Add new comment

Permalink In reply to by Anonymous (not verified)

No divisibility rules or 99 times table is needed for the proof.

If the number is 100a + 10b + c, and a>c then
100a + 10b + c
- 100c + 10b - a
= 100*(a-c) + (c-a) -- or, since c-a is negative
= 100*(a-c-1) + 90 + (10+c-a)
This shows that the middle digit is 9.
Then adding digits:
100*(a-c-1) + 90 + (10+c-a)
+ 100*(10+c-a) + 90 + (a-c-1)
= 1000 - 100 + 180 + 9 = 1089

Filtered HTML

  • Web page addresses and email addresses turn into links automatically.
  • Allowed HTML tags: <a href hreflang> <em> <strong> <cite> <code> <ul type> <ol start type> <li> <dl> <dt> <dd>
  • Lines and paragraphs break automatically.
  • Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.