# Writing a number in terms of other numbers.

• Mar 15th 2010, 04:42 PM
dmfnsdkjdj
Writing a number in terms of other numbers.
okay so im trying to figureout how i can get some numbers only using the numbers : 9,7,5,1 you can use any symbols like adding or substracting or square rooting etc but u gotta use each number only once and you gotta use all four of them. the numbers that i am trying to figure out are : 7,30,36,46,54,55,66,71,72,83,84,86,89,92-96,100 i would greatly appreciate if you could help me with this thanks.

for example:45=7x5+9+1
or 82= 9^(7-5)+1
• Mar 15th 2010, 07:31 PM
Soroban
Hello, dmfnsdkjdj!

I found a few of them . . .

. . $\displaystyle \begin{array}{ccc} 7 &=& 1\cdot(5+9-7) \\ \\ 36 &=& \sqrt{9}\cdot(5+7) \div 1 \\ \\ 55 &=& 5\cdot(1+7+\sqrt{9}) \\ \\ 71 &=& (5-1)^{\sqrt{9}}+7 \end{array}$

. .$\displaystyle \begin{array}{ccc} 84 &=& 7\cdot\sqrt{9}\cdot(5-1) \\ \\ 91 &=& 7\cdot(9+5-1) \\ \\ 96 &=& (1+5)(7+9) \\ \\ 100 &=& (1+9)^{(7-5)} \end{array}$
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