All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Three Digit Number (Posted on 2003-05-15) Difficulty: 4 of 5
Find a three-digit number containing three different digits where the following are all perfect squares:

  • (A) The sum of the first digit and the number formed by the second and third digits;
  • (B) The first digit multiplied by the number formed by the second and third digits and
  • (C) The sum of the three digits.

  • See The Solution Submitted by Ravi Raja    
    Rating: 3.8000 (5 votes)

    Comments: ( Back to comment list | You must be logged in to post comments.)
    Solution solution | Comment 4 of 28 |
    This program:

    FOR a = 1 TO 9
    FOR b = 0 TO 9
    FOR c = 0 TO 9
    t1 = a + 10 * b + c
    st1 = INT(SQR(t1) + .5)
    IF st1 * st1 = t1 THEN
    t2 = a * (10 * b + c)
    st2 = INT(SQR(t2) + .5)
    IF st2 * st2 = t2 THEN
    t3 = a + b + c
    st3 = INT(SQR(t3) + .5)
    IF st3 * st3 = t3 THEN
    PRINT a; b; c
    END IF
    END IF
    END IF
    NEXT
    NEXT
    NEXT

    Produces

    1 0 0
    2 0 2
    4 0 0
    8 0 8
    9 0 0
    9 1 6
    so that if "the number formed by the second and third digits" is not allowed to have a leading zero, then 916 is the only solution.
      Posted by Charlie on 2003-05-15 11:25:51
    Please log in:
    Login:
    Password:
    Remember me:
    Sign up! | Forgot password


    Search:
    Search body:
    Forums (0)
    Newest Problems
    Random Problem
    FAQ | About This Site
    Site Statistics
    New Comments (6)
    Unsolved Problems
    Top Rated Problems
    This month's top
    Most Commented On

    Chatterbox:
    Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information