Great Math Problem - PLEASE HELP !!!

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criss72

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Using 6, 1, 5, 2 you have to generate any of the following numbers: 74, 75, 79, 83, 84, 85, 89, 91, 94, 95, 97, 98. The rules are as follow:
  • you have to use the initial numbers 6, 1, 5 and 2 only ONCE
  • you can use any math operation: addition, multiplication, substraction, division, square root, power, factorial
  • you can combine the initial numbers to generate other numbers: i.e. 61, 16, 52, 25, 15, etc. that may help you
Example on how to generate
  • 32: 6power2-5+1
  • 100: square_root(16) x 5power2
  • 28: (6 x 5) - (2 x 1)
  • 86: 61 + 25
Any help you can provide is much appreciated.
 
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Hello, criss72!

Using 6, 1, 5, 2 you have to generate any of the following numbers:
. . 74, 75, 79, 83, 84, 85, 89, 91, 94, 95, 97, 98.

The rules:
. . You have to use the initial numbers 6, 1, 5 and 2 only ONCE
. . You can use these operations: add'n, subtr'n, mult'n, div'n, square root, power, factorial.
. . You can concatenate the digits to form other numbers: i.e. 61, 16, 52, 25, 15, etc.

Examples:
. . \(\displaystyle 32 \:=\:6^2 -5+1\)
. .\(\displaystyle 100 \:=\:\sqrt{16} \times 5^2\)
. . \(\displaystyle 28 \:=\:(6\times 5) - (2\times 1)\)
. . \(\displaystyle 86 \:=\:61 + 25\)
Click to expand...

Here are a few solutions:

. . \(\displaystyle \begin{array}{ccc} 79 &=& 2^6 + 15 \\ 83 &=& 5! - 6^2-1 \\ 84 &=& 5! - 6^2\!\cdot\!1 \\ 85 &=& 5! - 6^2 + 1 \\
\end{array}\)
 
Many Thanks. The only 3 left to generate are: 74, 89, 91. Any help is much appreciated.
 
criss72 said:
Using 6, 1, 5, 2 you have to generate any of the following numbers: 74, 75, 79, 83, 84, 85, 89, 91, 94, 95, 97, 98. The rules are as follow:
  • you have to use the initial numbers 6, 1, 5 and 2 only ONCE
  • you can use any math operation: addition, multiplication, substraction, division, square root, power, factorial
  • you can combine the initial numbers to generate other numbers: i.e. 61, 16, 52, 25, 15, etc. that may help you
Example on how to generate
  • 32: 6power2-5+1
  • 100: square_root(16) x 5power2
  • 28: (6 x 5) - (2 x 1)
  • 86: 61 + 25
Any help you can provide is much appreciated.
Click to expand...

DUPLICATE POST:

http://answers.yahoo.com/question/index?qid=20111106053208AANsggV

http://www.mathgoodies.com/forums/topic.asp?TOPIC_ID=34302

I see that you did not "generate" any of those numbers.

Are you going to admit to your "generating technique" to your teacher?
 
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Denis said:
I've often seen the decimal point used with these, so:
5! - 6/.2 - 1 = 89
5! - 6/.2 + 1 = 91

99% sure getting 74 is not possible.

This is a bit "obscure":
"you can use any math operation: addition, multiplication, substraction, division, square root, power, factorial"
By any, do you mean any of the ones listed, or REALLY any, like cube root?
Click to expand...

Denis, many thanks for 89 and 91. I'm not 100% if you can use cube root, however, I'll take anything at this moment :p
Thanks again Denis !!. Much appreciated.
 
criss72 said:
Denis, many thanks for 89 and 91. I'm not 100% if you can use cube root,
however, I'll take anything at this moment :p
Thanks again Denis !!. Much appreciated.
Click to expand...

No, criss72,

you should not be able to use a cube root, \(\displaystyle unless\)
there is a digit "3" to use for the index.


\(\displaystyle Or,\) to get around that, the following could be done
to work out a cube root (not for the desired values of the expression
necessarily, but these are illustrations):


\(\displaystyle \sqrt[(1 + 2)]{whatever} \ \ or \)



\(\displaystyle {whatever}^{[1/(5 - 2)]} \ \ or\)



\(\displaystyle {whatever}^{(2/6)}\)


------------------ --------------------- ---------------- -----------------

And the rules had better specify whether decimal points may be used or not.
 
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