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[natty]

This puzzle goes as follows and apparently can be solved using materials found in any typical household (i.e. nothing fancy).

A string comes out of holes on the opposite side of (say) a cardboard box. 

If you pull the string out from the left side till it stops, the length (that comes out) is (say) 12 inches but the length (of the string) that comes in (from the right) is 24 inches.    Similarly if you pull the string out from the right side, the length of string that comes out is 24 inches but the length that comes in from the left side is 12 inches  (before it disappears).

How does one construct this setup? Obviously it cant just be one continuous string as then the amount moved on both sides will be equal (whereas here it is in a 1:2 ratio although if it works for this then it can be made to work for other ratios as well). Presumably this will involve more than one string, perhaps connected inside the box in some interesting way.  Any ideas? Are pulleys or other contraptions involved in the solution? (although one would think that pulleys wont be found in the usual household)
   

 

[inoc]

This puzzle goes as follows and apparently can be solved using materials found in any typical household (i.e. nothing fancy).

A string comes out of holes on the opposite side of (say) a cardboard box. 

If you pull the string out from the left side till it stops, the length (that comes out) is (say) 12 inches but the length (of the string) that comes in (from the right) is 24 inches.    Similarly if you pull the string out from the right side, the length of string that comes out is 24 inches but the length that comes in from the left side is 12 inches  (before it disappears).

How does one construct this setup? Obviously it cant just be one continuous string as then the amount moved on both sides will be equal (whereas here it is in a 1:2 ratio although if it works for this then it can be made to work for other ratios as well). Presumably this will involve more than one string, perhaps connected inside the box in some interesting way.  Any ideas? Are pulleys or other contraptions involved in the solution? (although one would think that pulleys wont be found in the usual household)
   

 

two pulleys/cylinders, one with a circumference double that of the other, fixed so that they cannot move independent of one another, with the strings wound in opposite directions, should do the trick. shouldn't it? any ratio can be achieved thus.

[natty]

This puzzle goes as follows and apparently can be solved using materials found in any typical household (i.e. nothing fancy).

A string comes out of holes on the opposite side of (say) a cardboard box. 

If you pull the string out from the left side till it stops, the length (that comes out) is (say) 12 inches but the length (of the string) that comes in (from the right) is 24 inches.    Similarly if you pull the string out from the right side, the length of string that comes out is 24 inches but the length that comes in from the left side is 12 inches  (before it disappears).

How does one construct this setup? Obviously it cant just be one continuous string as then the amount moved on both sides will be equal (whereas here it is in a 1:2 ratio although if it works for this then it can be made to work for other ratios as well). Presumably this will involve more than one string, perhaps connected inside the box in some interesting way.  Any ideas? Are pulleys or other contraptions involved in the solution? (although one would think that pulleys wont be found in the usual household)
   

 

two pulleys/cylinders, one with a circumference double that of the other, fixed so that they cannot move independent of one another, with the strings wound in opposite directions, should do the trick. shouldn't it? any ratio can be achieved thus.

right.. this approach should work..

[schumi]

It is like a bicycle chain gear with ratio of 1:2. One rotation of the big gear yields 2 rotations of the smaller one. The smaller gear is attached to a cylinder that has a circumference of 12 and the bigger one is also attached to a cylinder of circumference 12.

The rope is wrapped around both the cylinders before being passed out on both sides. Pulling 12 inches on the side of the bigger gear rotates it once causing the smaller gear to rotate twice and pull in 24 inches.

Pulling out the rope 24 inches on the side of the smaller gear rotates the bigger gear once thereby pulling in the rope by 12 inches.