Brain Teaser No 3
Posted by: Don Atkinson on 11 March 2007
I know I started Brain Teaser No 1 about 5 years ago. ISTR another with No 2 in the title, so hopefully this is not duplicating somebody elses Brain Teaser No 3.....
Flight Around the World
A group of aeroplanes is based on a small island. Each plane holds just enough fuel to take it half way around the world. Any amount of fuel can be transfered from the tank of one aeroplane to another aeroplane whilst the planes are in flight. The ONLY source of fuel available to these aeroplanes is on this small island. Assume that there is no time lost when refueling, either in the air or on the ground.
What is the smallest number of aeroplanes required to ensure the flight of one aeroplane around the world on a great circle, assuming that all areoplanes have the same constant groundspeed and rate of fuel consumption and that all aeroplanes return safely to their island base.
Cheers
Don
Posted on: 23 August 2007 by PJT
quote:
Originally posted by long-time-dead:
what is " 4! " ?
...... other than 24........
4! = (4*3*2*1)
5! = (5*4*3*2*1)
and so on ad nauseum...
Posted on: 24 August 2007 by Don Atkinson
quote:
what is " 4! " ?
...... other than 24........
I think 4! is mathematically unique. (well, no more unique than 5! or 6! etc).
It conveys information in a more user-friendly way than "24"
And since the rules of this particular game don't allow anything other than four 4s plus any selection of the usual mathematical symbols, it is a neat way of writing "24" within the rules of the game. Bit like "sqrt 4" (=2) or 4^sqrt4 (=16)etc, etc
= mildly entertaining (for some)or totallly pathetic for others........
Cheers
Don
Posted on: 24 August 2007 by Don Atkinson
Just to illustrate the further usefulness of 4!
28 = ((4! x 4)/4) + 4
29 = 4! + 4 + 4/4
and one that doesn't need 4!
30 = (4 x 4 x sqrt4) - sqrt4
Cheers
Don
Posted on: 24 August 2007 by Ian G.
31 = 4! + (4!+4)/4
Posted on: 24 August 2007 by Alexander
Right, so introducing the windows calculator symbols(view mode "sign-tifik")
there are the little hats for "by the power of" and buttons that have 'int' and 'ln' and 'log'.
Int is for rounding off downward a number to an integer.
There is no need to know what ln and log are, but it's similar.
32= int(log(4!!))+ int(ln(4 ^ 4)) + 4
A Little Shop of Horrors
Posted on: 24 August 2007 by Don Atkinson
quote:
There is no need to know what ln and log are, but it's similar
For those who never did logs at school.....
ln is the natural log of a number and
log is log base 10 of a number
useful when making slide-rules etc
in Excel 4!! can be written as "fact(fact(4))" and you should get the right answer.
Of course I'm sure there are less elegant ways of generating 32...........
Cheers
Don
Posted on: 25 August 2007 by Alexander
quote:
Originally posted by Don Atkinson:
Of course I'm sure there are less elegant ways of generating 32...........
Don
That would a nice challenge indeed
I even have some ideas about how to do it. But you'll be spared further monstrosities because I'll be away for a week...
Alexander
Posted on: 25 August 2007 by Ian G.
Notation warning: n!! is different from (n!)!
n!! = n(n-2)(n-4) .... ending in either 1 or 2.
So 4!! = 8 whereas (4!)! = 24! , a huge number.
See here for more examples So how about
32 =4!! + 4!! + 4!! +4!!
Ian
!
Posted on: 25 August 2007 by Don Atkinson
quote:
whereas (4!)! = 24! , a huge number
I think Alex (and certainly me) were working on the basis of (4!)! because a huge number is required.
Thanks for the notation warning,,,,we learn something new every day!!
Cheers
Don
Posted on: 06 September 2007 by Alexander
33 = 4!+ 4!!+ 4/4 = int(ln (4!))* 44/4
Posted on: 07 September 2007 by steved
34 = 4(4+4)+sqrt(4)
Steve D
Posted on: 07 September 2007 by steved
This had me stumped for a while
35=(4^4 + 4!)/4!!
Steve D
Posted on: 07 September 2007 by Ian G.
36= 44-4-4
Posted on: 09 September 2007 by Don Atkinson
37 = ????
I'm afraid I resorted to my expression representing four ninths on this one.
quote:
And for later, there is an accepted expression for 4/9 (ie four ninths) which is .4 (with a further dot on top of the four) representing 0.444444.... ie 4/9.
But I'm sure there must be less elegant ways.....and probably far more simple ways.
Cheers
Don
Posted on: 09 September 2007 by Alexander
37=4^4-4!- int(ln(4!))
but it's a bit of a defeat when having to resort to rounding off numbers.
Posted on: 09 September 2007 by Don Atkinson
quote:
but it's a bit of a defeat when having to resort to rounding off numbers.
37 = ((4x4)+.4[with a further dot on top of the four])/.4[with a further dot on top of the four]
in other words (for clarity)
((four times four) plus four-ninths) all divided by four-ninths
Cheers
Don
Posted on: 12 September 2007 by Alexander
38=4*4+ 4!-sqrt(4)
Posted on: 16 September 2007 by Don Atkinson
39 = (4*4 -.4)/.4 (and hence its pretty obvious how I would generate 41)
Cheers
Don
Posted on: 24 September 2007 by Matthew T
40 = 4! * sqrt4 - 4 - 4
41 = (4!!)!/(4!!)!! - 4!! ^ (sqrt4)
Posted on: 24 September 2007 by Matthew T
Are we allowed to use multifactorials, such tirple or quadruple factorials? Might avoid the dubious 0.44444...
Matthew
Posted on: 27 September 2007 by Alexander
quote:
Originally posted by Matthew T:
Are we allowed to use multifactorials, such tirple or quadruple factorials? Might avoid the dubious 0.44444...
Matthew
Allowed... what about a guideline that you aim for a simple formula, but resort to dirty tricks if you don't see another way out.
4^4 -4! +sqrt(4)=42
44 - 4/4 = 43
44-4+4 =44
44+4/4=45
cheers.
Posted on: 27 September 2007 by Alexander
4! *sqrt(4) - sqrt(4) =46
Posted on: 27 September 2007 by Alexander
4! * sqrt(4) -4/4 =47
4! * sqrt(4) -4 +4 =48
4! * sqrt(4) +4/4 =49
4! * sqrt(4) +4/sqrt(4) =50
Posted on: 27 September 2007 by Don Atkinson
.....and just to upset Matthew with another (dubious) .444444
51 = 4! * sqrt(4) + sqrt(4/.4[with a dot above it])
Cheers
Don
Posted on: 28 September 2007 by steved
52 = (4! x sqrt(4)) + Sqrt(4) + sqrt(4)
53 = 44 + sqrt(4/.4[with a dot above it])
54 = (4! x sqrt(4)) + 4 + Sqrt(4)
55 = 44/(.4 x sqrt(4))
Steve D
