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 (+, - , ×, ÷) 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

(9²) – (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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