Dominoes: Difference between revisions

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correct formula
m (different source for formula)
m (correct formula)
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</pre>
===Extra credit task ===
<lang julia>""" From https://wwwen.mathwikipedia.cmu.eduorg/~bwsullivwiki/domino-tilings.pdfDomino_tiling#Counting_tilings_of_regions
The number of ways to cover an m X n rectangle with m * n / 2 dominoes, calculated
independently by Temperley & Fisher (1961) and Kasteleyn (1961), is given by
Line 208:
function dominotilingcount(m, n)
return BigInt(floor(prod([prod(
[abs(big"24.0" * (cospi(j / (m + 1)))^2 + 2 * im4 * (cospi(k / (n + 1))) for k in 1:n])^2
for k in 1:(n+1)÷2]) for j in 1:(m+1)÷2]
)))
end
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println("Possible flip configurations: $flips")
println("Possible permuted arrangements with flips: ", flips * arrang * perms)
</lang>{{out}}
<pre>
Arrangements ignoring values: 16710655338091292697
Permutations of 28 dominos: 304888344611713860501504000000
Permuted arrangements ignoring flipping dominos: 509488404340715971133309942207348736000000394128248414528672328712716288000000
Possible flip configurations: 268435456
Possible permuted arrangements with flips: 136764752145912471077652891125763304499183616000000105797996085635281181632579889767907328000000
</pre>
 
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