
He is no longer feared,
all due to Harker's brave rescuers most of whom defined a Repeating Unit
as a number made up entirely of 1s so that R1 = 1; R2 = 11; R3 = 111; R4
= 1111 etc. Investigating by division: 11/7 = 1.571...; 111/7 =
15.857...; 1111/7 = 158.714...; 11111/ 7 = 11587.28...; 111111/7 =
15873. So, 15873 is the smallest whole number which, when multiplied by
7, gives a repeating unit. Extending the question to find what other
numbers will also work, we know 3 must be the smallest number to work
because a number ending in 1 will be odd and it will not divide by 2.
11/3 = 3.666...; 111/3 = 37. The number 4 will not work for the same
reason 2 does not work, and 6 won't work, neither will 8. Any number
multiplied by 5 will end in 0 or 5, so 5 won't work, so 9 will be the
next number to try.
Amarjeet Kaur of
Ludhiana started dividing by 7 taking dividend firstly 11. Remainder is
4. Then, she takes dividend 111, now the remainder is 6, takes 1111, now
the remainder is 5, takes 11111, and the remainder is 2, takes 111111and
the remainder is zero, and the answer is 15873. The second smallest
whole number is 15873015873, which is 1000001 times larger than the
first one, says Dr Vikas Handa. To have 1 in the product, you may even
start by selecting digit 3 at one's place in the required number. We
carry over 2. To have another 1, we should look for a product of 7 with
9 in one's place, which is 49; carrying on, we reach 15873.
The following rescuers were the first
ones to arrive: Vikas Vashisht, Dr Manjit Singh, Parveen Bajaj, Pareena
Bawa, Sourabh Kumar Kakkar, Navneet Kad (Ludhiana), Sunny Ahuja
(Amritsar), Anil Chaudhry, Rashmi Anand, Rakesh Anand, Ajit Partap Singh
(Ludhiana), Abhi Rana, Prerna Aggarwal (Panchkula), Nitin Khanna, Kamal
Sethi (Hisar), Sanjay Chawla, Jaskirat Singh Jassal (Amritsar), Bhawna
Garg (Mandi Gobindgarh), Mrinal Goyal (Kurukshetra), Divyadeep Modi
(Malerkotla), Dr Tarsem Lal (Khanna) and Sameer Madan. There was so much
mail that even Dracula got sacred and ran away. (Dedicated to Bram
Stoker. Write at The Tribune or adityarishi99@yahoo.co.in)
