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- #!/usr/bin/ruby
- # A perfect square N has a splitting representation (S) if it's possible to segment
- # the decimal representation of N into a list of integers L, such that sum(L) = sqrt(n).
- # See also:
- # https://oeis.org/A104113
- # https://projecteuler.net/problem=719
- func S_representation(n) {
- var v = n.isqrt
- var D = n.digits
- D.ordered_partitions({|*t|
- if (t.sum{.digits2num} == v) {
- return t
- }
- })
- return false
- }
- for n in (2 .. 1000 -> map { _*_ }) {
- var arr = S_representation(n) || next
- say ("sqrt(#{n}) = ", arr.flip.map{.digits2num}.grep.join(' + '))
- }
- __END__
- sqrt(81) = 8 + 1
- sqrt(100) = 10
- sqrt(1296) = 1 + 29 + 6
- sqrt(2025) = 20 + 25
- sqrt(3025) = 30 + 25
- sqrt(6724) = 6 + 72 + 4
- sqrt(8281) = 8 + 2 + 81
- sqrt(9801) = 98 + 1
- sqrt(10000) = 100
- sqrt(55225) = 5 + 5 + 225
- sqrt(88209) = 88 + 209
- sqrt(136161) = 1 + 361 + 6 + 1
- sqrt(136900) = 1 + 369
- sqrt(143641) = 14 + 364 + 1
- sqrt(171396) = 17 + 1 + 396
- sqrt(431649) = 4 + 3 + 1 + 649
- sqrt(455625) = 45 + 5 + 625
- sqrt(494209) = 494 + 209
- sqrt(571536) = 5 + 715 + 36
- sqrt(627264) = 62 + 726 + 4
- sqrt(826281) = 826 + 2 + 81
- sqrt(842724) = 842 + 72 + 4
- sqrt(893025) = 8 + 930 + 2 + 5
- sqrt(929296) = 929 + 29 + 6
- sqrt(980100) = 980 + 10
- sqrt(982081) = 982 + 8 + 1
- sqrt(998001) = 998 + 1
- sqrt(1000000) = 1000
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