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  1. # 1
  2. def diagsum(n):
  3.     return sum([4 * x**2 - 6 * x + 6 for x in range(3, n + 1) if x % 2 != 0]) + 1
  4.  
  5. print('Sum of diagonal elements:', diagsum(1013))
  6. print()
  7.  
  8. # 2
  9. from itertools import permutations
  10.  
  11. def numsolutions():
  12.     num = 0
  13.     for perm in permutations('0123456789', 5):
  14.         if perm[0] == '0' or perm[1] == '0' or perm[2] == '0':
  15.             continue
  16.         r, s, x, z, v = perm
  17.         if int(r + s + r + x) + int(z + v + v) == int(s + r + x + s):
  18.             print('[' + r + s + x + z + v + ']:', r + s + r + x, '+', z + v + v, '=', s + r + x + s)
  19.             num += 1
  20.     return num
  21.  
  22. print('Solutions:', numsolutions())
  23. print()
  24.  
  25. # 3
  26. import collections
  27.  
  28.  
  29. def same_permutation(a, b, c):
  30.     d = collections.defaultdict(int)
  31.     for x in str(a):
  32.         d[x] += 2
  33.     for x in str(b):
  34.         d[x] -= 1
  35.     for x in str(c):
  36.         d[x] -= 1
  37.     return not any(d.values())
  38.  
  39.  
  40. def lower():
  41.     i, i2, i5 = 1, 2, 5
  42.     while not same_permutation(i, i2, i5):
  43.         i += 1
  44.         i2, i5 = i * 2, i * 5
  45.     return i
  46.  
  47.  
  48. l = lower()
  49. print(l, ': 2x = ', 2 * l, ': 5x = ', 5 * l)
  50.  
Success #stdin #stdout 0.5s 28384KB
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Sum of diagonal elements: 693520565

[12795]: 1217 + 955 = 2172
[23895]: 2328 + 955 = 3283
Solutions: 2

142857 : 2x =  285714 : 5x =  714285
https://ideone.com/poqTZB
language:
Python 3 (python  3.12)
created:
8 years ago
visibility:
public

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