rookie1ja 13 Report post Posted March 30, 2007 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 cm^{2}. 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. Belt - solution The original length of belt was 96 cm. A magic rectangular belt always shrinks its length to 1/2 and width to 1/3 whenever its owner wishes something. After three such wishes, its surface (Edit: surface area of the front side) was 4 cm^{2}. What was the original length, if the original width was 9 cm? Share this post Link to post Share on other sites

Guest Report post Posted June 8, 2007 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? Share this post Link to post Share on other sites

Guest Report post Posted June 9, 2007 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] Share this post Link to post Share on other sites

Guest Report post Posted June 11, 2007 Oh - I get it - Thanks! Share this post Link to post Share on other sites

Guest Report post Posted June 18, 2007 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. Share this post Link to post Share on other sites

Guest Report post Posted June 25, 2007 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 Share this post Link to post Share on other sites

Guest Report post Posted June 29, 2007 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. Share this post Link to post Share on other sites

Guest Report post Posted July 14, 2007 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. Share this post Link to post Share on other sites

Guest Report post Posted August 9, 2007 this s not a puzzle at all.... Share this post Link to post Share on other sites

Guest Report post Posted October 24, 2007 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 Share this post Link to post Share on other sites

Guest Report post Posted November 1, 2007 96 if I got my halvsies and thirdsies right. by the by heres the question.............. If a person with a 96cm waist was wearing the belt, would he/she be suffocated on the first, second, or third wish? I would have wished the belt didn't shrink Share this post Link to post Share on other sites

Guest Report post Posted November 6, 2007 Width is (((9/3)/3)/3) = 1/3 after 3 wishes Area is 4cm (squared) so final length is 4 / 1/3 = 12 So original length is (((12*2)*2)*2) = 96 I know everyone has said it before, just confirming my working! Share this post Link to post Share on other sites

Guest Report post Posted November 10, 2007 i tought he wished to make it a diffrent size....but if you want to go though all of that complication Share this post Link to post Share on other sites

Guest Report post Posted November 27, 2007 Belt - Back to the Logic Puzzles A magic rectangular belt always shrinks its length to 1/2 and width to 1/3 whenever its owner wishes something. After three such wishes, its surface was 4 cm2. What was the original length, if the original width was 9 cm? I hate to be anal, but a belt is three dimensional. Even if the thickness of the belt were small enough to be neglegable, the belt would still have a front and a back. At most, the surface area of one side is 2 cm^2, resulting in an original length of 48 cm. You could just change the puzzle to state that "After three such wishes, the surface area of the front side was 4 cm^2." Share this post Link to post Share on other sites

rookie1ja 13 Report post Posted November 27, 2007 Belt - Back to the Logic Puzzles A magic rectangular belt always shrinks its length to 1/2 and width to 1/3 whenever its owner wishes something. After three such wishes, its surface was 4 cm2. What was the original length, if the original width was 9 cm? I hate to be anal, but a belt is three dimensional. Even if the thickness of the belt were small enough to be neglegable, the belt would still have a front and a back. At most, the surface area of one side is 2 cm^2, resulting in an original length of 48 cm. You could just change the puzzle to state that "After three such wishes, the surface area of the front side was 4 cm^2." puzzle edited Share this post Link to post Share on other sites

Guest Report post Posted December 5, 2007 Belt - Back to the Logic Puzzles A magic rectangular belt always shrinks its length to 1/2 and width to 1/3 whenever its owner wishes something. After three such wishes, its surface was 4 cm2. What was the original length, if the original width was 9 cm? I hate to be anal, but a belt is three dimensional. Even if the thickness of the belt were small enough to be neglegable, the belt would still have a front and a back. At most, the surface area of one side is 2 cm^2, resulting in an original length of 48 cm. You could just change the puzzle to state that "After three such wishes, the surface area of the front side was 4 cm^2." puzzle edited I believe this is one of those puzzles that you take literally and when the owner makes a wish the belts lengt goes to 1/2. Not that it is half each wish. It never says that it is each time. Share this post Link to post Share on other sites

Guest Report post Posted December 11, 2007 Hello! i am new to this. Let me put the solution in this way. Let the original lenght = x cm. and the given width = 9 cm. 1st wish: lenght =x/2 cm; width =9/3=3 cm; 2nd wish: lenght =x/4 cm; width =1 cm; 3rd wish: lenght =x/8 cm; width =1/3 cm; After three wishes: The given Surface area A (say) = 4 cm2; Surface area A = length * width; 4 cm2 =(x/8 )*(1/3) cm2; x = 4 *24= 96 cm; The original length x= 96 cm; Share this post Link to post Share on other sites

Guest Report post Posted December 12, 2007 I did it kinda like everyone else... 1. I divided 9 ( the original width) by 3, 3(new width) by 3, then 1( new, new , width) by 3, for the 3 wishes. This gave me 1/3 for the resulting width. 2. Next, i divided 4cm squared by 1/3, and got 12. 3. I doubled thise 3 times ( for the 3 wishes) to get 96, the original width. Share this post Link to post Share on other sites

Guest Report post Posted March 19, 2008 simple i just used an equation to solve: L= Length W= Width 1/8L (1/27W) = 4 then just put 9 in for the width and solved for the length (FYI i got 1/8 from placing 1/2 to the third power since it was wished to shrink 3 times, and did the same for the length- 1/3 ^ 3) Share this post Link to post Share on other sites

Guest Report post Posted March 26, 2008 (edited) 96 cm Edited March 26, 2008 by scuttill Share this post Link to post Share on other sites

Guest Report post Posted June 5, 2008 l/8*w/27=4 l=4*8*27/9=96 Share this post Link to post Share on other sites

Guest Report post Posted May 11, 2010 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? you got the first bit right, the width after three wishes is 1/3cm, but then you said the area was 16cm. its meant to be 4cm^2, which is not the same as 16cm so instead of 1/3 * L = 16cm, it should be 1/3 * L = 4 to find length after 3 wishes i havent checked my answer, but looking at your post, that jumped out at me. hope it helps Share this post Link to post Share on other sites