Monday, April 30, 2012

Nine Nine Nine Nine

Using only four 9s and standard arithmetic operations, it is possible to produce each of the numbers from 1 to 20.


For example,
1 = (9 + 9) / (9 + 9)
2 = (9 + √9) / (9 - √9)


Can you do the others?


(Kevin Hinks, Plymouth, MI)
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1 comment:

  1. © ρɤιταɱ ʂαɧαApril 30, 2012 at 5:41 PM

    Let me try,

    3 = (9+9+9)/9
    4 = (9+√9)/(9/√9) = (9/√9)+(9/9)
    5 = {(9+9)/9}+√9
    6 = {(9+9)/9}*√9
    7 = √9+√9+(9/9)
    8 = (√9*√9)-(9/9)
    9 = (9*√9)/(9/√9) = √9+√9+(9/√9)
    10 = 9+{(√9*√9)/9}
    11 = 9+{(9+9)/9}
    12 = √9+√9+√9+√9 = (√9*√9)+(9/√9)
    13 = 9+√9+(9/9)
    14 = ?
    15 = (√9*√9)+√9+√9
    16 = ?
    17 = 9+9-(9/9)
    18 = 9+√9+√9+√9
    19 = 9+9+(9/9)
    20 = ?

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