Try this beautiful problem from the PRMO, 2018 based on Digits of number.
Digits of number – PRMO 2018
Consider all 6-digit numbers of the form abccba where b is odd. Determine the number of all such 6-digit numbers that are divisible by 7.
- is 107
- is 70
- is 840
- cannot be determined from the given information
Check the Answer
But try the problem first…
Answer: is 70.
PRMO, 2018, Question 3
Higher Algebra by Hall and Knight
Try with Hints
abccba (b is odd)
=7p+(c-a) where p is an integer
Now if c-a is a multiple of 7
hence number of ordered pairs of (a,c) is 14
since b is odd
number of such number=\(14 \times 5\)=70.
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