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

Key Concepts




Check the Answer

But try the problem first…

Answer: is 70.

Suggested Reading

PRMO, 2018, Question 3

Higher Algebra by Hall and Knight

Try with Hints

First hint

abccba (b is odd)




=7p+(c-a) where p is an integer

Second Hint

Now if c-a is a multiple of 7


hence number of ordered pairs of (a,c) is 14

Final Step

since b is odd

number of such number=\(14 \times 5\)=70.

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