# Enigmatic Code

Programming Enigma Puzzles

## Enigma 1477: In transit

From New Scientist #2639, 19th January 2008

Six air travellers had to change planes at Gatwick airport. Mr and Mrs Apex landed at 08:00, Mr and Mrs Club landed at 08:10 and Mr and Mrs Economy landed at 08:15.

Then, one of the men and one of the women departed at 08:45, another man and woman departed at 8:55 and the remaining man and woman departed at 09:10.

All six people had a different length of time between landing and departing, with more than one husband having a shorter wait than his wife.

List the six names in increasing order of the time they spent waiting between landing and departing.

[enigma1477]

### One response to “Enigma 1477: In transit”

1. Jim Randell 3 December 2012 at 9:59 pm

The following Python program runs in 35ms.

```from itertools import permutations, product
from enigma import sprintf

# consider the departure times
# the different times are distributed amongst each gender group
for (th, tw) in product(permutations((45, 55, 70)), repeat=2):
# compute the waiting times
(Ah, Aw) = (th[0], tw[0])
(Ch, Cw) = (th[1] - 10, tw[1] - 10)
(Eh, Ew) = (th[2] - 15, tw[2] - 15)
# all waiting times are different
if len(set((Ah, Aw, Ch, Cw, Eh, Ew))) != 6: continue
# husbands that wait shorter than their wives
hs = list((h, w) for (h, w) in ((Ah, Aw), (Ch, Cw), (Eh, Ew)) if h < w)
if len(hs) < 2: continue
# output the result
r = list(sorted(zip((Ah, Aw, Ch, Cw, Eh, Ew), product("ACE", ("Mr", "Mrs")))))
print(', '.join(sprintf("{w}m: {p[1]} {p[0]}") for (w, p) in r))
```

Solution: The travellers in order of waiting time (from shortest wait to longest) are: Mr Economy, Mrs Club, Mrs Economy, Mr Apex, Mr Club, Mrs Apex.

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