Enigma 1477 - In transit
Chappy
New Scientist magazine, 19 January 2008.
by Susan Denham.
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.
Ciao,
Chappy.
Richard Heathfield
matter. In my working (puzzle text is spoiler), the misreading is made
evident via a note, and my "with one bound he was free" deduction is made
clear at the end.
Chappy said:
The possible waits are:
08:00 - 08:45 (45 minutes)
08:00 - 08:55 (55 minutes)
08:00 - 09:10 (70 minutes)
08:10 - 08:45 (35 minutes)
08:10 - 08:55 (45 minutes)
08:10 - 09:10 (60 minutes)
08:15 - 08:45 (30 minutes)
08:15 - 08:55 (40 minutes)
08:15 - 09:10 (55 minutes)
Mr Apex waited either 45, 55, or 70 minutes.
Mrs Apex waited either 45, 55, or 70 minutes.
Mr Club waited either 35, 45, or 60 minutes.
Mrs Club waited either 35, 45, or 60 minutes.
Mr Economy waited either 30, 40, or 55 minutes.
Mrs Economy waited either 30, 40, or 55 minutes.
We will call the three departing flights X, Y, Z (in that departure order).
Fantasy: Mr A waits 45 minutes for X. Then:
Fantasy: Mrs A waits 55 minutes for Y. Then:
Mr C waits 60 minutes for Y.
Mrs C waits 35 minutes for X.
Mr E waits 40 minutes for Y. Contradiction (three passengers for Y,
and indeed three for X when we add in Mrs E, but none for Z).
Fantasy: Mr A waits 45 minutes for X. Then:
Fantasy: Mrs A waits 70 minutes for Z. Then:
Mr C waits 60 minutes for Z.
Mrs C waits 35 minutes for X.
Mr E waits either 40 minutes for Y or 55 minutes for Z.
Mrs E waits either 30 minutes for X or 40 minutes for Y.
To avoid three passengers for X, Mrs E has to wait
40 minutes for Y, which means Mr E has to wait 55 minutes
for Z (because he must have a longer wait than his wife,
as Mr A has a shorter wait than /his/ wife). But this gives
three passengers for Z!
[NOTE: AT THIS POINT, IT IS CLEAR THAT, WHERE THE PUZZLE TEXT READS "more
than one husband having a shorter wait than his wife.", I'VE MISREAD
"SHORTER" AS "LONGER"! Bearing this in mind, we continue with the
erroneous reasoning...]
So it is now clear that Mr A cannot be the man who leaves on flight X.
Therefore, either Mr C or Mr E departed on Flight X and therefore had a
shorter wait than their wife, so Mr A must have had a longer wait than his
wife.
Fantasy: Mr A waits 55 minutes for Y. Then:
Mrs A waits 45 minutes for X.
Mr E and Mrs E had waits of 30 and 40 minutes for flights X and Y.
Mr C and Mrs C must both be on Z, making their waiting times the
same - a contradiction.
So we now know that Mr A waited 70 minutes for flight Z (because he didn't
wait 45 minutes for X or 55 minutes for Y).
Fantasy: Mr A is joined by Mrs E, who waits 55 minutes to join him on Z.
Then:
Mrs A waits 45 minutes for X.
Mr and Mrs C wait 35 and 60 minutes (in some order) because their
45 option is taken by Mrs A. So they are catching X and Z, which
means Z has too many passengers.
We deduce that Mr A must be joined by Mrs C on Flight Z (for which she
waits 60 minutes).
Summary of facts known so far:
Mr A waits 70 minutes for Flight Z.
Mrs C waits 60 minutes for Flight Z.
Mrs C waits longer than Mr C, so she is the long-suffering wife, and Mrs A
and Mrs E are the short-suffering wives.
Mr E can't be catching Flight Z, but he must out-wait his wife, so he must
be catching Flight Y after a wait of 40 minutes, and Mrs E is on Flight X.
This leaves Mrs A and Mr C. Z is full, so they must be catching X and Y in
some order. That puts Mr C on Flight X and Mrs A on Flight Y.
Passenger Wait time Departing at
Mr Apex 70 minutes 09:10 (Flight Z)
Mrs Apex 55 minutes 08:55 (Flight Y)
Mr Club 35 minutes 08:45 (Flight X)
Mrs Club 60 minutes 09:10 (Flight Z)
Mr Economy 40 minutes 08:55 (Flight Y)
Mrs Economy 30 minutes 08:45 (Flight X)
Condition checks:
"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." Flight X: MR C, MRS E. Flight Y: MR E, MRS A. Flight Z: MR A, MRS
C. Check.
"All six people had a different length of time between landing and
departing," 70, 55, 35, 60, 40, 30: Check.
"with more than one husband having a shorter wait than his wife." Mr A wait
exceeds Mrs A wait. Mr E wait exceeds Mrs E wait. POW! We discover the
error.
And now there's a lovely little escape hatch through which I can jump (and
which is no doubt very obvious to everyone else, but I was delighted to
discover it, as it saved me a lot of re-work). Clearly, if more than one
husband has a shorter wait than his wife, it must mean that more than one
wife had a longer wait than her husband. So all I have to do to make my
*reasoning* work correctly is to swap the Mr's and Mrs's around. And in
fact the solution I've got, although incorrect, is only incorrect insofar
as the titles are the wrong way round, which is easily fixed.
And so the *real* solution is:
Mr Economy (30 minutes), Mrs Club (35), Mrs Economy (40), Mr Apex (55), Mr
Club (60), Mrs Apex (70).
--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999
Ed Murphy
The possible durations are as follows:
45 55 70 <- arrived at 8:00
35 45 60 <- arrived at 8:10
30 40 55 <- arrived at 8:15
^^ departed at 8:45
^^ departed at 8:55
^^ departed at 9:10
Of these, we must omit one of the 45's, one of the 55's, and one
other, while leaving two entries in each row and column. We can't
leave out the top middle 55 in conjunction with either 45, so we
must leave out the lower right 55. Omitting either 45 then forces
us to omit the other 45 as well, so the following durations remain:
55 70
35 60
30 40
Whatever 30's gender is, 40 is opposite, 55 is same, 70 is opposite,
60 is same, 35 is opposite. This gives two possibilities, one of
which violates the "more than one husband having a shorter wait than
his wife" condition. Thus, the solution is:
30 = Mrs. Economy
35 = Mr. Club
40 = Mr. Economy
55 = Mrs. Apex
60 = Mrs. Club
70 = Mr. Apex
Topi Linkala
Impossible. At Gatwick from landing to gate takes more than hour. So
even if you landed 08:00 you cannot make 09:10 flight. ;-)
Topi
--
"The whole problem with the world is that fools and fanatics are
always so certain of themselves, but wiser people so full of doubts."
- Bertrand Russell
"How come he didn't put 'I think' at the end of it?" - Anonymous
Jeffrey Turner
Not up to its usual standards - I got it.
Mr. E 30 min
Mrs. C 35 min
Mrs. E 40 min
Mr. A 55 min
Mr. C 60 min
Mrs. A 70 min
Amazingly ;) neither of the available 45 minute layovers was
"used."
--Jeff
--
"The power of the Executive to cast a man into prison without
formulating any charge known to the law, and particularly to
deny him the judgment of his peers, is in the highest degree
odious and is the foundation of all totalitarian government
whether Nazi or Communist."
- Winston Churchill, Nov. 21, 1943
Chappy
This only has 1 husband (Mr. C) having a shorter wait than his wife,
but the correct solution is obtain simply by switching all the sexes.
Ciao,
Chappy.
Derek Holt
Well, I guess now you mention it, there is nothing in the puzzle
statement that prohibits any of them having sex-change operations
while in transit!
Derek Holt.