Saturday, November
30, 2002 

AKIRA Kurosava of Japan directed Seven Samurai, which inspired Hollywood to produce The Magnificent Seven, which inspired India to make Sholay. These, however, are works of fiction; reallife legends are more inspiring, one of which is that of Teiji Takagi and his student. The sword of Samurai is no longer an ancestral property; it belongs to the courageous, the Ten Samurai. The question was: the decimal expression of a natural number ‘a’ consists of ‘n’ digits, while that of a^3 consists of ‘m’ digits. Can n+m be equal to 2001? "The cube of the
smallest n digit number consists of (3n2) digits. The cube of the
biggest n digit number consists of 3n digits. This way, the cube of any
ndigit number may consist of either 3n2 digits or 3n1 digits or 3n
digits. This implies that m+n is equal to either (3n2)+n=4n2 or
(3n1)+n=4n1 or (3n) +n=4n, so, m+n can never be equal to (4n3), so,
m+n can never be equal to 2001. If the natural number consists of 500
digits, its cube will consist of either 1498 or 1499 or 1500 digits, so,
m+n will be equal to either 1998 or 1999 or 2000. If the natural number
consists of 501 digits, its cube will consist of either 1501 or 1502 or
1503 digits, so, m+n will be equal to either 2002 or 2003 or 2004, but,
in no case can m+n be equal to 2001," says U. K. Gupta (DE
Planning, GMT Sangrur), our first Samurai, leader of the pack, followed
closely by Deepankar Garg, the second Samurai. 
Sushane: "Prof. Takagi regarded the sword as the source of all his courage, which made him so successful. When he saw the sword showing the same effect on that child as it did on him years ago, he gave it to him with the thought that that the child, too, would make his nation proud." Dr Vikas: "The Samurai sword was given to the student probably because only this particular student dared to attempt the seemingly difficult problem." Ravinder: "After reading the article till the question in the last paragraph, I paused for some time, thinking of the answer. As no solution came to mind, I went further. The moment, the sword was seen, with a flash came the answer. Maybe, Takagi had no heir; or none of his heirs was competent enough to carry the sword." Suhail: "The sword was given by the Emperor to the select the best soldiers of Japan. By giving the sword to him, Takagi wanted to do the same thing and convey to his student that one should never be afraid to attempt anything." Varun: "The student had understood the real meaning of what was written on the sword and, maybe, he was more deserving than anybody else in the Takagi family to keep the sword." Rohit: "Takagi was influenced by the student’s intellect." Takagi wrote textbooks,
important for the development of Japanese mathematics at school and
university levels at that time. A New Course of Arithmetic, published in
1904, developed real numbers using a new approach. The First World War
started in 1914 and no scientific information reached Europe for four
years and some said this would be the end of Japanese science. Then, he
had few colleagues and wanted this tribe to increase, by inducting the
best, the Samurai. His Tokyo house was destroyed in bombing near the end
of World War II, after which, he returned to the village of his birth,
returning to Tokyo in 1947 to live with his eldest son… and inspire
generations. Write at The Tribune or adityarishi99@yahoo.co.in. 