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Obtain the number 1500 by using the operations $×, +, -, ÷$ on the numbers $1, 2, 3, 4, 5, 6, 7, 8, 9,$ in that order. Brackets are allowed, but you cannot join digits to form multi-digit numbers: for example, you may not write $1$ next to $2$ and call this $12$.

A possible solution is: $(1+2+3+4)×5×(6+7+8+9)$

Another solution: $(1÷(2×3))(4×5)(6×7+8)(9)$

My question: Is there a way to guess/know how many solutions are there?

Ahmed Amir
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    Can you use the computer brute-force? – kotomord Nov 24 '16 at 14:16
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    @kotomord What do you mean by "the computer brute-force". I think you simply mean to run a program to check every order? Actually, I want to solve this by hand. – Ahmed Amir Nov 24 '16 at 14:19
  • Program method has a problem - how to union (1 +2 +3), 1 + (2+3) and (1+2) +3? – kotomord Nov 24 '16 at 14:35
  • @kotomord I'm not familiar with programming. Whatever, it's not the solving way I'm looking for, but it may help to check someone's answer. I think it has 7-9 solutions. (: – Ahmed Amir Nov 24 '16 at 14:51

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