Done puzzle 64

[project-euler.git] / euler33.ipynb

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       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
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   "source": [
    "digits = (0..9).to_a\n",
    "digits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
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      ]
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     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "pairs = digits.repeated_permutation(2).select {|ds| !ds.include?(0)}.to_a\n",
    "pairs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
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    {
     "data": {
      "text/plain": [
       ":to_r"
      ]
     },
     "execution_count": 46,
     "metadata": {},
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   "source": [
    "class Array\n",
    "  def to_i\n",
    "    self.map {|d| d.to_s}.join.to_i\n",
    "  end\n",
    "  \n",
    "  def to_r\n",
    "    Rational(self[0].to_i, self[1].to_i)\n",
    "  end\n",
    "end"
   ]
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  {
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   "execution_count": 10,
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    {
     "data": {
      "text/plain": [
       ":to_digits"
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     },
     "execution_count": 10,
     "metadata": {},
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   ],
   "source": [
    "class Numeric\n",
    "  def to_digits\n",
    "    self.to_s.split('').map {|d| d.to_i}\n",
    "  end\n",
    "end "
   ]
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  {
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   "execution_count": 7,
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    {
     "data": {
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       "[10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]"
      ]
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     "execution_count": 7,
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   ],
   "source": [
    "digits.repeated_permutation(2).select {|ds| ds[0] != 0}.map {|ds| ds.to_i}.to_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 5]"
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     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "25.to_digits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
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      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pairs.permutation(2).to_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
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       "3240"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fractions = pairs.permutation(2).select {|n, d| n.to_i < d.to_i}.to_a\n",
    "fractions.length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
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       "1188"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fractions = pairs.permutation(2).select {|n, d| n.to_i < d.to_i}.to_a\n",
    "fractions = fractions.select {|n, d| n.any? {|nd| d.include?(nd)}}\n",
    "fractions.length"
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   "cell_type": "code",
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(3/11), (15/56), (5/19), (15/58), (15/59), (15/61), (3/13), (15/71), (1/5), (5/27), (3/17), (15/91), (3/19), (16/17), (8/9), (16/19), (16/21), (8/13), (16/31), (4/9), (16/41), (8/23), (16/51), (2/7), (16/61), (8/31), (16/63), (1/4), (16/65), (8/33), (16/67), (4/17), (16/69), (16/71), (4/19), (16/81), (8/43), (16/91), (1/6), (17/18), (17/19), (17/21), (17/27), (17/31), (17/37), (17/41), (17/47), (1/3), (17/57), (17/61), (17/67), (17/71), (17/72), (17/73), (17/74), (17/75), (17/76), (17/77), (17/78), (17/79), (17/81), (17/87), (17/91), (17/97), (18/19), (6/7), (9/14), (18/31), (9/19), (18/41), (3/8), (6/17), (9/29), (18/61), (9/34), (18/71), (3/13), (2/9), (9/41), (18/83), (3/14), (18/85), (9/43), (6/29), (9/44), (18/89), (18/91), (9/49), (19/21), (19/29), (19/31), (19/39), (19/41), (19/49), (19/51), (19/59), (19/61), (19/69), (19/71), (19/79), (19/81), (19/89), (19/91), (19/92), (19/93), (19/94), (1/5), (19/96), (19/97), (19/98), (19/99), (21/22), (21/23), (7/8), (21/25), (21/26), 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(1/2), (13/28), (26/61), (13/31), (26/63), (13/32), (2/5), (13/33), (26/67), (13/34), (26/69), (13/36), (13/38), (13/41), (13/43), (13/46), (13/48), (27/28), (27/29), (27/32), (27/37), (9/14), (27/47), (27/52), (9/19), (27/62), (27/67), (27/71), (3/8), (27/73), (27/74), (9/25), (27/76), (27/77), (9/26), (27/79), (27/82), (9/29), (27/92), (27/97), (28/29), (7/8), (14/19), (2/3), (7/12), (7/13), (14/29), (14/31), (7/17), (7/18), (14/39), (28/81), (14/41), (28/83), (1/3), (28/85), (14/43), (28/87), (7/22), (28/89), (7/23), (2/7), (29/32), (29/39), (29/42), (29/49), (29/52), (29/59), (29/62), (29/69), (29/72), (29/79), (29/82), (29/89), (29/91), (29/92), (29/93), (29/94), (29/95), (29/96), (29/97), (29/98), (29/99), (31/32), (31/33), (31/34), (31/35), (31/36), (31/37), (31/38), (31/39), (31/41), (31/43), (31/51), (31/53), (31/61), (31/63), (31/71), (31/73), (31/81), (31/83), (31/91), (1/3), (32/33), (16/17), (32/35), (8/9), (32/37), (16/19), (32/39), (16/21), (32/43), (8/13), (32/53), (16/31), (32/63), (4/9), (32/73), (16/41), (32/83), (8/23), (32/93), (33/34), (33/35), (11/12), (33/37), (33/38), (11/13), (33/43), (33/53), (11/21), (33/73), (33/83), (11/31), (34/35), (17/18), (34/37), (17/19), (34/39), (34/41), (17/21), (34/43), (17/22), (34/45), (17/23), (34/47), (17/24), (34/49), (34/53), (17/27), (34/63), (17/32), (34/73), (17/37), (34/83), (17/42), (34/93), (17/47), (35/36), (35/37), (35/38), (35/39), (35/43), (7/9), (35/51), (35/52), (35/53), (35/54), (7/11), (5/8), (35/57), (35/58), (35/59), (5/9), (7/13), (35/73), (7/15), (35/83), (7/17), (35/93), (7/19), (36/37), (18/19), (12/13), (36/43), (18/23), (36/53), (9/14), (36/61), (18/31), (4/7), (9/16), (36/65), (6/11), (36/67), (9/17), (12/23), (36/73), (9/19), (36/83), (18/43), (12/31), (3/8), (37/38), (37/39), (37/43), (37/47), (37/53), (37/57), (37/63), (37/67), (37/71), (37/72), (37/73), (1/2), (37/75), (37/76), (37/77), (37/78), (37/79), (37/83), (37/87), (37/93), (37/97), (38/39), (38/43), (19/24), (38/53), (19/29), (38/63), (19/34), (38/73), (19/39), (38/81), (19/41), (38/83), (19/42), (38/85), (19/43), (38/87), (19/44), (38/89), (38/93), (19/49), (39/43), (39/49), (39/53), (39/59), (13/21), (13/23), (39/73), (39/79), (39/83), (39/89), (3/7), (39/92), (13/31), (39/94), (39/95), (13/32), (39/97), (39/98), (13/33), (41/42), (41/43), (41/44), (41/45), (41/46), (41/47), (41/48), (41/49), (41/51), (41/54), (41/61), (41/64), (41/71), (41/74), (41/81), (41/84), (41/91), (41/94), (42/43), (21/22), (14/15), (21/23), (42/47), (7/8), (6/7), (21/26), (7/9), (21/31), (21/32), (7/12), (21/37), (21/41), (1/2), (21/46), (21/47), (43/44), (43/45), (43/46), (43/47), (43/48), (43/49), (43/53), (43/54), (43/63), (43/64), (43/73), (43/74), (43/83), (43/84), (43/93), (43/94), (44/45), (22/23), (44/47), (11/12), (44/49), (22/27), (11/16), (22/37), (11/21), (22/47), (45/46), (45/47), (15/16), (45/49), (15/17), (45/52), (45/53), (5/6), (9/11), (45/56), (15/19), (45/58), (45/59), (45/64), (9/13), (45/74), (3/5), (15/28), (9/17), (45/94), (9/19), (46/47), (23/24), (46/49), (23/27), (23/28), (46/61), (23/31), (46/63), (23/32), (46/65), (23/33), (46/67), (23/34), (2/3), (23/37), (23/38), (23/42), (23/43), (23/47), (23/48), (47/48), (47/49), (47/54), (47/57), (47/64), (47/67), (47/71), (47/72), (47/73), (47/74), (47/75), (47/76), (47/77), (47/78), (47/79), (47/84), (47/87), (1/2), (47/97), (48/49), (8/9), (24/29), (3/4), (12/17), (24/37), (8/13), (16/27), (24/41), (48/83), (4/7), (48/85), (24/43), (16/29), (6/11), (48/89), (24/47), (24/49), (49/54), (49/59), (49/64), (49/69), (49/74), (49/79), (7/12), (49/89), (7/13), (49/92), (49/93), (49/94), (49/95), (49/96), (49/97), (1/2), (49/99), (51/52), (51/53), (17/18), (51/55), (51/56), (17/19), (51/58), (51/59), (51/61), (51/65), (51/71), (17/25), (17/27), (3/5), (51/91), (51/95), (52/53), (26/27), (52/55), (13/14), (52/57), (26/29), (52/59), (26/31), (4/5), (13/18), (52/75), (26/41), (52/85), (13/23), (52/95), (53/54), (53/55), (53/56), (53/57), (53/58), (53/59), (53/63), (53/65), (53/73), (53/75), (53/83), (53/85), (53/93), (53/95), (54/55), (27/28), (18/19), (27/29), (54/59), (27/32), (54/65), (27/37), (18/25), (9/14), (54/85), (27/47), (54/95), (55/56), (55/57), (55/58), (55/59), (11/13), (11/15), (11/17), (11/19), (56/57), (28/29), (56/59), (56/61), (28/31), (8/9), (7/8), (56/65), (28/33), (56/67), (14/17), (56/69), (56/75), (14/19), (56/85), (28/43), (56/95), (7/12), (57/58), (57/59), (57/65), (57/67), (57/71), (19/24), (57/73), (57/74), (19/25), (3/4), (57/77), (19/26), (57/79), (57/85), (19/29), (3/5), (57/97), (58/59), (58/65), (29/34), (58/75), (29/39), (58/81), (29/41), (58/83), (29/42), (58/85), (29/43), (2/3), (29/44), (58/89), (58/95), (29/49), (59/65), (59/69), (59/75), (59/79), (59/85), (59/89), (59/91), (59/92), (59/93), (59/94), (59/95), (59/96), (59/97), (59/98), (59/99), (61/62), (61/63), (61/64), (61/65), (61/66), (61/67), (61/68), (61/69), (61/71), (61/76), (61/81), (61/86), (61/91), (61/96), (62/63), (31/32), (62/65), (31/33), (62/67), (31/34), (62/69), (31/36), (31/38), (31/41), (31/43), (31/46), (31/48), (63/64), (63/65), (21/22), (63/67), (63/68), (21/23), (63/73), (63/76), (63/83), (63/86), (21/31), (21/32), (64/65), (32/33), (64/67), (16/17), (64/69), (32/37), (16/19), (16/21), (32/43), (32/47), (2/3), (65/66), (65/67), (65/68), (65/69), (13/15), (65/76), (13/17), (65/86), (13/19), (65/96), (66/67), (33/34), (22/23), (33/38), (33/43), (11/16), (67/68), (67/69), (67/71), (67/72), (67/73), (67/74), (67/75), (67/76), (67/77), (67/78), (67/79), (67/86), (67/87), (67/96), (67/97), (68/69), (17/19), (34/39), (68/81), (34/41), (68/83), (17/21), (4/5), (34/43), (68/87), (17/22), (68/89), (17/24), (34/49), (69/76), (69/79), (69/86), (69/89), (69/91), (3/4), (23/31), (69/94), (69/95), (23/32), (69/97), (69/98), (23/33), (71/72), (71/73), (71/74), (71/75), (71/76), (71/77), (71/78), (71/79), (71/81), (71/87), (71/91), (71/97), (72/73), (36/37), (24/25), (18/19), (72/77), (12/13), (72/79), (36/41), (24/29), (18/23), (72/97), (73/74), (73/75), (73/76), (73/77), (73/78), (73/79), (73/83), (73/87), (73/93), (73/97), (74/75), (37/38), (74/77), (37/39), (74/79), (37/42), (74/87), (37/47), (74/97), (75/76), (75/77), (25/26), (75/79), (15/17), (25/29), (15/19), (75/97), (76/77), (38/39), (76/79), (38/43), (76/87), (19/24), (76/97), (77/78), (77/79), (77/87), (77/97), (78/79), (26/27), (39/41), (78/83), (13/14), (78/85), (39/43), (26/29), (39/44), (78/89), (78/97), (39/49), (79/87), (79/89), (79/91), (79/92), (79/93), (79/94), (79/95), (79/96), (79/97), (79/98), (79/99), (81/82), (81/83), (27/28), (81/85), (81/86), (27/29), (81/88), (81/89), (81/91), (81/98), (82/83), (41/42), (82/85), (41/43), (82/87), (41/44), (82/89), (41/46), (41/49), (83/84), (83/85), (83/86), (83/87), (83/88), (83/89), (83/93), (83/98), (84/85), (42/43), (28/29), (21/22), (84/89), (42/47), (6/7), (85/86), (85/87), (85/88), (85/89), (17/19), (85/98), (86/87), (43/44), (86/89), (43/48), (43/49), (87/88), (87/89), (87/97), (87/98), (88/89), (44/49), (89/91), (89/92), (89/93), (89/94), (89/95), (89/96), (89/97), (89/98), (89/99), (91/92), (91/93), (91/94), (91/95), (91/96), (91/97), (13/14), (91/99), (92/93), (46/47), (92/95), (23/24), (92/97), (46/49), (92/99), (93/94), (93/95), (31/32), (93/97), (93/98), (31/33), (94/95), (47/48), (94/97), (47/49), (94/99), (95/96), (95/97), (95/98), (95/99), (96/97), (48/49), (32/33), (97/98), (97/99), (98/99)]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fractions = pairs.permutation(2).select {|n, d| n.to_i < d.to_i}.to_a\n",
    "fractions = fractions.select {|n, d| n.any? {|nd| d.include?(nd)}}\n",
    "fractions = fractions.map {|n, d| Rational(n.to_i, d.to_i)}\n",
    "fractions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(11/12), (11/13), (11/14), (11/15), (11/16), (11/17), (11/18), (11/19), (11/21), (11/31), (11/41), (11/51), (11/61), (11/71), (11/81), (11/91), (12/13), (6/7), (4/5), (3/4), (12/17), (2/3), (12/19), (4/7), (6/11), (12/23), (1/2), (12/25), (6/13), (4/9), (3/7), (12/29), (12/31), (3/8), (12/41), (2/7), (4/17), (3/13), (12/61), (6/31), (12/71), (1/6), (4/27), (6/41), (12/91), (3/23), (13/14), (13/15), (13/16), (13/17), (13/18), (13/19), (13/21), (13/23), (13/31), (13/32), (13/33), (13/34), (13/35), (13/36), (13/37), (13/38), (1/3), (13/41), (13/43), (13/51), (13/53), (13/61), (13/63), (13/71), (13/73), (13/81), (13/83), (1/7), (13/93), (14/15), (7/8), (14/17), (7/9), (14/19), (2/3), (7/12), (14/31), (7/17), (14/41), (1/3), (14/43), (7/22), (14/45), (7/23), (14/47), (7/24), (2/7), (14/51), (7/27), (14/61), (7/32), (14/71), (7/37), (14/81), (1/6), (2/13), (7/47), (15/16), (15/17), (5/6), (15/19), (5/7), (3/5), (15/31), (3/7), (15/41), (1/3), (5/17), (15/52), (15/53), (5/18), (3/11), (15/56), (5/19), (15/58), (15/59), (15/61), (3/13), (15/71), (1/5), (5/27), (3/17), (15/91), (3/19), (16/17), (8/9), (16/19), (16/21), (8/13), (16/31), (4/9), (16/41), (8/23), (16/51), (2/7), (16/61), (8/31), (16/63), (1/4), (16/65), (8/33), (16/67), (4/17), (16/69), (16/71), (4/19), (16/81), (8/43), (16/91), (1/6), (17/18), (17/19), (17/21), (17/27), (17/31), (17/37), (17/41), (17/47), (1/3), (17/57), (17/61), (17/67), (17/71), (17/72), (17/73), (17/74), (17/75), (17/76), (17/77), (17/78), (17/79), (17/81), (17/87), (17/91), (17/97), (18/19), (6/7), (9/14), (18/31), (9/19), (18/41), (3/8), (6/17), (9/29), (18/61), (9/34), (18/71), (3/13), (2/9), (9/41), (18/83), (3/14), (18/85), (9/43), (6/29), (9/44), (18/89), (18/91), (9/49), (19/21), (19/29), (19/31), (19/39), (19/41), (19/49), (19/51), (19/59), (19/61), (19/69), (19/71), (19/79), (19/81), (19/89), (19/91), (19/92), (19/93), (19/94), (1/5), (19/96), (19/97), (19/98), (19/99), (21/22), (21/23), (7/8), (21/25), (21/26), (7/9), (3/4), (21/29), (21/31), (21/32), (21/41), (1/2), (7/17), (21/52), (21/61), (21/62), (21/71), (7/24), (7/27), (21/82), (3/13), (21/92), (22/23), (11/12), (22/25), (11/13), (22/27), (11/14), (22/29), (11/16), (11/21), (11/26), (11/31), (11/36), (11/41), (11/46), (23/24), (23/25), (23/26), (23/27), (23/28), (23/29), (23/31), (23/32), (23/33), (23/34), (23/35), (23/36), (23/37), (23/38), (23/39), (23/42), (23/43), (23/52), (23/53), (23/62), (23/63), (23/72), (23/73), (23/82), (23/83), (1/4), (23/93), (24/25), (12/13), (8/9), (6/7), (24/29), (3/4), (12/17), (24/41), (4/7), (24/43), (6/11), (8/15), (12/23), (24/47), (1/2), (24/49), (6/13), (4/9), (12/31), (3/8), (1/3), (12/37), (12/41), (2/7), (6/23), (12/47), (25/26), (25/27), (25/28), (25/29), (25/32), (5/7), (25/42), (5/9), (25/51), (25/52), (25/53), (25/54), (5/11), (25/56), (25/57), (25/58), (25/59), (25/62), (5/13), (25/72), (1/3), (25/82), (5/17), (25/92), (5/19), (26/27), (13/14), (26/29), (13/16), (13/18), (13/21), (13/23), (1/2), (13/28), (26/61), (13/31), (26/63), (13/32), (2/5), (13/33), (26/67), (13/34), (26/69), (13/36), (13/38), (13/41), (13/43), (13/46), (13/48), (27/28), (27/29), (27/32), (27/37), (9/14), (27/47), (27/52), (9/19), (27/62), (27/67), (27/71), (3/8), (27/73), (27/74), (9/25), (27/76), (27/77), (9/26), (27/79), (27/82), (9/29), (27/92), (27/97), (28/29), (7/8), (14/19), (2/3), (7/12), (7/13), (14/29), (14/31), (7/17), (7/18), (14/39), (28/81), (14/41), (28/83), (1/3), (28/85), (14/43), (28/87), (7/22), (28/89), (7/23), (2/7), (29/32), (29/39), (29/42), (29/49), (29/52), (29/59), (29/62), (29/69), (29/72), (29/79), (29/82), (29/89), (29/91), (29/92), (29/93), (29/94), (29/95), (29/96), (29/97), (29/98), (29/99), (31/32), (31/33), (31/34), (31/35), (31/36), (31/37), (31/38), (31/39), (31/41), (31/43), (31/51), (31/53), (31/61), (31/63), (31/71), (31/73), (31/81), (31/83), (31/91), (1/3), (32/33), (16/17), (32/35), (8/9), (32/37), (16/19), (32/39), (16/21), (32/43), (8/13), (32/53), (16/31), (32/63), (4/9), (32/73), (16/41), (32/83), (8/23), (32/93), (33/34), (33/35), (11/12), (33/37), (33/38), (11/13), (33/43), (33/53), (11/21), (33/73), (33/83), (11/31), (34/35), (17/18), (34/37), (17/19), (34/39), (34/41), (17/21), (34/43), (17/22), (34/45), (17/23), (34/47), (17/24), (34/49), (34/53), (17/27), (34/63), (17/32), (34/73), (17/37), (34/83), (17/42), (34/93), (17/47), (35/36), (35/37), (35/38), (35/39), (35/43), (7/9), (35/51), (35/52), (35/53), (35/54), (7/11), (5/8), (35/57), (35/58), (35/59), (5/9), (7/13), (35/73), (7/15), (35/83), (7/17), (35/93), (7/19), (36/37), (18/19), (12/13), (36/43), (18/23), (36/53), (9/14), (36/61), (18/31), (4/7), (9/16), (36/65), (6/11), (36/67), (9/17), (12/23), (36/73), (9/19), (36/83), (18/43), (12/31), (3/8), (37/38), (37/39), (37/43), (37/47), (37/53), (37/57), (37/63), (37/67), (37/71), (37/72), (37/73), (1/2), (37/75), (37/76), (37/77), (37/78), (37/79), (37/83), (37/87), (37/93), (37/97), (38/39), (38/43), (19/24), (38/53), (19/29), (38/63), (19/34), (38/73), (19/39), (38/81), (19/41), (38/83), (19/42), (38/85), (19/43), (38/87), (19/44), (38/89), (38/93), (19/49), (39/43), (39/49), (39/53), (39/59), (13/21), (13/23), (39/73), (39/79), (39/83), (39/89), (3/7), (39/92), (13/31), (39/94), (39/95), (13/32), (39/97), (39/98), (13/33), (41/42), (41/43), (41/44), (41/45), (41/46), (41/47), (41/48), (41/49), (41/51), (41/54), (41/61), (41/64), (41/71), (41/74), (41/81), (41/84), (41/91), (41/94), (42/43), (21/22), (14/15), (21/23), (42/47), (7/8), (6/7), (21/26), (7/9), (21/31), (21/32), (7/12), (21/37), (21/41), (1/2), (21/46), (21/47), (43/44), (43/45), (43/46), (43/47), (43/48), (43/49), (43/53), (43/54), (43/63), (43/64), (43/73), (43/74), (43/83), (43/84), (43/93), (43/94), (44/45), (22/23), (44/47), (11/12), (44/49), (22/27), (11/16), (22/37), (11/21), (22/47), (45/46), (45/47), (15/16), (45/49), (15/17), (45/52), (45/53), (5/6), (9/11), (45/56), (15/19), (45/58), (45/59), (45/64), (9/13), (45/74), (3/5), (15/28), (9/17), (45/94), (9/19), (46/47), (23/24), (46/49), (23/27), (23/28), (46/61), (23/31), (46/63), (23/32), (46/65), (23/33), (46/67), (23/34), (2/3), (23/37), (23/38), (23/42), (23/43), (23/47), (23/48), (47/48), (47/49), (47/54), (47/57), (47/64), (47/67), (47/71), (47/72), (47/73), (47/74), (47/75), (47/76), (47/77), (47/78), (47/79), (47/84), (47/87), (1/2), (47/97), (48/49), (8/9), (24/29), (3/4), (12/17), (24/37), (8/13), (16/27), (24/41), (48/83), (4/7), (48/85), (24/43), (16/29), (6/11), (48/89), (24/47), (24/49), (49/54), (49/59), (49/64), (49/69), (49/74), (49/79), (7/12), (49/89), (7/13), (49/92), (49/93), (49/94), (49/95), (49/96), (49/97), (1/2), (49/99), (51/52), (51/53), (17/18), (51/55), (51/56), (17/19), (51/58), (51/59), (51/61), (51/65), (51/71), (17/25), (17/27), (3/5), (51/91), (51/95), (52/53), (26/27), (52/55), (13/14), (52/57), (26/29), (52/59), (26/31), (4/5), (13/18), (52/75), (26/41), (52/85), (13/23), (52/95), (53/54), (53/55), (53/56), (53/57), (53/58), (53/59), (53/63), (53/65), (53/73), (53/75), (53/83), (53/85), (53/93), (53/95), (54/55), (27/28), (18/19), (27/29), (54/59), (27/32), (54/65), (27/37), (18/25), (9/14), (54/85), (27/47), (54/95), (55/56), (55/57), (55/58), (55/59), (11/13), (11/15), (11/17), (11/19), (56/57), (28/29), (56/59), (56/61), (28/31), (8/9), (7/8), (56/65), (28/33), (56/67), (14/17), (56/69), (56/75), (14/19), (56/85), (28/43), (56/95), (7/12), (57/58), (57/59), (57/65), (57/67), (57/71), (19/24), (57/73), (57/74), (19/25), (3/4), (57/77), (19/26), (57/79), (57/85), (19/29), (3/5), (57/97), (58/59), (58/65), (29/34), (58/75), (29/39), (58/81), (29/41), (58/83), (29/42), (58/85), (29/43), (2/3), (29/44), (58/89), (58/95), (29/49), (59/65), (59/69), (59/75), (59/79), (59/85), (59/89), (59/91), (59/92), (59/93), (59/94), (59/95), (59/96), (59/97), (59/98), (59/99), (61/62), (61/63), (61/64), (61/65), (61/66), (61/67), (61/68), (61/69), (61/71), (61/76), (61/81), (61/86), (61/91), (61/96), (62/63), 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(87/88), (87/89), (87/97), (87/98), (88/89), (44/49), (89/91), (89/92), (89/93), (89/94), (89/95), (89/96), (89/97), (89/98), (89/99), (91/92), (91/93), (91/94), (91/95), (91/96), (91/97), (13/14), (91/99), (92/93), (46/47), (92/95), (23/24), (92/97), (46/49), (92/99), (93/94), (93/95), (31/32), (93/97), (93/98), (31/33), (94/95), (47/48), (94/97), (47/49), (94/99), (95/96), (95/97), (95/98), (95/99), (96/97), (48/49), (32/33), (97/98), (97/99), (98/99)]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fractions = pairs.permutation(2).select {|n, d| n.to_i < d.to_i}.to_a\n",
    "fractions = fractions.select {|n, d| n.any? {|nd| d.include?(nd)}}\n",
    "fractions = fractions.map {|f| f.to_r}\n",
    "fractions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[1, 1] - [1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[2], [2, 3]]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "li = [2,3]\n",
    "small = li.dup\n",
    "small.delete_at(small.index(3) || small.length)\n",
    "[small, li]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1], [1, 1]]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "li = [1, 1]\n",
    "small = li.dup\n",
    "small.delete_at(small.index(1) || small.length)\n",
    "[small, li]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":remove_common"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def remove_common(f)\n",
    "  n, d = f\n",
    "  pairs = []\n",
    "  n.each do |digit|\n",
    "    if d.include?(digit)\n",
    "      n2 = n.dup\n",
    "      n2.delete_at(n2.index(digit) || n2.length)\n",
    "      d2 = d.dup\n",
    "      d2.delete_at(d2.index(digit) || d2.length)\n",
    "      pairs << [n2, d2]\n",
    "    end\n",
    "  end\n",
    "  pairs\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[[2], [3]], [[2], [3]]]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "remove_common([[2, 2], [2, 3]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(2/3), (2/3)]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "remove_common([[2, 2], [2, 3]]).map {|f| f.to_r}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       ":curious"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def curious(f)\n",
    "  full = f.to_r\n",
    "  remove_common(f).any? {|f2| f2.to_r == full}\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[[1, 6], [6, 4]], [[1, 9], [9, 5]], [[2, 6], [6, 5]], [[4, 9], [9, 8]]]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fractions = pairs.permutation(2).select {|n, d| n.to_i < d.to_i}.to_a\n",
    "fractions = fractions.select {|n, d| n.any? {|nd| d.include?(nd)}}\n",
    "curious_fractions = fractions.select {|f| curious f}\n",
    "curious_fractions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1/100)"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fractions = pairs.permutation(2).select {|n, d| n.to_i < d.to_i}.to_a\n",
    "fractions = fractions.select {|n, d| n.any? {|nd| d.include?(nd)}}\n",
    "curious_fractions = fractions.select {|f| curious f}.map {|f| f.to_r}\n",
    "curious_fractions.reduce(:*)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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   "mimetype": "application/x-ruby",
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