MIND GAMES
Phoney number
Aditya Rishi

The 10-digit phone number of Sahiban is 3816547290. Mirza got it from 47 sources. One of the neatest solutions came from Vimal Jit Kaur.

To obtain this number using the clues that the number is smallest using all the digits from 0 to 9 and the first digit is divisible by 1, the first 2 digits (taken as a 2-digit number) are divisible by 2 and so on, she had to consider the following facts and tests:

(1) That the digits at even places should be even and at odd places should be odd. (2) Since the first digit is divisible by 1, it includes nine digits from 1 to 9. Discarding the even digits and 5 for its divisibility test by 5, the probability was only for 1, 3, 7, and 9. (3) A number is divisible by 2 if it is an even number. (4) A number is divisible by 3 if the sum of its digits is divisible by 3. (5) A number is divisible by 4 if the last two digits are divisible by 4. (6) A number is divisible by 5 if the last digit is 5 or 0. (7) A number is divisible by 6 if the last digit is even and the sum of the digits is divisible by 3. (8) A number is divisible by 8 if the last three digits are divisible by 8. (9) A number is divisible by 9 if the sum of the digits is divisible by 9. (10) A number is divisible by 10 if the number ends with a 0.

Since the position of 5 and 0 was certain at fifth and tenth place, respectively, and the number had to be the smallest number fulfilling the given conditions, she started with 1 and after a few permutations and combinations, arrived at the answer. However, Vijayesh Narayan Singh (Department of Mathematics, PU) came up with the most methodical approach.

The other angels who came to Mirza’s rescue were (in alphabetical order): Aman Gill (Department of Mathematics, PU), Ankit Garg (Thapar, Patiala), Arshdeep Singh, Charan Amrit Pal Singh, Divya Sood, Dr R. Chawla (Professor of Biochemistry, Christian Medical College and Hospital Ludhiana), Dr Suman Preet, Dr Tarsem Lal, Geetika Gupta (Thapar, Patiala), Gemini Mittal, Gitesh Bansal, Harjot Singh Dod (Army School, Phagwara), Harvinder Pal Singh, Himanshu Sachdeva (PEC), Inderpreet Kaur and Umeshwer Singh, Jarnail Singh (SAS Nagar), Madhur Sharma, Manjinder Singh Arora (Muktsar), Mansha Singh (VPO Ghanauli, Ropar), Mohit Rodeja, Namrita Sarkaria (class XI, Ludhiana), Natasha Miglani (Fatehabad), Navdeep Singh, Puneet Sandhu, Puneet Singh (Class VIII, Vivek High School), Raghav Talwar, Rahul Khanna (NIT, Jalandhar), Rajat Kalsy, Rajat Pal Gupta (PEC), Rajesh Garg (Mohindra College, Patiala), Rajiv Goyal, Rakesh Satija (Phillaur), Ravinder Thakur, Ravneet Kotwal, Rishabh Garg (Patiala), Sandeep Kaur Gill (AIET, Faridkot), Saurabh Sood, Shilp Kumar (PEC), Sudhir Dhamija (PEC), Suhail Singh Shergill, U.K. Gupta (DE, Phones, Malout). (Write at The Tribune or adityarishi99@yahoo.co.in)