!Fred v.Q7a dp-j 29Oct95 3PM

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 Subject:- Chris's ANSWER ref. 8BS-45


  * * LIGHT ENTERTAINMENT * *
  * * LIGHT ENTERTAINMENT * *

 Well really Chris! I ran ANSWER, got
 bored, made a coffee, thought about 
the problem, wrote the program, went back
 to the Master and STILL had to wait 
for it to finish. I do hope your ambulance
 has a better algorithm under the bonnet
 or it's in for a 'stiff' dose of Brady-
 Cardia. OK, OK, so that's my copy of
 8BS-46 up the spout. (That's true -Ed.)

 * * IN THE DARK * *

 The problem posed gives two equations
 as follows :-

  a)   m + w + c = 100
 and  b)  10m + .5w + .125c = 100

 Two equations and three unknowns: m, w
 and c (the number of men, women and
 children respectively). So algebra is
 out, well nearly, and it's back to
 trial and error.
 The most obvious points are :-

 1)  m has to be <10 (To leave
 some cash for the others)

 2) Even if there ain't any
 children, with m=5 it would
 need 100 women to make up
 the `100 total, and that's
 already too many people (105) So m>5.

 3)  c must be a multiple of 4
 as the total amount for the
 children must be a multiple
 of 50p else it would be
 impossible to end up with
 `100 exactly.

 4)  c cannot be >96 (Too many
 people for `100 total).

 We could refine the possible range of
 values still further but the algorithm
 for computer solution is so simple that
 it can be counter productive to
 introduce further conditions. The
 listing is a nested FOR/NEXT loop :-

F.c=4TO96S.4:F.m=6TO9:IF10*m+.5*(100-m-c)
+.125*c=100 P.'m" men"'100-m-c" women"'c"
 children" ELSE N.:N.

 Yes that's it!  A one-liner.


 * * THE SWITCH ON * *

 Start the ambulance Chris and forget
 the de-caffeinated. No time to hang
 about. 100 TachyCardias on the way;
 a `10 tip from the men, 50p from.......
To see the answer:-
 …Press Q/q and…COPY <Return> the above
 one-liner now,
 then …Press f0 to return to this text.


 * * SEARCH LIGHTS * *

 OK Chris? You also asked if there was
 a way of finding other variations.
 Just run the one-liner as above with
 the =100 changed to =101.5 or whatever.
 Also change the 10*m to 8*m (`8 each),
 and/or the .50*(100-m-c) to say :-
 .75*(100-m-c) to give 75p to the women.
 Change this 100 to say 85 for fewer
 people in total... etc, etc. You may
 or may not get an answer. If not you may
 have to change the FOR loop limits or
 STEP value to accord with the numbers
 that you select, as I did at the start.
 Or maybe you found an impossible one!
 (Some values may of course make it
 tedious to solve by hand, see PENCIL
 TORCH below).

 Press…Q/q and…COPY the one-liner again
  but type a line number first, say 10.
 The program will now stay permanently
 in memory so you can then…RUN, LIST etc
 and play around with the variables.
…f0 to get back to text, or…f5 after a
 mode change.


 * * SEEN THE LIGHT? * *

 Anyone spot the lulu? What about the
 ELSE in the one-liner? It means the
 search stops as soon as an answer is
 found. Maybe there is more than one
 answer?
 To find out remove ELSE and write it
 in normal Basic line format.(The one-liner
 will not perform without the ELSE ).
 Think about it!

Try this:-

 10V.14
 20F.c=4TO96S.4:F.m=6TO11
 30x=10*m+.5*(100-m-c)+.125*c
 40IFx>=100 AND x<=120 P.'m" men, ";100-m-c"
 women, ";c" children = ` ";x
 50N.:N.:V.15

 This gives all the solutions for total
 sums of money from `100 to `120.
 Note the wider m range, 6-11, and when
 it's run notice the negative women!
 Nothing unusual about that. Mathematics
 is never wrong, just canny. At least I
 can imagine two universes, one full of
 positive women, the other with negative
 ones. You chance your luck by falling
 through the 'The Black Hole' megapub.
 Could make an arcade game!

 …Q/q, (NEW), COPY program, RUN etc.
 then…f0 to return here.
 or…f5 after a mode change.


 Bet you're sorry you asked. Best get
 on to the game.  OVER TO YOU.


 * * PENCIL TORCH * *

 Forget the computer. Take a look at
 this nearly-algebra I mentioned at
 the start of this lot. Multiply equation
 a) by 10 :-

  10m + 10w + 10c = 1000
 and subtract equation b)
  10m + .5w + .125c = 100
 We get:-  9.5w + 9.875c = 900

 By sheer good fortune this tells us
 that w and c must be numerically nearly
 the same value since their coefficients
 9.5 and 9.875 are similar. Their mean
 value will be roughly 900/(9.5+9.875) = 46.45
 Now the guessing:-
 Say c=44 (nearest multiple of 4 to 46.45 )
 and w=47 (a bit bigger) to give mean value
 = (44+47)/2=45.5. A bit low perhaps but carry 
on.
 check 9.5*47 + 9.875*44 = 881
 No joy, should be 900.
 Try c=44 w=49 Mean =46.5, that's better
 check 9.5*49 + 9.875*44 = 900
  Voila, j'ai got eet!

So the answer is c=44 w=49
   m=(100-44-49)=7.

 Now to be rigorous (mortis, already?)
 we should also do a few checks with c
 a bit bigger (=48) than w, to make sure
 there isn't another solution to this
 equation. But I'll leave that to you.

 Lemma. If I've convinced you that for
 overall speed and simplicity you don't
 need to bother with that computer .....
 donations gratefully accepted.


 * * MOON SHINE * *

 I wonder why our schools do all that
 Shakespeare crap? Big deal; so '......
 Birnam wood do come to Dunsinane.'?
 Very inane. Typical lefty trick to
 confuse the ambulance drivers and put
 the Health Service in schtuck, if you
 ask me.

 And he was useless with Assembler did
 you know? The fool couldn't think in a
 straight line and you should see his
 algorithms, all out of step with his
 metre;ruddy Euro nonsense, obviously
 he started it all. Give him 25.4mm and
 he  was kilometre-ing through Agincourt,
 and flogging our lamb up a Venetian
 canal in dollops of 0.4535924 kg to
 some damn Shylock.

 And all that depraved bit about Pistol
 loading his revolver. We can well do
 without the sex stuff. Oh, excuse me,
 here's the Avon lady...... Where was I?
 Ahem, yes. Our educationalists should
 tailor the curriculum to concise
 logical thought disciplines and away
 with all the arty crafty, irrational,
 bow-legged deviousness.

 Or as Shakespeare himself, on finally
 seeing the light, said, albeit rather
 circuitously as usual,

 What manner of man be this
 Whose orbs do hang in parenthesis?

 thus clearly dangling a testimonial to
 the supremacy of the sciences.
 In view of this celebrated admission I
  challenge our Education Minister to
ˆ illuminate‰ her own viewpoint.