# Math challenge!

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Can you think of another way to make 20 and 9 using only the numbers 2, 3, 4 once each and any combination of brackets, addition, subtraction, division and multiplication. No number 1, no exponents.

So 20=4(2+3) and 9=2+3+4

Good luck!

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So... Not yet? :)

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I tried to approach this systematically.

9=3x3, the only way to factor. And you cannot create a factor 3 from the numbers 2 and 4 if each can be used only once. So it must be a sum, and since you use all three numbers, there should not be a different way.

20 =4x5=10x2. No other factors. There is only one way to make 5 from 2 and 3, the way you did. There is no way to make 10 from 3 and 4 with your restrictions.

Numbers are too small to make 20 by addition or a sum of a number and a product of two numbers (12 is the largest product)

So no, I do not think it is possible to express them differently within the given constraints (unnecessary parentheses and use of commutative property don't count as "different")

ETA: If we lift the restriction that each number can be used only once, I see different ways.

Edited by regentrude
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I tried to approach this systematically.

9=3x3, the only way to factor. And you cannot create a factor 3 from the numbers 2 and 4 if each can be used only once. So it must be a sum, and since you use all three numbers, there should not be a different way.

20 =4x5=10x2. No other factors. There is only one way to make 5 from 2 and 3, the way you did. There is no way to make 10 from 3 and 4 with your restrictions.

Numbers are too small to make 20 by addition or a sum of a number and a product of two numbers (12 is the largest product)

So no, I do not think it is possible to express them differently within the given constraints (unnecessary parentheses and use of commutative property don't count as "different")

ETA: If we lift the restriction that each number can be used only once, I see different ways.

What she said.

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That's what I came up with, too. So glad our family isn't alone! I'm dying to see what happens when they correct at school tomorrow. Thanks guy So!

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You'll have to update here!

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There's a game that's great for this - it's a little spinner thing with dice in it called Numbler Jumbler.  You can use each number once but you can do exponents (and must, pretty often).

Here it is:

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