Dominoes: Difference between revisions
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2025 layouts found.
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===Extra credit task ===
<lang julia>""" From https://en.wikipedia.org/wiki/Domino_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
"""
function dominotilingcount(m, n)
return BigInt(floor(prod(
[prod(
[big"4.0" * cospi(j / (m + 1)) + 4 * cospi((k / (n + 1))) for k in 1:n÷2]
) for j in 1:m÷2]
)))
end
arrang = dominotilingcount(7, 8)
perms = factorial(big"28")
flips = 2^28
println("Arrangements ignoring values: $arrang")
println("Permutations of 28 dominos: ", perms)
println("Permuted arrangements ignoring flipping dominos: ", arrang * perms)
println("Possible flip configurations: $flips")
println("Possible permuted arrangements with flips: ", flips * arrang * perms)
</lang>{{out}}
<pre>
Arrangements ignoring values: 158862606
Permutations of 28 dominos: 304888344611713860501504000000
Permuted arrangements ignoring flipping dominos: 48435356964042922005589392359424000000
Possible flip configurations: 268435456
Possible permuted arrangements with flips: 13001767133165637372142823086764897337344000000
</pre>
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