43 lines
1.4 KiB
Text
43 lines
1.4 KiB
Text
using Combinatorics
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toi(set) = parse(Int, join(set, ""))
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drop1(c, set) = toi(filter(x -> x != c, set))
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function anomalouscancellingfractions(numdigits)
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ret = Vector{Tuple{Int, Int, Int, Int, Int}}()
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for nset in permutations(1:9, numdigits), dset in permutations(1:9, numdigits)
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if nset < dset # only proper fractions
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for c in nset
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if c in dset # a common digit exists
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n, d, nn, dd = toi(nset), toi(dset), drop1(c, nset), drop1(c, dset)
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if n // d == nn // dd # anomalous cancellation
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push!(ret, (n, d, nn, dd, c))
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end
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end
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end
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end
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end
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ret
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end
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function testfractionreduction(maxdigits=5)
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for i in 2:maxdigits
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results = anomalouscancellingfractions(i)
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println("\nFor $i digits, there were ", length(results),
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" fractions with anomalous cancellation.")
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numcounts = zeros(Int, 9)
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for r in results
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numcounts[r[5]] += 1
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end
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for (j, count) in enumerate(numcounts)
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count > 0 && println("The digit $j was crossed out $count times.")
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end
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println("Examples:")
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for j in 1:min(length(results), 12)
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r = results[j]
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println(r[1], "/", r[2], " = ", r[3], "/", r[4], " ($(r[5]) crossed out)")
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end
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end
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end
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testfractionreduction()
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