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The 3-digit Number (Posted on 2005-10-16) Difficulty: 3 of 5
Let abc be a 3-digit number.
Find it, if acb + bca + bac + cba + cab = 3961.

See The Solution Submitted by nickson    
Rating: 2.0000 (3 votes)

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Solution No computers! | Comment 8 of 18 |
We can write abc+acb+bca+bac+cba+cab= 3961+abc. The left side equals 222x(a+b+c). We need (a+b+c)>16, so 222x(a+b+c) is greater than 3961.

Trying by hand (a+b+c)=17, 18, 19, 20, we finally get 222x20=4440; 4440-3961=479; 4+7+9=20, so abc=479.

  Posted by Federico Kereki on 2005-10-17 06:07:29
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