# Thread: Place parentheses in arithmetical expression to make it equal to larger than 39

1. ## Place parentheses in arithmetical expression to make it equal to larger than 39

This is Brainteaser 256 from page 3 of the March/April 1999 issue of Quantum Magazine in the address below. **

(After you go to the link, you might have to wait several seconds for that Quantum Magazine issue to load to your screen.)

The magazine's alleged apparent sole answers are the two located on the top of page 52 as you scroll down on
the following address to this issue:

**

http://static.nsta.org/pdfs/QuantumV9N4.pdf

At last count, I found an additional 12 solutions by hand (read: without using a computer).

Can any of you find any of these 14 solutions or possibly any others?

Place parentheses in the following expression so that it is equal to a number greater than 39:

$\displaystyle 2 \div 2 - 3 \div 3 - 4 \div 4 - 5 \div 5$

This will use standard Order of Operations.

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I'm going to put my own clarification into the problem:

The number greater than 39 is allowed to be an integer, or a rational number which is not equivalent to an integer,
depending on the placement of the parentheses.

Also, to be considered a unique/valid solution, if any pair of parentheses can be removed in an expression, and you
still get your target number, you must remove each of those pairs, as applicable.

If more than one expression (solution) is equal to the same number, then each expression is valid so long as it
$\displaystyle 2 \div (( 2 - 3) \div(3( - 4 \div 4 - 5)) \div 5) = 180$