176 by omitting 3's |
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12358/25384 = 1258/2584 by omitting 3's |
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12359/61795 = 1235/6175 by omitting 9's |
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12364/32596 = 1364/3596 by omitting 2's |
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12379/61895 = 1237/6185 by omitting 9's |
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12386/32654 = 1386/3654 by omitting 2's |
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There are 4 2-digit fractions of which: |
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2 have 6's omitted |
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2 have 9's omitted |
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There are 122 3-digit fractions of which: |
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9 have 3's omitted |
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1 have 4's omitted |
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6 have 5's omitted |
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15 have 6's omitted |
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16 have 7's omitted |
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15 have 8's omitted |
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60 have 9's omitted |
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There are 660 4-digit fractions of which: |
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14 have 1's omitted |
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25 have 2's omitted |
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92 have 3's omitted |
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14 have 4's omitted |
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29 have 5's omitted |
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63 have 6's omitted |
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16 have 7's omitted |
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17 have 8's omitted |
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390 have 9's omitted |
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There are 5087 5-digit fractions of which: |
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75 have 1's omitted |
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40 have 2's omitted |
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376 have 3's omitted |
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78 have 4's omitted |
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209 have 5's omitted |
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379 have 6's omitted |
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591 have 7's omitted |
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351 have 8's omitted |
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2988 have 9's omitted</pre> |
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=={{header|Visual Basic .NET}}== |
=={{header|Visual Basic .NET}}== |