Posted by **Henry** on Friday, January 9, 2009 at 2:00am.

"How many different equivalent expressions for a particular number can be found?"

Various constraints can be (and need to be) applied, such as the use of integers only, the number of expressions listed, a restricted choice of digits, or operations etc.

List ten mathematically different expressions equivalent to 46, using the digits 2, 4, 5, 7, and 9.

You may use any or all digits in a single expression. You may not repeat any digits in any one expression. You may use any mathematical operation that is valid, and does not repeat the use of a digit IN ANY FORM!

At least one expression should use all five digits.

At least one expression should use all four arithmetic operators (+, - , ื, ๗) at least once.

One expression might even use all five digits AND all four operators!

For example: If you have the digits 1, 3, 5, 8, and 2,and use them to write equivalent expressions for the number 24, you could write: 3 ื 8, or 23 + 1, but you cannot write: 13 ื 2 − 2, because the "2" is used twice in the one expression.

My solutions so far are:

(5 ื 7) + (9 + 4) 2 = 46

(9ฒ) (7 ื 5) = 46

(√9 ื 7 ื 2) + 4 = 46

(9 ื 5) + ( 7 2) 4 = 46

(9 ื 4) + (5 + 7) 2 = 46

I'm having troubles with the other five..

Also what are the ESSENTIAL (BIG) mathematical ideas (concepts) that are IN the problem?

And how can i generalise these ideas that are particular to the problem, to a broader context that still focuses on the problem.

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