nytimes

from math import sqrt
from itertools import permutations

def squarable(sides):
	area = sum(map(lambda (a,b): a*b, sides))
	S = sqrt(area)
	if S == int(S):

		# check Ken's conditions

		(H,A),(B,C),(D,E),(F,G),(X,Y) = sides
		return S == (A+B) == (C+D) == (E+F) == (G+H) == (F+X+B) == (H+Y+D) and \
			     (A == F+X) and (C == H+Y) and (E == B+X) and (G == D+Y)

solutions = set()
for (H,A,B,C,D,E,F,G,X,Y) in permutations((1,2,3,4,5,6,7,8,9,10)):
	sides = ((H,A),(B,C),(D,E),(F,G),(X,Y))
	if squarable(sides):
		sol = sorted(map(lambda (a,b): (min(a,b), max(a,b)), sides))
		solutions.add(tuple(sol))
print "%d solutions" % len(solutions)
for sol in solutions: print sol