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Starstruck!

It is bright sunshine outside but I am seeing stars! There are exactly 33 stars that seem to be winking at me.

Nothing like a good story book on a Sunday. I was reading one, but Partho came and interrupted me.

He had a piece of paper with all these stars or asterisk marks I told you about. He thrust the paper at me and said, "Solve it."

It looked like a long division problem. But except for an 8 in the quotient and 0 in the remainder, there were not other digits - all were asterisk marks. There were 33 asterisk marks in all. "What is there to solve?" I asked. "This is a cryptarithm; this is a long division where the digits of the divisor, dividend, quotient, and all the intervening numbers have been replaced by asterisk marks. The final remainder is 0, while the quotient has an 8 in the middle. You have to replace all the asterisk marks with actual digits," he explained. "Hey, there are 33 asterisk marks, and if I go finding all of them it will take me a year!" I exclaimed. "Alright, just find the divisor, dividend and quotient," Partho said with a grin. Clever fellow! If I could find the divisor, dividend, and quotient, then I could find all the other digits as well.

Anyway, here is the long division problem. The divisor is a three-digit number, the dividend is an eight-digit number, and the quotient is a five-digit number with 8 in the hundreds place. The final remainder is 0.

Cryptarithm problem

"And, yes, remember that the divisor, dividend, quotient, and the intervening numbers don't have leading zeroes," Partho said. Looking at my blank face he explained that if, for instance, I encountered the number 356 then it wouldn't be written as 0356. The numbers don't have leading zeroes.

"You solve this while I read this storybook," he said and snatched the book from me. "You won't get the book back unless you solve it," he said and went away.

Please help me solve this so that I get my book back.






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  • Union Public Service Commission - www.upsc.gov.in
  • IIT-Kharagpur - www.iitkgp.ac.in
  • Indian Statistical Institute - www.isical.ac.in
  • Indian Institute of Technology Madras - www.iitm.ac.in
  • Indian Institute of Management, Ahmedabad - www.iimahd.ernet.in
  • Indian Institute of Mass Commission - www.iimc.nic.in
  • IIT Bombay - www.iitb.ac.in
  • Indian School of Mines, Dhanbad - www.ismdhanbad.ac.in
  • Birla Institute of Technology, Ranchi - www.bitmesra.ac.in
  • Central Institute of Fisheries Nautical and Engineering Training - www.cifnet.nic.in
  • Indian Institute of Information Technology, Allahabad (Deemed University) - www.iiita.ac.in
  • Central Marine Fisheries Research Institute, Kochi - www.cmfri.com
  • Tata Institute of Social Sciences, Mumbai - www.tiss.edu