Brain Teaser No 3

Many thanks Adam,

I couldn't find it even with the search function and thought it had simply disappeared into the ether.

As you can see, Alex needs to close out his battlefield teaser - Alex??

Cheer and many thanks

Don

quote:

Originally posted by Don Atkinson:
I couldn't find it even with the search function

I searched under your "recent posts" - although No 3 threw me.

Don,

The battlefield task, now I see. Yes, well, the challenge was made simple to make it open to everyone. With a free history lesson thrown in. Your answer is of course correct.

A new question could be: think up 5 possible different meanings of "admin bump"

Alexander

quote:

A new question could be: think up 5 possible different meanings of "admin bump"

Far too difficult............

Try this one instead -

I have a large caraffe containing 500ml of red wine and an other containing 500ml of water. I transfer 150ml of wine into the water and stir, then transfer 150ml of the mixture back to the red wine caraffe and stir.

Is there now more water in the wine caraffe or more wine in the water caraffe?

cheers

Don

Water into wine

I think each container has the same proportion of the "other" liquid - ie the wine container has approx 23% water, and the water container has approx 23% wine.

Steve D

quote:

I think each container has the same proportion of the "other" liquid

Spot-on Steve, well done.

So, how many times would you have to repeat this excercise (150ml transfer from one to the other and back) before the percentage of wine in water was the same in each caraffe?

Cheers

Don

For practical purposes, the mixture tends towards 50/50 after around 20 or so transfers (measuring to 4 dp).
For mathematical purposes, I suspect the answer is that it would take an infinite number of transfers of 150ml (or any other value less than 500ml for that matter)to get an exact 50/50 mix.
The only way to get a 50/50 mix would be to pour all the contents of one container into the other on the first transfer.

Steve D

I suspect this has been done here already. In any case to actually calculate this seems, hm, almost indecent.

Step 1: after you have moved a quantity of mixture from left to right and the same quantity back, you have equal quantities. So the 'wine' caraffe , size C, will have C/2 + X amount of wine and less, C/2-X, amount of water while the other caraffe will have C/2-X wine + C/2+X water. The size of the vessel/glass/spoon doesn't matter. It doesn't even matter if the mixture is homogeneous. The experiment can be done with oil and vinegar.

Step 2: here it's necessary to stir well to have a perfect mixture. If the wine caraffe at any stage has C/2 + X wine , C/2-X water and you add a glass from the other caraffe with whatever quantity small c less than a full caraffe, then the amount of water added is c/2+x, with small x always smaller than large X to respect the ratio c/C. Because x is smaller than X the wine caraffe can never reach the 50/50 ratio for wine/water.

Admin bump, meaning 1: the bulge where cables pass under the carpet, that you keep stumbling over when you pass the server room on your way to get some coffee.

Steve, Alex,

Nice explanations and, of course, absolutely right answers.

Cheers

Don

Admin bump(2):Large coffee stain on a shirt.

Admin bump(3): analogous to a speed bump, an 'admin bump' is a worthless piece of beaurocracy which slows progress to an irritating crawl.

Just to avoid the need for Admin bump (4)....

Using four fours, and mathematical symbols, can you write an expression for each of the numbers 1 to 100 ?

For example 2 = (4/4) + (4/4)

Ok, just to keep it within the bounds of practicality, try an expression for the number 13 for starters.

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.

Also the usual symbol for sqrt is acceptable, even though there is an implied figure of 2

And 4.4 is acceptable (four point four) even though there is an implied 10 (the number base)

Cheers

Don

44/4 + sqrt(4) = 13

1=(4+4)/(4+4)
3 = (4+4+4)/4
4 = (4+4)*sqrt(4)/4
5 = (4*4 +4)/4
6 = 4+sqrt(4) +4 -4 ( a cheap trick!)
7 = 4+sqrt(4) +4/4
8= 4*4*sqrt(4)/4
9 = 4+4 + 4/4
10 = 4+4+( 4/sqrt(4))
11 = 44 /sqrt(4) / sqrt(4)
12 = 4*4 -sqrt(4)- sqrt(4)
13 = 44/4 +sqrt(4)
14 = 4+4+4+ sqrt(4)
15 = 4*4 - 4/4
16 = 4+4+4+4
17 = 4*4 + 4/4



This could get compulsive....
Ian

Admin bump (fore): golf term. A mound in the rough which has as its main purpose to hide a shack from view that's used by technical personnel.

18= 4*sqrt(4)*sqrt(4)+sqrt(4).

19= 4! - 4 - 4/4 ...

Are factorials allowed ? (says Ian who hadn't thought of it )


20 = 4* ( 4 + 4/4)
21 = ( 44 - sqrt(4) ) /sqrt(4)
22 = 4! - (4+4)/4

quote:

Are factorials allowed ?

Yes !!!!

And one aspect of brain teasers is that lots of people see an answer and say "doh!....I hadn't thought of that!!!!"

Cheers

Don

okay then...
23 = (atoi (strcat (itoa (fix (sqrt 4))) (itoa (fix (- 4 (/ 4 4))))))

(ducks)

must be at least one ; missing

24 = 4*(4+4/sqrt(4))

Alex,

String theory, as Acad will confirm, is not allowed - there is no shred of evidence that it works..............

....or have I misunderstood your use of strings .....he he

Cheers

Don

25 = 4! + ((4/4)4) NB the last 4 means the fourth power

Steve D

Of course it's valid Don, trust me I'm doing little more than concatenating "2" and "3" into string "23" and converting it to an integer.
Any language can handle that.

26 = 44/sqrt(4)+4

Actually this stuff could be good inocculation for people who believe in numerology.

One can always hope.

27 = 4! + 4 - 4/4

what is " 4! " ?

...... other than 24........