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Math Help - Find a number

  1. #1
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    urgent!! please help~~~~

    When a positive integer N is written in base 6 , it is a four digit number such that all its four digits are the same. When N is written in base ten, it is a three digit number such that all its three digits are equal. Find the decimal representations of all such numbers N.

    Please help!!!!!!!! desperate!!!! THAANK YOU!!!!
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by fring
    When a positive integer N is written in base 6 , it is a four digit number such that all its four digits are the same. When N is written in base ten, it is a three digit number such that all its three digits are equal. Find the decimal representations of all such numbers N.

    Please help!!!!!!!! desperate!!!! THAANK YOU!!!!
    (aaaa)_6=(bbb)_{10}
    (216+36+6+1)a=(100+10+1)b
    259a=111b
    7a=3b
    a=3,b=7

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  3. #3
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    Hello, fring!

    I will assume that you know something about number bases.
    Otherwise, you shouldn't be trying problems like this . . .


    When a positive integer N is written in base 6 , it is a 4-digit number such that all its digits are equal.
    When N is written in base ten, it is a 3-digit number such that all its digits are equal.
    Find the decimal representations of all such numbers N.

    In base-6: N \:=\:aaaa_6 \:=\:6^3a + 6^2a + 6a + 6 \:=\:259a

    In base-10: N \:=\:bbb_{10} \:=\:10^2b + 10b + b \:= \:111b

    Hence: . 259a \:= \:111b\quad\Rightarrow\quad 7a = 3b

    Since a is a digit in base-6 and b is a digit in base-10,
    . . the only solution is: a = 3,\;b = 7

    Therefore: . N \:=\:3333_6 \:= \:777_{10}

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