msubbara wrote:
...find the smallest number such that if the last digit is removed and placed at the beginning to become the first digit, this new number is nine times the original one. The solution given in the book itself is the astronomical fijure
10,112,359,550,561,797,752,808,988,764,044,943,820,224,719. What would be the solution if we do similar operation with the last two digits and ask '99 times the original number", or replace the last three digits similarly to get 999 times the original number etc.
For 99, the answer is 10001010203050813213455904636832003232649762602283 05889483786241034447924032730578846348115971310233 35690473785230831397110819274674209516112738660470 75462167895747045156076371350641478937266390544499 44438832205273259925244974239822204263056874431760 78391756743105364178199818163450853621577937165370 23941812304273158904939892918476613799373674108495 80765733912516415799575714718658450348520052530558 64228709970704111526416809778765531871906253156884 53379129204970199 For 999, the answer has 146011 digits. Here are the beginning and end. 10009019028047075122197319516836353189542732275007 ... 17596013609623232856088945033979012992004997001999 -- Don Reble djr@nk.ca