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Math Challenge

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A three-digit number increases by 9 if we exchange the second and third digits. The same three-digit number increases by 90 if we exchange the first and second digits. By how much will the value increase if we exchange the first and third digits?

  • Math Challenge -

    well, the second digit must be 9 more than the third. as in 09...or, it is the complement to 9 (as in 1), as in X23,so the switched is X32 (nine more).

    Complements: N,N+1 (as in 12, 23, 32, 43, and so on.

    Not the second hint..the first and second:
    BAx-ABx=90 so a,b must be complements also, as above.

    Lets check; 123
    first hint: 132-123=9
    second hint:213-123=90 checks

    Lets check another: 456
    first hint: 465-456=9
    second hint:546-456=90 checks.
    so there are a multitude of answers for what the number is.

    HOWEVER, the answer to the question asked is interesting.

    In the first case, 321-123=198
    in the second case,654-456=198

    hmmmm, very interesting. Why don't you try a few more?

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