Home > Python > Car Talk Puzzler #4: Flipping Ages

Car Talk Puzzler #4: Flipping Ages


RAY: This was sent in many weeks ago by Wendy Gladstone, and as usual I tweaked it a little bit.

She writes: “Recently I had a visit with my mom and we realized that the two digits that make up my age when reversed resulted in her age. For example, if she’s 73, I’m 37. We wondered how often this has happened over the years but we got sidetracked with other topics and we never came up with an answer.

“When I got home I figured out that the digits of our ages have been reversible six times so far. I also figured out that if we’re lucky it would happen again in a few years, and if we’re really lucky it would happen one more time after that. In other words, it would have happened 8 times over all. So the question is, how old am I now?”

Question
Answer

Here’s the fourth in my Car Talk Puzzler series; today I’m going to be using Python because it’s my current favorite language, and because it’s well suited to filtering, mapping, etc.  I won’t put too much commentary here.

#  Find all the ages such that the second age is the reverse of the first  age.  Don't worry that there are a lot of impossibilities; we'll fix it  through filtering
# Note that [::-1] is the slice operator that says iterate backwards through the string; this effectively reverses the list.
 matching_ages = map(lambda x:(x, int(str(x)[::-1])), range(0,100))
 matching_ages
 # OUT: [(0, 0), (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (7, 7),  (8, 8), (9, 9), (10, 1), (11, 11), (12, 21), (13, 31), (14, 41), (15,  51), (16, 61), (17, 71), (18, 81), (19, 91), (20, 2), (21, 12), (22,  22), (23, 32), (24, 42), (25, 52), (26, 62), (27, 72), (28, 82), (29,  92), (30, 3), (31, 13), (32, 23), (33, 33), (34, 43), (35, 53), (36,  63), (37, 73), (38, 83), (39, 93), (40, 4), (41, 14), (42, 24), (43,  34), (44, 44), (45, 54), (46, 64), (47, 74), (48, 84), (49, 94), (50,  5), (51, 15), (52, 25), (53, 35), (54, 45), (55, 55), (56, 65), (57,  75), (58, 85), (59, 95), (60, 6), (61, 16), (62, 26), (63, 36), (64,  46), (65, 56), (66, 66), (67, 76), (68, 86), (69, 96), (70, 7), (71,  17), (72, 27), (73, 37), (74, 47), (75, 57), (76, 67), (77, 77), (78,  87), (79, 97), (80, 8), (81, 18), (82, 28), (83, 38), (84, 48), (85,  58), (86, 68), (87, 78), (88, 88), (89, 98), (90, 9), (91, 19), (92,  29), (93, 39), (94, 49), (95, 59), (96, 69), (97, 79), (98, 89), (99,  99)]

# Here we filter by only allowing matches in which the  mother's age is greater than that of the child.  Note the use of a  lambda expression, basically an anonymous function.
filtered1 = filter(lambda (mother,child):mother > child, matching_ages)
 filtered1
 # OUT: [(10, 1), (20, 2), (21, 12), (30, 3), (31, 13), (32, 23), (40,  4), (41, 14), (42, 24), (43, 34), (50, 5), (51, 15), (52, 25), (53, 35),  (54, 45), (60, 6), (61, 16), (62, 26), (63, 36), (64, 46), (65, 56),  (70, 7), (71, 17), (72, 27), (73, 37), (74, 47), (75, 57), (76, 67),  (80, 8), (81, 18), (82, 28), (83, 38), (84, 48), (85, 58), (86, 68),  (87, 78), (90, 9), (91, 19), (92, 29), (93, 39), (94, 49), (95, 59),  (96, 69), (97, 79), (98, 89)]

# Assume that the mother was at least 15 when she had the kid, and no more than 60
filtered2 = filter(lambda(mother, child):mother-child >= 15 and mother-child < 60, filtered1)
 filtered2
 # OUT: [(20, 2), (30, 3), (31, 13), (40, 4), (41, 14), (42, 24), (50,  5), (51, 15), (52, 25), (53, 35), (60, 6), (61, 16), (62, 26), (63, 36),  (64, 46), (71, 17), (72, 27), (73, 37), (74, 47), (75, 57), (82, 28),  (83, 38), (84, 48), (85, 58), (86, 68), (93, 39), (94, 49), (95, 59),  (96, 69), (97, 79)]
 len(filtered2)
 # OUT: 30

# Create a new list comprised of the differences in age between mother and child
 age_diff = map(lambda(mother,child):mother-child, filtered2)
 age_diff
 # OUT: [18, 27, 18, 36, 27, 18, 45, 36, 27, 18, 54, 45, 36, 27, 18, 54, 45, 36, 27, 18, 54, 45, 36, 27, 18]
 sorted(age_diff)
 # OUT: [18, 18, 18, 18, 18, 18, 18, 27, 27, 27, 27, 27, 27, 36, 36, 36, 36, 36, 45, 45, 45, 45, 54, 54, 54]

# The puzzler states that it's will happen a total of 8 times; that matches the age difference of 18 years

 filter(lambda(mother,child):mother-child == 18, filtered3)
# OUT: [(20, 2), (31, 13), (42, 24), (53, 35), (64, 46), (75, 57), (86, 68), (97, 79)]

Thus the mother is currently 75 years old and the daughter is 57.  Tada

 

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