Test – 2nd June-Level 1B Home › Forums › Math Olympiad, I.S.I., C.M.I. Entrance › RMO › Test – 2nd June-Level 1B Tagged: #Number theory This topic contains 1 reply, has 2 voices, and was last updated by Aritra 1 week ago. Viewing 2 posts - 1 through 2 (of 2 total) Author Posts June 11, 2019 at 5:25 pm #29151 Aruna RamachandranParticipant A two digit number formed by any 2 adjacent digits of a 2017 digit umber is divisible by 17 or 23. if the last digit of the 2017 digit number is 1.Find the first digit? Reverse the digits 1746 and we get 6741, the new number is larger than the original number by 4725. How many four digit number can satisfy such condition? June 11, 2019 at 8:02 pm #29152 AritraModerator solution of problem 1 ) working backward see that 17 gives 17, 34,51,68,85 as its two digit multiple and 23 gives 23,56,69,92 as its two digit multiple now last digit is 1 so the second last digit must be 5 now if it 5 then the third last digit is 8 then the 4th last digit must be 6 now if it is 6 then 5th last digit is 5 again so now we get back to 5 again so there will be a pattern like this ……6856856851 using this pattern we can conclude that the 1st digit must be 6 ( why? think with division by 3) so , we are done This reply was modified 1 week ago by Aritra. Author Posts Viewing 2 posts - 1 through 2 (of 2 total) You must be logged in to reply to this topic.