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Pantomime
Posted: Tuesday, March 1, 2011 11:35:44 AM

Rank: Advanced Member

Joined: 2/25/2011
Posts: 81
Neurons: 236
Location: France
Okay,here's a little game for you people of the world.Whistle

We consider a guy driving a boat ( engined ). He first leaves the coast and passes a first buoy that indicates as distance a two digits number such as AB. Then he goes on and passes a second buoy that indicates the number of the first buoy put the other way around. He finally passes the third buoy that indicates a 3 digits number such as A0(zero )B ( the first and third digits respectively being the first and second digits of the first buoy).
As from the first buoy he goes at a constant speed.
What numbers do the buoys indicate and at what speed is he going as from the first buoy ?Brick wall


*No formulae are required. Brute force logic is sufficient.
*You do not care at what speed he was going before the first buoy, the situation is to be considered as from the first buoy.


Poor skeleton couldn't attend the ball, he had no body to go with.
Pantomime
Posted: Wednesday, March 2, 2011 7:25:18 AM

Rank: Advanced Member

Joined: 2/25/2011
Posts: 81
Neurons: 236
Location: France
Any takers ?

I'm surprised Thar has not found out yet Angel

Poor skeleton couldn't attend the ball, he had no body to go with.
DeepBlueSea
Posted: Friday, March 4, 2011 4:59:12 PM
Rank: Newbie

Joined: 3/4/2011
Posts: 7
Neurons: 32,547
AB is 16.
BA is 61. The difference between them is 45.
Adding another 45 to 61 gives A0B which is 106 :)

Good question Applause
Pantomime
Posted: Saturday, March 5, 2011 12:37:02 PM

Rank: Advanced Member

Joined: 2/25/2011
Posts: 81
Neurons: 236
Location: France
Jolly good, what method did you use ?

I think mine was way too complicated, I would be glad to hear yoursBoo hoo!

Poor skeleton couldn't attend the ball, he had no body to go with.
excaelis
Posted: Saturday, March 5, 2011 1:50:50 PM

Rank: Advanced Member

Joined: 6/30/2010
Posts: 10,981
Neurons: 32,652
Location: Toronto, Ontario, Canada
AAARGH !! PIRATES !!! ABANDON SHIP !!!


( Just keepin' it topical...)

Sanity is not statistical
tootsie
Posted: Saturday, March 5, 2011 2:05:17 PM

Rank: Advanced Member

Joined: 9/11/2010
Posts: 6,886
Neurons: 23,730
excaelis wrote:
AAARGH !! PIRATES !!! ABANDON SHIP !!!


( Just keepin' it topical...)


Applause was going to attempt it had the starting speed been given, however I prefer to swim....x

I'm not lost for I know where I am. But however, where I am may be lost. Winnie-the-Pooh
abcxyz
Posted: Saturday, March 5, 2011 2:31:15 PM

Rank: Advanced Member

Joined: 11/13/2009
Posts: 1,061
Neurons: 3,200
Location: India
Pantomime wrote:
Jolly good, what method did you use ?

I think mine was way too complicated, I would be glad to hear yoursBoo hoo!


BA-AB=A0B-BA
(b-a)*9=a00-b0+b-a
(b-a)8=a00-b0
(b-a)8 has 0 as its unit digit only if b-a=5, as b,a<10
b-a=5
(b-a)8=40
then from the equation,
a0-b=4
then a must be 1, because otherwise a0-b would have been greater than 10.
a=1, b=6.
P.S. we already have a thread for these probs -> http://forum.thefreedictionary.com/postst14521_Maths--Logics-problems-.aspx
There is also the other thread -> http://forum.thefreedictionary.com/postst7628_Open-ended-questions.aspx

In this world there is no literate population that is poor and no illiterate population that is other than poor. - J.K.Galbraith
Pantomime
Posted: Saturday, March 5, 2011 5:23:59 PM

Rank: Advanced Member

Joined: 2/25/2011
Posts: 81
Neurons: 236
Location: France
Mine was the following :

I noticed that for AB to BA the difference grows by a factor of nine that goes * X for each + 1 increment to B and that said factor goes one step forwards when A goes one digit up, like such :

23 to 32 is 9
24 to 42 is 18

34 to 43 is 9
35 to 53 is 18.

I know that I must add 90 to AB to get AoB
Since speed is constant you must add 45 to AB and BA. and since 9*5= 45 you've got to take the fifth rank as from AB ( for 23 you go 4 up as the first rank is included in the first AB (23) hence 27 to 72 is indeed 45 ).
Hence AB + 90 = AoB, 45+ A = B
Then I tried with 27 to 72 which is 45, 5+2(A) = 7 = B but 4+ 7(B) = 11 and it has to produce a 10, if B continues going 1 up 4 + B will take + 1 each time.

Ok but what if you get 4 + B = 20 or 30 or 40 ?

If A goes + 1 it gives you 38 to 83 and 5 + 3 = 8 ( ok here but as said above 4 + B will equal 12 ), 49 to 94 = 45 but 5 + 4 = 9 and 5 + A cannot equals B.

So as you cannot add + 1 to either A or B and as it does not work as from 27 to 72 the only solution left is A = 1 and B = 6. A goes 1 down and as you have to respect the 'rank" thing it has to be 12 + 4 "ranks" up = 16.


And it worked ! !!!


I told you it was way too complicated Drool

@ abcxyz
I still don't understand where the second line of your equation comes from, though.Brick wall

Poor skeleton couldn't attend the ball, he had no body to go with.
abcxyz
Posted: Saturday, March 5, 2011 8:35:25 PM

Rank: Advanced Member

Joined: 11/13/2009
Posts: 1,061
Neurons: 3,200
Location: India
Pantomime wrote:

@ abcxyz
I still don't understand where the second line of your equation comes from, though.Brick wall


ba-ab=a0b-ba

ba=b0+a, or b*10+a, like if b=2,a=3, then ba=23=20+3
ab=a0+b
a0b=a00+b
ba-ab=b0+a-a0+b=(b-a)*10-(b-a)=(b-a)*9
similarly a0b-ba=a00-b0+b-a
Is it clear now?

In this world there is no literate population that is poor and no illiterate population that is other than poor. - J.K.Galbraith
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