Saturday, January 17, 2004

Not a paper tiger
Aditya Rishi

STEVE Waugh folded a newspaper a few times more than 30 and he was over the Moon. While the Australian dressing room will not be the same without him, his last test left Sachin and many of us quite astonished. Though Steve has this habit of turning the impossible into possible, was he serious in this case?

Rishabh Singla, a class XII student from Ludhiana, says: "The average thickness of a newspaper, though varying from newspaper to newspaper, yet on an average is about 2 thou [0.05 mm] to 4 thou [0.1 mm]. Any number of folds made on newspaper correspond to 2 to the power that number of folds (If we make 2 folds, then it's 2^2=4 layers [.4 to .2 mm]. This is valid even for 2 to the power zero [which is 1] ).

Now, 2^30= 65536*256*64=1073741824 number of folds, and dividing by the thickness of the newspaper, it becomes 107374.1824 metre for a newspaper of thickness 0.1 mm and 53687.0912 metre for a newspaper of thickness 0.05 mm. It means that possibly Steve was talking of a newspaper of thickness 0.05 mm. He is serious when he says that a few more folds would have taken it to the Moon.

The average distance of the Moon from the Earth is 3,84000 km or 384000000 metre. To obtain the number of folds needed to reach this thickness, divide this by distance already covered to get additional number of folds needed w.r.t. powers of 2. Then 53687.0912 metre multiplied by 2 to the power 12 is 219902325.5552 metre and to the power 13 is 439804651.1104 metre, so in the 43rd fold, it will cross the Moon while in the 42nd fold, it will be in the path.

Ankush Aggarwal, a class XI student from Government Shamsher Senior Secondary School, Nahan, has sent in an almost identical solution and Suhail Singh Shergill seems to agree with their view.

"Steve was serious indeed. 30 folds of his newspaper resulted in increasing the thickness of the newspaper by a factor of 2 with each fold. It means that 30 folds increased the thickness of paper 2^30=roughly more than a billion times (1,073,741,824 times) which was 54 km. The thickness of the paper (54 km/1,073,741,824) comes out to be roughly 0.05 mm. If the newspaper is folded 13 more times, that is a total of 43 folds, it will reach well beyond the Moon, but Steve should be careful, as additional 9 folds (52 folds) may be too hot a task, as it may take one though the Sun," says Dr Vikas Handa.

However, realistically, the maximum number of times a newspaper can be folded is 8. Most of you have agreed on 7 or even 9. Karan Kapany gets his Test cap. (Write at The Tribune or