Olympiad workbookIOQMBasics of Mathematics
Let N be the smallest positive integer such that N +2 ~N +3 ~N + +9 ~N is a number all whose digits are equal. What is the sum of the digits of N ?
Correct answer
37
Step-by-step solution
aligned & N Z ⁺ & P = N +2 ~N +3 ~N + +9 ~N =45 ~N & 45= 555 . .5 _ a times aligned Only 55 .5 can be repeated as 45 N will have units place =0 or 5 Also as 45 ~N multiple of ' 9 ' also. aligned & If a=9 555555555 45 =N & N=12345679 aligned Sum of digits of N =37 .