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Olympiad workbook
Exam
Olympiad workbook
Subject
IOQM
Chapter
Permutation and Combination

Olympiad workbook · IOQM · Permutation and Combination

Consider the set of all 6 -digit numbers consisting of only 3...

Consider the set of all 6 -digit numbers consisting of only 3 digits, a,b,ca, b, c, where a,b,ca, 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?100 ?Consider the set of all 6 -digit numbers consisting of only 3 digits, a, b, c , where a, b, c are distinct. Suppose the

Correct answer

98

Step-by-step solution

\begin{array}{|l|l|l|l|l|l|} \hline & & & & & \\ \hline \end{array} with a,b,c\mathrm{a}, \mathrm{b}, \mathrm{c} distinct digit sum of all ' 6 ' digit number =593999406=593999406 Let a,b,c≠0a, b, c \neq 0 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 number =35×(a+b+c)×111111=243+111111×(a+b+c)=26999973×(a+b+c)=593999406a+b+c=223 digit abc number sets =985,958n=98\begin{aligned} & \text { sum of number }=3^5 \times(a+b+c) \times 111111 \\ & =243+111111 \times(a+b+c) \\ & =26999973 \times(a+b+c)=593999406 \\ & a+b+c=22 \\ & 3 \text { digit abc number sets } \\ & =985,958 \\ & n=98\end{aligned}
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