Number Theory

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  • #76597
    Crazy Gamer
    Participant

    <p></p>

    #76666
    Kanishk Sharma
    Participant

    <p>• The number of digits in any number ‘X’ written in decimal notation is given as : 10ᵃ ≤ X ≤ 10ᵇ<br />=> a ≤ log X ≤ b [ where ‘a’ and ‘b’ ∈ N₀ ]<br />=> Number of digits of ‘X’ is : ( a + 1 )</p><p>→ Number of digits of 4444⁴⁴⁴⁴ is given by :<br />• 4444⁴⁴⁴⁴ < 10000⁴⁴⁴⁴ = 10¹⁷⁷⁷⁶<br />=> Number of digits in ‘X’ is lesser than 17776 ( approx. 16211 ) <br />=> A < 16211 • 9<br />=> A < 145899 <br />=> Sum of digits of ‘A’ is maximum when A = 99999 <br />=> B ≤ 45</p><p>→ Sum of digits of ‘B’ is maximum at B = 39 , i.e., 12<br />=> B ≤ 12</p>

    #76721
    Crazy Gamer
    Participant

    <p>Do we nned to know logarith to sopve this sum?</p>

    #76722
    Crazy Gamer
    Participant
    1. Do we need to know logarithm to solve this sum?
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