## Welcome to BrainDen.com - Brain Teasers Forum

 Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-)
Guest Message by DevFuse

# Belt

21 replies to this topic

### #1 rookie1ja

rookie1ja

Senior Member

• 1344 posts
• Gender:Male
• Location:Slovakia

Posted 30 March 2007 - 03:42 PM

Magic Belt - Back to the Cool Math Games
A magic wish-granting rectangular belt always shrinks to 1/2 its length and 1/3 its width whenever its owner makes a wish. After three wishes, the surface area of the belt’s front side was 4 cm2.
What was the original length, if the original width was 9 cm?

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.
Pls visit New Puzzles section to see always fresh brain teasers.

Spoiler for Solution

Spoiler for old wording

• 0

Optical Illusions
Support BrainDen

"To start: Press any key... Where's the 'any' key?" - Homer Simpson

### #2 ezkoalmc

ezkoalmc

Newbie

• Members
• 2 posts

Posted 08 June 2007 - 08:21 PM

I am new here and I may be all wrong, but when I worked this out I got 192 or double 96.
Here's my work:
Original width = 9
1st wish: 9 * 1/3 = 3
2nd wish: 3 * 1/3 = 1
3rd wish: 1 * 1/3 = 1/3

Current width is 1/3 cm. Total area must be 1/3 * L = 16 cm
L = 16 / 1/3 = 48
Current Length must be 48 cm.
Working backwards: 3rd wish = 48
2nd wish = 48 * 2 = 96
1st wish = 96 * 2 = 192 original length.
What did I miss?
• 0

### #3 iknowall

iknowall

Newbie

• Members
• 7 posts

Posted 09 June 2007 - 02:28 AM

I am new here and I may be all wrong, but when I worked this out I got 192 or double 96.
Here's my work:

Original width = 9
1st wish: 9 * 1/3 = 3
2nd wish: 3 * 1/3 = 1
3rd wish: 1 * 1/3 = 1/3

Current width is 1/3 cm. Total area must be 1/3 * L = 16 cm

L = 16 / 1/3 = 48
Current Length must be 48 cm.
Working backwards: 3rd wish = 48
2nd wish = 48 * 2 = 96
1st wish = 96 * 2 = 192 original length.
What did I miss?

u got the area wrong
u said

Total area must be 1/3 * L = 16 cm

Its not 4 squared which does equal 16, it is 4 cm squared
ex: a square with a width and length of 2 = 4 cm2 not 16

so actually the total area of belt after 3 wishes is 1/3*L = 4 cm2
1/3= 0.33
4 * 0.33 = 12

12*2= 24
24*2= 48
48*2= 96

[if u really want to get technical 1/3 = 0.333333333333333333333333333333 and so on so its not exactly 96]
• 0

### #4 ezkoalmc

ezkoalmc

Newbie

• Members
• 2 posts

Posted 11 June 2007 - 02:14 PM

Oh - I get it - Thanks!
• 0

### #5 mdsl

mdsl

Junior Member

• Members
• 51 posts

Posted 18 June 2007 - 01:27 PM

so actually the total area of belt after 3 wishes is 1/3*L = 4 cm2
1/3= 0.33
4 * 0.33 = 12

12*2= 24
24*2= 48
48*2= 96

[if u really want to get technical 1/3 = 0.333333333333333333333333333333 and so on so its not exactly 96]

1/3 does equal .33 repeated but your math is wrong.

4 * 0.33 does not = 12, but it doesn't matter because you were supposed to divide which does give you 12.

0.33 * L = 4 => L = 4 / 0.33

4 / 0.33 = 4 * 3 = 12, no decimals.

So the answer is exactly 96.
• 0

### #6 steve1011

steve1011

Newbie

• Members
• 1 posts

Posted 25 June 2007 - 07:27 PM

If you want to do it with the fraction instead of breaking it down to decimals it is even simpler.

4/(1/3)=4*3=12
• 0

### #7 Mythx

Mythx

Newbie

• Members
• 6 posts

Posted 29 June 2007 - 09:08 PM

Width after three wishes:
9*(1/3)*(1/3)*(1/3) = 9*(1/3)^3 = 9*(1/27) = 1/3

Length after three wishes:
surface = length * width
length = surface / width
length = 4/(1/3) = 4*3 = 12

Original length:
12/(1/2)/(1/2)/(1/2) = 12/(1/2)^3 = 12/(1/8) = 96

4 / (9 * (1/3)^3) / (1/2)^3 = 96 cm
4 / (9/27) * 8 = 96 cm

And the correct denotation of 1/3 would be 0.33... (with two or three dots) in which case the dots mean that the number is being repeated.
• 0

### #8 Genius

Genius

Newbie

• Members
• 1 posts

Posted 14 July 2007 - 12:54 PM

One other method of solving it would be,

If x,y are the original length and width resp.

xy=area

After each wish, length and width become 1/2 and 1/3 of the original resp.

Thus, the new area, after a wish = 1/6*old area.

As three wishes were made, and the final area being 4, the initial area is thus = 4*6*6*6 = 864

Width = 9 (given)
Length = 864/9=92.
• 0

### #9 ibrahim_zulu18

ibrahim_zulu18

Newbie

• Members
• 3 posts

Posted 09 August 2007 - 02:33 PM

this s not a puzzle at all....
• 0

### #10 bowfinger

bowfinger

Newbie

• Members
• 1 posts

Posted 24 October 2007 - 11:25 AM

let's assume original length is a and original width is b :
after 1st wish the area = a/2* b/3
after 2nd wish the area = a/4*b/9
after 3rd wish the area = a/8*b/27
the area after 3rd wish is given as 4 and the width is 9
therefore a/8*9/27=4 , 9a = 4*8*27
thus a = 96 cms

I hope it's the right way
• 0

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users