Consider the set of all 6 -digit numbers consisting of only 3 digits, a, b, c , where a, b, c are distinct. Suppose the sum of the these numbers is 593999406 . What is the largest remainder when the three digit number abc is divided by 100 ?

Step-by-step solution

array |l|l|l|l|l|l| & & & & & array with a , b , c distinct digit sum of all ' 6 ' digit number =593999406 Let a, b, c 0 aligned & sum of number =3^5 (a+b+c) 111111 & =243+111111 (a+b+c) & =26999973 (a+b+c)=593999406 & a+b+c=22 & 3 digit abc number sets & =985,958 & n=98 aligned